High Power Fiber Lasers: A Review

IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 20, NO. 5, SEPTEMBER/OCTOBER 2014

0904123

High Power Fiber Lasers: A Review Michalis N. Zervas and Christophe A. Codemard (Invited Paper)

Abstract—In this paper, we summarize the fundamental properties and review the latest developments in high power fiber lasers. The review is focused primarily on the most common fiber laser configurations and the associated cladding pumping issues. Special attention is placed on pump combination techniques and the parameters that affect the brightness enhancement observed in single-mode and multimode high power fiber lasers. The review includes the major limitations imposed by fiber nonlinearities and other parasitic effects, such as optical damage, transverse modal instabilities and photodarkening. Finally, the paper summarizes the power evolution in continuous-wave and pulsed ytterbium-doped fiber lasers and their impact on industrial applications. Index Terms—Beam quality, brightness, cladding-pumping, fiber amplifiers, fiber lasers, high power, holmium-doped, industrial lasers, material processing, modal instabilities, optical damage, optical fibers, optical fiber nonlinearities, optical pulses, photodarkening, pump combiners, thulium-doped, transverse mode instabilities, ytterbium-doped.

I. INTRODUCTION IBER lasers [1], [2] were proposed and studied as a promising laser configuration soon after the discovery and first laser demonstration by Maiman [3]. Ever since lasers have played central role in the fast developing field of Photonics, which in turn has revolutionized existing, as well as, enabled entire new scientific and industrial sectors [4]. Lasers exploit the quantum effect of stimulated emission to generate light and share a number of common features, such as an active medium to provide gain, an optical cavity to enhance and control the optical field and a pumping source to provide the energy [5]. However, the details of these features play an important role in differentiating the laser performance, the power scaling capabilities, stability, footprint and cost. Different gasfilled tubes, crystal rods and discs have been traditionally used as active media, incorporated in various bulk-optic cavities. Fiber lasers are the latest entry in the solid-state laser technology arena [6], fast increasing their penetration in all sectors of industrial, medical and directed energy application space [7]. There are a number of features that differentiate fiber lasers from the other existing laser technologies and give them su-

F

Manuscript received January 20, 2014; revised March 29, 2014; accepted April 23, 2014. The work was partially supported by the EPSRC Center for Innovative Manufacturing in Photonics, University of Southampton. M. N. Zervas is with the Optoelectronics Research Center, University of Southampton, Southampton, SO17 1BJ, U.K., and also with SPI Lasers, Southampton, SO30 2QU, U.K. (e-mail: [email protected]). C. A. Codemard is with SPI Lasers, Southampton, SO30 2QU, U.K. (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSTQE.2014.2321279

perior overall performance. Due to large surface-to-volume ratio, fiber lasers provide better thermal management and total elimination of thermal lensing, which plagues solid-state crystal counterparts. The well controlled spatial distribution of the signal, provided by the continuous guidance, results in superior beam quality and stability, while small quantum defect, as well as, low cavity and transmission losses result in record wall-plug efficiencies. Also, fiber lasers show turn-key operation and small foot print. Their unique properties, in particular the output power stability and unparalleled beam quality at high output powers, have increased their market penetration and have enabled a number of new applications [7]. The amorphous nature of glass host in the fiber core produces inhomogeneously broadened active-ion emission and absorption spectra, which are wider than they would be in crystals [8], [9]. This enables fiber lasers to be widely tuned and work efficiently from continuous-wave (CW) operation to ultra-short optical pulses. They show high gain, which enables masteroscillator power amplifier (MOPA) and cascaded amplifier configurations and makes them suitable for average power scaling. However, the small saturation energy, associated with the relatively small—compared to solid-state rod counterparts—fiber core diameter compromises the energy storage capabilities and high energy operation. Over the last decade, the performance advances in fiber lasers have been spectacular making fiber lasers a successful, fast increasing commercial business currently worth over $800 M/year, with compound annual growth rate of about 13%—the highest among the different laser technologies [7]. Key for the power scaling of high power fiber (YDF) lasers are the developments in major technologies, such as high-quality passive and active fibers, high-power passive fiber components, including, beam combiners, fiber Bragg gratings (FBG), isolators, cladding mode strippers and end caps, and bright diode laser pump modules. The expansion of the high-power fiber laser field has been already captured in a number of excellent reviews and book monographs available in the literature [6], [10]–[14]. The fast observed pace though warrants frequent reviews of the latest developments. This paper summarizes the fundamental properties and reviews the latest developments in high power fiber lasers, which so far have been the most commercially successful. The review is focused primarily on the most commonly used fiber laser configurations and the issues related to cladding pumping, the preferred technique for power scaling. Special attention is given on pump combination techniques and the parameters that affect the brightness enhancement observed in high power fiber lasers. The review also includes the major limitations imposed by fiber nonlinearities and other parasitic effects, such as optical damage and photodarkening and gives a brief account of

1077-260X © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.

0904123


Fig. 2.

Fig. 1. Cladding-pumped fiber laser configurations (a) hybrid end-pumped (b) all-fiber end-pumped and (c) all fiber intra-pumped.

transverse mode instabilities (TMI). The paper summarizes the power evolution in continuous-wave and pulsed ytterbiumdoped fiber lasers and their impact on material processing and other industrial applications. It concludes with the future prospects in the field of high power fiber lasers. II. FUNDAMENTALS A. Fiber Laser Cavity Configurations The gain in fiber lasers is provided by fibers of various types with cores doped with active rare-earth ions, such as ytterbium, erbium, thulium, or holmium. Typically the cavity is formed either by bulk mirrors placed on either fiber end, or FBGs [15] written directly into the fiber core [16]. The pumping is achieved by combining laser diodes (single emitters, bars or stacks) and launching either in the core or cladding of the fiber. 1) Most Common Fiber Laser Configurations: A number of different configurations have been used for fiber laser demonstrations, depending on the active fiber and availability in pumping technology. The most commonly used fiber laser configurations are shown in Fig. 1(a)–(c). Fig. 1(a) shows a hybrid end-pumped arrangement with the active fiber placed inside an optical cavity formed by two bulk mirrors, a high reflector (HR) with R > 99% and a lower reflectivity output coupler. The pump is launched through the fiber ends with appropriately placed dichroic mirrors (DM) that transmit the signal and reflect the pump wavelengths or vice versa. Fig. 1(b) shows an all-fiber end-pumped configuration, where the bulk-optic mirrors are replaced by intra-core FBGs and the combined pumps are launched through the FBGs. This configuration puts extra stress on the FBGs as they are subjected to strong pump and signal powers and special care should be taken to protect them. Finally, Fig. 1(c) shows an all-fiber configura-

Schematic of cladding pumping principle of operation.

tion with intra-cavity pump launching, which alleviates some of these issues. High power hybrid fiber laser configurations require careful bulk-optic mirror alignment and special fiber-end facet preparation [17], [18] to avoid unwanted backreflections, as well as, avoid surface damage. Such configurations are primarily more suitable for high power lab demonstrations [19]–[21] or low average power laser systems. However, the overall robustness of the laser can be improved if mirrors are butt-coupled or directly deposited onto the fiber facet [22]. Such approaches are more suitable for multimode (MM) operation. All fiber configurations, on the other hand, are preferable if all the benefits of the fiber technology are to be harnessed, and such systems are suitable for service-free, reliable industrial systems [23]–[30]. FBGs are usually written in single-mode (SM) fibers, which in addition to wavelength can also determine the output beam modality. B. Cladding Pumping In his seminal paper [1] E. Snitzer states that “the major disadvantage (of the fiber laser) is that of getting the pump power into the fiber. However, it should be possible to overcome this difficulty with proper design of the fiber and the illuminating optics.” Subsequently in 1988 E. Snitzer proposes an elegant solution to this problem in the form of cladding pumping [31], [32] which has proven to be the most powerful enabling technique for power scaling fiber lasers. In cladding pumping schemes (see Fig. 2), instead of launching into the highly restrictive—in terms of size and numerical aperture (NA)—active core, high-power low-brightness pump light is launched into the much larger, in size and numerical aperture, cladding. As the pump light rays propagate down the highly multimoded fiber cladding they cross and get absorbed gradually by the active core. However, the generated light is efficiently trapped inside the much smaller size and lower NA core, and as a result the cladding-pumped amplifier or laser output is much brighter and intense. In this respect, cladding-pumped fiber lasers are extremely efficient brightness converters (see Appendix A for definitions). From the definition of brightness (see Appendix A), the maximum pump power that can be launched into a circular fiber cladding is given by 2 1 πN A2cl = Bp λ2p Np . Ppin = Bp πrcl 2

(1)

The launched power is proportional to the brightness of the pump source (Bp ), the square of the cladding radius (rcl ),

ZERVAS AND CODEMARD: HIGH POWER FIBER LASERS: A REVIEW

0904123

Fig. 4.

Fig. 3. Modal space for multimode step-index fibers. Region I (II) shows the group of modes overlapping (non-overlapping) with the doped core.

and numerical aperture (NAcl ). Alternatively, the maximum launched pump power isproportional to the number of supported pump modes Np = Vcl2 2, where Vcl is the cladding V-number. Therefore, power scaling in fiber lasers relies on the development of high brightness pump modules (see Section B.3)), and fibers with high cladding NA and large cladding area. However, the launched pump power cannot be increased indefinitely due to limitations imposed by the practically achievable NA, the onset of nonlinear effects and optical damage (see Section III). The overall cladding-pumped fiber laser and amplifier length depends on the pump absorption coefficient (αC P ), which scales as αC P = ηS αco (Aco /Acl ), where αco is the small-signal 2 pump absorption when launched into the core, and Aco = πrco is the doped core area. ηS is a coefficient, which defines the effectiveness of modal absorption of the various mode scrambling techniques. ηS = 1 implies that all cladding modes are excited equally, overlap equally with the doped core and are absorbed uniformly. This can only be achieved by a cladding shape that fully scrambles the propagating modes [33]. In the case of a straight circular fiber with centered core, this assumption applies to all LP 0n modes, which correspond to meridional rays, and only to a small fraction of the LPm n (m 0) modes, corresponding to skew rays. The majority of the LPm n (m = 0) modes miss the doped core entirely. For a straight fiber with circular cladding the fraction of modes, which overlap with the doped core and are effectively absorbed, is approximated by ηS ≈ (πrco )/(2rcl ) [34]. Fig. 3 shows the power overlap with the doped core in the cladding modal space, in the case of a fiber with rco = 3 μm, rcl = 65 μm, and NAcl = 0.46. It is shown that the majority of the overlapping modes (region I) have ∼10% of their power within the doped core, independently of their order. The steep transition between regions I and II is defined by the higher order modes whose internal caustic coincides with the active core perimeter [34]. In order to improve the overall pump absorption, a number of fiber designs have been proposed which break the cladding’s rotational symmetry and increase the fraction of cladding modes overlap with the active core. Equivalently, we can consider that

Cladding-pumped fiber cross-sections.

these improved designs “scatter” skew rays towards the active core [35]–[42]. Fig. 4 shows a number of commonly used cladding-pumped fiber cross-sections. The pump NA is defined by the choice of the outer cladding material. Typically, these fibers use fluorinated polymer outer cladding giving NAs of ∼0.46. In this case, at high power operation special cooling arrangements are required to avoid excess heating of the polymer. Cooling requirements are relaxed considerably if low index fluorosilicate glass is used as the inner cladding. Unfortunately, although such glass–glass interface has superior power and thermal handling capabilities, the obtained NAs with current technologies are rather low (∼0.22– 0.26), reducing the amount of pump power that can be launched. In this case, large diameter coiling is required to avoid excessive pump bend-induced loss. Also, compatibility with standard high power TFB fused combiners would also be compromised. To overcome these problems, novel jacketed-air clad (JAC) fiber designs [Fig. 4(d)] have been developed, which rely on a row of cylindrically arranged air holes to provide effectively a glass/air interface with N As > 0.8 [43], [44]. Such JAC fibers can also be used to reduce the cladding diameters considerably, increase the pumping rate and enable efficient 3-level operation, e.g., at 980 nm [45]. The choice of the cladding perturbation should be consider judiciously in order to maximize mode scrambling, while avoiding excess scattering loss [46]. It was found, for example, that for the same material compositions, the effective NA of rectangular fibers is smaller than that of circular fibers and the pump light propagation loss in rectangular inner-cladding fibers [Fig. 4(c)] is larger [47]. Boron-doped stress elements can be incorporated into the inner cladding to maintain polarization. In the case of cladding pumped hi-bi fibers, the low refractive index of the borosilicate stress-applying elements ensures that pump light will not be trapped in these elements, and their presence along with the applied stresses scrambles helical modes/skew rays within the inner cladding [48], [49]. From the various inner-cladding shapes, shown in Fig. 4, the ones with multiple truncations, e.g. Fig. 4(f) and (g), are shown to be more efficient in mode scrambling [38]. In most practical cases, breaking the cladding cross-section rotational symmetry alone is not enough to absorb effectively the launched pump power over the entire fiber length and over all wavelengths. In order to increase the pump absorption close to its limiting value, given by the core over cladding area ratio, the modes should be continuously mixed over the entire length,

0904123


Fig. 5. Effect of longitudinal mode mixing and wavelength on pump absorption, in Yb 3 + -doped alumina-silicate fiber lasers [34].

which is achieved by properly perturbing the fiber along its length [50], [51], using periodic/quasi-periodic fiber bending [52], [53] or fiber tapering [54]. Fig. 5 plots the increase in pump absorption of a claddingpumped fiber as a function of length for different wavelengths, with and without mode mixing. In this case the mode mixing is achieved by periodic fiber bending. It is shown that in the case without mode mixing, the pump absorption at both wavelengths is small and saturates quickly with fiber length. In this + case, pumping at 976 nm, the Yb3 absorption peak, offers no significant advantage over 940 nm. This results in an effective absorption spectrum deformation and can be observed irrespective of the pumping scheme (discussed in Section II) [34]. Mode mixing, increases the pump absorption considerably and restores to large extent the absorption (in dB) linearity with length. However, at the 976 nm absorption peak the absorption still saturates with length, demonstrating that wavelengths with higher absorption require stronger mode mixing. Nonlinear pump absorption affects the signal evolution and overall efficiency in fiber laser cavities [55]. More importantly, though, for fixed overall pump absorption it results in highly non-uniform heat generation along the fiber length, with most of the heat generated over short length at the launching side. Cladding pumping has also been implemented for power scaling in planar waveguide lasers [56]–[58]. 1) Brightness Enhancement in Cladding-Pumped Lasers: It has already been mentioned that cladding pumping combined with high output beam quality, in addition to power scaling, provides extraordinary brightness enhancement. The brightness enhancement factor is given by 2 V 2 cl 2 λp Bsout ∗ Ncl ≈ ηoo (2) ηB = in = ηoo Bp λs Nco Vco2 2 where Bsout and Bpin are the brightness of the output signal and input pump (see Appendix A), respectively. ηoo = Psout Ppin is the optical-to-optical power conversion efficiency, where Psout and Ppin are the output signal and input pump powers, respectively. Ncl (Nco ) is the total number of cladding (core) modes (including degenerate spatial orientations and orthogonal polarizations). The maximum brightness enhancement factor is simply proportional to the ratio of the cladding pump mode to

Fig. 6 Brightness enhancement factor for different cladding radii and NAs and single-mode signal output (λp = 945 nm and η o −o = 75%).

Fig. 7. Main cladding-pumping schemes for (a)–(c) end-pumping, and (d)–(f) side-pumping.

signal core mode numbers. In the case of single mode core, Nco = 2. Fig. 6 plots the brightness enhancement factor in single-mode, cladding-pumped fiber lasers and amplifiers as a function of the cladding radius for different cladding NAs and λp = 945 nm and optical-to-optical efficiency of 75%. For commonly used fibers with cladding radius between 65 and 250 μm and NA larger than 0.4 the expected brightness enhancement factor lies between 103 and 104 . 2) Cladding-Pumping Schemes: Over the years, a number of different cladding pumping schemes have been proposed in pursue for higher fiber laser output power. These schemes can be broadly classified into two main categories of end-pumping and side-pumping. Fig. 7(a)–(c) shows schematically the main end-pumping techniques used to-date, while Fig. 7(d)–(f) shows the most prevalent side-pumping techniques. Fig. 7(a) shows free-space geometric combination of pump modules [59], while Fig. 7(b) shows a scheme based on TFBs [60], [61]. The number of combined free space or fiber-coupled pump modules depends on the cladding diameter and NA and is restricted by the e´ tendue conservation principle (see Appendix A). Fig. 7(c) shows an end-pumping scheme where the pump modules are wavelength multiplexed, using a series of bulk-optic


Fig. 8.

Pump combination modules for cladding pumping.

wavelength-division-multiplexing (WDM) couplers [20]. In geometric combination schemes [see Fig. 7(a) and (b)], the brightness of the combined pump module is usually lower than the brightness of the contributing pump modules. It is equal in the lossless case. In contrast, in wavelength-multiplexed schemes [see Fig. 7(c)], since multiple aligned beams are superimposed, the brightness of the pumping module is actually increased. It should be mentioned that, in this case, the spectral brightness (see Appendix A) of the module is reduced. This though is not a major handicap given that most dopants in silica fibers show large absorption bandwidths. In the aforementionedend-pumping schemes the signal beam is usually intertwined with the pump-combiner optics. In high power laser systems, the overlap of strong pump and signal beams increases the risk of bulk optics and fiber end-face failures. In the case of the fiber tapered bundle, special care should be taken to minimize signal losses in the taper region. Fig. 7(d) shows a side-pumping scheme based on total internal reflection taking place in a V-groove milled in the cladding [62]. Such an invasive approach, although employed in low powers [63], it is very difficult to be scaled to the currently achieved kilowatt levels. Fig. 7(e) shows a side-pumping scheme consisting of an angle-polished [64], [65] or tapered [66] pump fiber attached to or fused into the cladding of the signal fiber. The angle-polished fiber approach pump scheme is found not only to launch light into the cladding but also to leak out, which leads to efficiency loss and compromises the laser integrity [67]. Fig. 7(f) shows a side-pumping scheme based on a multi-fiber assembly in optical contact surrounded and held together by a common low-index polymer cladding, applied the usual way during the drawing (trade name GTWave) [68], [69]. Removing part of the polymer over-cladding frees the individual fiber members, which then can be accessed independently. Such fiber assembly provides multiple ports for pump power to be injected into the cladding and be absorbed by the core of the optically coupled signal fiber. A variant of this scheme uses multiple bare pump and signal fibers held together by an external heat-shrunk tube [70]. In the side-pumping schemes, the signal path is kept separate from the pump injection paths. This simplifies the optical design and enhances the overall laser robustness. Finally, the side-pumping scheme, based on evanescently-coupled fibers

0904123

[Fig. 7(f)], has the additional advantage of distributing the pump power more uniformly along the fiber length, resulting in better heat management [71]. 3) Pump Combination Schemes for Cladding Pumping: High-brightness, high-power pumping modules are key components for the development of robust, high-power fiber lasers. Pump brightness is a commodity that should always be spared and used wisely. Once it has been compromised, it cannot be recovered by passive means. Single broad-area emitters launched into MM fibers (typically 105/125 μm, and 0.22 NA) reduce to ∼1/100 of their initial brightness. After fast axis collimation, this is primarily due to the large mismatch between the rectangular shape of the diode emitting aperture and the receiving circular fiber. This mismatch is even more pronounced in the case of diode bars. In order to fully utilize the brightness of pump fibers, a number of different techniques have been developed to re-organize and aggregate the outputs of high power single-diode emitters, as well as, minimize the in-between “dead” space of diode bars or stacks and turn them into high brightness modules suitable for cladding-pumping high power fiber lasers. The pump combination in most of the cases is achieved in two stages. It involves a relatively low count combined single-emitter diodes, or diode mini-bars (stage #1), feeding into a tapered multi-fiber bundle (stage #2). These can then be used for either end- or side-coupling into the active fiber cladding, using one of the schemes presented in Fig. 7. The brightness of a combined multiple-pump module can in some cases exceed the brightness of the individual pump elements [72]. This can be achieved if mutual coherence is established across the pump lasers and the output of the entire source behaves as a single spatial supermode. The resulting brightness can in this case be equal to the sum of the individual laser brightness. Another way to increase the brightness of the combined module is to use pump lasers with different eigenproperties, such as wavelength or polarization. Passive optical elements such as diffraction gratings or polarizing beam splitters, respectively, can be used to multiplex several beams [72]. In the case of wavelength combination, the spectral brightness is reduced and these modules can only be used with active ions with broad absorption spectra, such as Yb3+ around 940 nm. High brightness laser pump sub-modules capable of coupling over 100 W of optical power into a 105 μm, 0.15 NA fiber at 976 nm have been demonstrated with N A < 0.13 and an electrical to optical efficiency >40% [73]. The pump submodule brightness is ∼0.21 W/(μm2 sr). Such sub-modules have been spliced to a 7:1 fused fiber combiner, providing 500 W coupled into a 220 μm, 0.22 NA fibers. The resulting combined pump module brightness reduces to ∼0.086 W/(μm2 sr). Commercially available pump modules using TFBs and geometrically combined single, large-area emitters can provide 140 W in 106.5 μm, 0.22 NA fibers. The resulting brightness is 0.1 W/(μm2 sr) [74]. Also, wavelength-beam-combined pump modules, using diode stacks, have been demonstrated, which provide 200 W at 91 Xnm in 200 μm/0.22 NA fibers [75]. The resulting brightness is 0.04 W/(μm2 sr), less than half to what has been achieved with geometrically combined single emitters. Seven such modules were then combined with a 7:1

0904123


tapered fused fiber bundle to provide ∼1.5 kW pump power in 400 μm diameter fiber. Most of the measured pump insertion loss in combined modules is due to the brightness loss across the tapered fiber combiner. Therefore, designs closer to the brightness limit are considerably more sensitive to variations of the input power distribution as a function of NA [76] By proper design and optical loss minimization in both directions, TFBs with kW-level power handling capabilities are possible [75], [77], [78]. A number of different pump modules, using different combination techniques, have been developed. The choice of diode type (e.g., single emitter or bar size) and optimum arrangement (i.e., number of emitters and input NA) is finally influenced by the resulting wall-plug efficiency, life-time, manufacturability and final cost. These considerations favour large area, single emitters and small-size diode bars. In addition to MM TFBs, used extensively to combine MM pumps, there have been demonstrations of SM-to-MM TFBs. Up to three hundred 0.12 NA, 9 μm-core and 125 μm-clad single mode fibers can be combined into a single output multi-mode fiber with 0.15 NA, 105 μm-core and 125 μm-clad diameter [79]. The SM-to-MM TFBs can be used to combine the outputs of high power SM fiber lasers into a scaled-up MM output beams for industrial applications. It can also be used to combine short wavelength, SM fiber lasers for cladding in-band (or tandem) pumping [80] of other fiber lasers. This is the prevalent pumping scheme in SM diffraction-limited fiber lasers with >3 kW output power [30], [81], [82]. Finally, both MM TFBs and SM-to-MM TFBs have been used together to demonstrate multi-kW fiber laser outputs [83] First, single-emitter diodes are combined by 91:1 MM TFBs to produce 900 W pump modules, which are used to claddingpump SM fiber lasers. Seven such SM fiber lasers were then combined with SM-to-MM combiners to produce >4 kW MM output beam. The limit in power scaling of pump and/or signal fused TFBs will be ultimately set by the NA and power handling capabilities of coating materials.

C. Active Ion Spectroscopy and Pump Wavelength Selection A number of rare-earth dopants have been incorporated successfully into optical fibers, using modified chemical vapor deposition (MCVD) process [84], to form lasers. They include Nd3+ [85], Er3+ [86], Er3+ /Yb3+ [87], Yb3+ [88], Tm3+ [89], and Ho3+ [90]. From the extended range of dopants used in fiber lasers, we consider here only the Yb3+ and Tm3+ ions, which so far have shown excellent power scaling with output powers exceeding 1 kW (see Fig. 22). Yb3+ comprises a simple two-level system and provides efficient lasing around the 1 μm window. Fig. 9(a) shows a typical energy diagram of Yb3+ ions in silica, with indicative sub-level Stark splitting. The exact sub-level splitting depends on the glass composition and Yb3+ concentration [91], [92]. Stark splitting enables three- or four-level-system operation, depending on the choice of pump and lasing wavelengths. Fig. 9(b) plots typical emission and absorption cross-sections in aluminosilicate and phosphosilicate fibers [93]. The emission and absorption spectra details and level lifetimes depend on the host mate-

Fig. 9. (a) Typical energy level diagram of Yb 3 + ions in silica, (b) typical emission and absorption cross-sections in aluminosilicate (thicker lines) and phosphosilicate (thinner lines) fibers (the arrow shows the peak emission and absorption for phosphosilicate fibers).

Fig. 10. (a) Typical energy level diagram of Tm 3 + ions (only lower levels are shown), and (b) typical emission and absorption cross-sections in aluminosilicate fibers [96].

rial [94]. Although phosphosilicate glasses reduce considerably the emission and absorption cross-sections, they allow for much larger dopant concentrations, without significant clustering effects [95], and reduce or even eliminate photo-darkening effects (see Section III-D). The simplicity of the Yb3+ energy-level structure also eliminates other efficiency reduction effects, such as excited-state absorption, multiphonon non-radiative decay and concentration quenching. Yb3+ shows a broadband absorption spectrum, extending from ∼850 to ∼1080 nm, enabling multi-pump or multiwavelength pumping schemes, which in turn facilitate power scaling. The broadband absorption spectrum also enables the use of unstabilized and low cost pumps, simplifying the design and reducing the overall cost and long-term stability of high power fiber lasers. Interestingly, the small but finite absorption in the 1010–1020 nm band enables in-band (or tandem) pumping with high brightness fiber lasers, which is key for the power scaling to multi-kW levels [26], [30]. In addition, the broadband emission spectrum enables wide wavelength coverage and tunability, from 980 nm to about 1100 nm and short pulse (down to few 10 s of fs) amplification. The Tm3+ ion, on the other hand, shows a much more complex energy-level structure. Fig. 10(a) shows the lower energy levels of a Tm3+ ion. The diagram indicates the main


Fig. 11.

0904123

Typical efficiency budget for Yb 3 + -doped fiber lasers.

ground-state absorption transitions and the most important, in the context of this review, lasing transition around 2 μm. Fig. 10(b) shows typical Tm3+ emission and absorption crosssections in aluminosilicate fibers [96]. The most technologically important absorption bands are the one around 1600 nm, which enables in-band pumping with high power Er3+ -doped fiber lasers, and the 790 nm band, which can make efficient use of available powerful diode pumps through the cross-relaxation process [97]. Cross-relaxation creates two excited Tm3+ ions in the upper laser level for every absorbed pump photon and can potentially result in 100% optical-to-optical efficiency. Crossrelaxation in Tm3+ -doped fiber lasers pumped at 790 nm has resulted in record 74% efficiency and provides the root for efficient power scaling [97]. D. Fiber Laser Efficiency Budget Emission and absorption cross-sections define also to a large extent the efficiency of a laser system. Along with the fiber parameters, they define the signal saturation energy and power extraction efficiency. The choice of pumping wavelength defines the fundamental heat dissipation limit through the quantum defect (pump/signal wavelength ratio), as well as, the absorption and total fiber length. Fig. 11 shows a typical power efficiency budget for Yb3+ doped fiber lasers. In addition to the fundamental loss due to the quantum defect, there are inevitable loss contributions from excess pump and signal losses and nonoptimized cavity. These losses can be minimized by proper choice of core and cladding materials and proper cavity design (choice of optimum reflector wavelength and strength). Losses due to the quantum defect depend on the choice of pumping and lasing wavelengths. In the case of in-band (or tandem) pumping, the quantum defect can be very small (∼1%) and the optical-to-optical output efficiency can be increased considerably. However, if the conversion efficiency of the (fiber or disc) pump laser is taken into account, the overall efficiency drops again to the levels shown above. Nevertheless, in-band pumping is a powerful approach for effective heat management, and power scaling SM fiber lasers beyond 3 kW relies almost exclusively on it.

Fig. 12. (a) Beam quality for different modes as a function of V number of step-index fiber, (b) M 2 of highest-order mode (dashed line), average M 2 (assuming mode equipartition) (and measured M 2 for different V-number fiber lasers (experimental data taken from Ref. [103]).

E. Beam Quality Laser beam quality can be defined in a number of different ways. The M 2 definition, based on the second moment of the beam intensity profile, is the most commonly used method [98], [99]. From a practical point of view, though, the “quality” of a laser beam depends on the specific application for which the beam is intended for. The M 2 parameter denotes also how many times faster the beam diverges compared to a diffraction-limited Gaussian beam with the same waist diameter. Therefore, it can be defined as the ratio of the beam-parameter product (BPPB ) of the beam in question divided by the BPPG of a diffractionlimited Gaussian beam, namely [99]: M2 =

BPPB ωB θ B π = = ωB θ B BPPG ωG θ G λ

(3)

where ωB and θB are the mode-field radius and far-field divergence of the beam. For Gaussian beams M 2 = 1, while for any other practical beam M 2 > 1. The beam quality of a fiber laser output can be tailored by proper fiber design. Fig. 12(a) shows the M 2 variation, calculated by the second moment of the corresponding mode intensity profile, as a

0904123


function of the normalized frequency (V number) of a stepindex fiber, for different modes. The M 2 of the fundamental mode (FM) LP01 is shown to depart considerably from 1 for V < 1.5. This is due to the increased evanescent extension into the cladding and departure from the Gaussian profile. It follows closely the LP01 mode-to-core radius ratio variation with V number, as approximated by Marcuse’s formula [100]. The same behavior is observed for all modes as they approach cutoff and their field extends deep into the cladding. The modes LPm 1 , corresponding to skew rays or whispering gallery modes with high orbital momentum, show considerably lower M 2 , which grows at a much slower rate compared to other LPm n modes of the family characterized by the same composite mode number p = 2n + m [101]. Within each p family, the LP0n modes, which correspond to meridional rays or modes with no orbital momentum, show the highest and fastest growing M 2 . This resembles the M 2 behavior of elegant Laguerre–Gaussian (LG) modes, compared with the standard LG modes supported by cavities with cylindrical symmetry [102]. In the case of real fibers with complex refractive-index profiles (RIPs) the mode intensity distributions differ from the corresponding mode distributions of the step-index fiber and, therefore, show different values of M 2 . The M 2 of an incoherent MM beam is given by the weighted average of the M 2 of the participating modes [104]. In this case, the centroid of the beam is stationary [105], [106]. Using simple arguments applicable to MM fibers [107], it can be shown that the M 2 of the group of modes characterizedby the composite mode number p is given by Mp2 = πrco θpout λ = πp/4, where θpout is the half-angle divergence of the mode in free space. 2 The weighted-average 2 < M > of a MM beam can then be approximated by M ≈ π (2pm ax + 1)/12 = π/12 + V /3, where pm ax = 2V /π and both polarizations are counted [108]. The weighted-average < M 2 > is obtained when all supported modes are equally excited. For a given V number, the M 2 of the highest-order mode group (p = pm ax ) can be approximated by Mm2 ax = V /2. Fig. 12(b) plots the weighted average < M 2 > and the Mm2 ax of a step index fiber, as a function of the V number. It also shows the measured M 2 of the output of kW-level fiber lasers as a function of the V-number of the active fiber [103]. In practice, the number of modes and their relative power depends on the gain saturation level, their overlap with the active region and effective modal reflectivities [109]. For relatively low V numbers (V < 8) the lower-order modes dominate and the M 2 remains small. For higher V-number fibers, though, the higherorder modes (HOMs) attain substantial power and the output beam quality approaches the equipartition < M 2 > value. From the relations derived above and Eqn. (A-2), it can be deduced that the brightness of a MM beam is inversely proportional to the core V number squared. A similar relation (∝ 1/D2 ) has been predicted for MM VCSEL devices in the limit of large D [110]. A drastically different situation arises in the case of coherent MM beams in large-mode area (LMA) fibers. Even with large HOM content (e.g., 30% LP11 ) the resulting M 2 can be deceptively low (M 2 < 1.1), depending on the relative phase between LP01 and HOMs. However, significant changes in beam shape,

peak intensity, and pointing stability can occur by varying the relative phase of the constituent fiber modes [106], [111]. F. Fiber Types High power fiber lasers require the development of active and passive LMA fibers, in order to reduce peak intensities and diminish nonlinear effects. In most occasions these fibers end up being multimoded, and they are operated in the SM or low-mode (LM) regime by introducing sufficient HOM differential losses, without increasing significantly the FM loss. This becomes increasingly challenging as the fiber dimensions increase and the mode effective index differences decrease. Additionally, in the presence of unavoidable small external perturbations, such as fiber drawing or packaging-induced microbending, small modal effective index differences enhance modal cross-coupling between FM and HOMs. This results in efficiency and beam quality deterioration. 1) Active Fibers: Modality in MM fibers is generally controlled by properly matching the FM at the input [112], launching through a mode-field adapter (MFA) [113], [114] and/or by properly bending of the fiber [115]. However, in the last case, care should be taken to avoid excessive bending, which exceeds the safe bend-induced stresses level. This level depends on the fiber outer diameter. Depending on the core radius and NA in active fibers, bending does not always reduce modality or improves output beam quality. This is due to induced mode coupling, modal deformation and modal gain competition [116], [117]. Furthermore, in high-power lasers and amplifiers short LMA active fiber lengths and small cladding diameters are needed in order to maximize pump absorption and minimize lengthdependent nonlinear effects. However, small cladding diameter and low-NA LMA fibers have the disadvantage of being extremely sensitive to external perturbations, which has adverse effects on efficiency and optical beam quality [112], [118]. Another issue associated with low-NA, LMA active fibers is related to the uniformity of the refractive index across the core area. Making low NA, highly doped Yb3+ fibers requires high phosphorous concentration to increase dopant solubility. This, in addition to increasing the core refractive index, results usually in refractive index central dips due to uncontrolled phosphorous evaporation in MCVD fabricated fibers. Such refractive index feature can deteriorate the beam quality and power stability of LMA fiber lasers. An alternative method has been demonstrated, which places much less stringent requirements on the MCVD process. Solid rod has been fabricated, with small index step and quasi-uniform doping to form the core region of a LMA photonic crystal fiber (PCF) laser, by repeated “stacking and drawing” [119] of Yb3+ doped and undoped silica. The ensemble therefore can form an effective-index medium with V < 1.3. The composite doped rod has been then stacked along with silica capillaries to form a PCF in the usual manner [120]. Solid active fibers with similar novel core structures composed of small doped cores to give a LMA structure with a low effective core NA and without a central dip have also been demonstrated [121], [122]. In another approach, based on PCF technology, by adjusting the hole size and spacing of the air-holes around the LMA doped core, effectively single


mode operation has been achieved for core diameters up to 100 μm [123]. LMA fibers have been demonstrated using solid-core PCF technology utilizing the “modal sieve” effect [124]. LMA operation has been extended even further with very large-mode-area (VLMA) fiber designs using large-pitch PCFs (LPFs). These fibers use claddings with hole-to-hole spacing of ∼10–30 times the operating wavelength. The aforementioned designs offer different degrees of HOM leakage or delocalization into the cladding [125], [126]. Compared to LMA PCFs, LPFs relax considerably the fabrication tolerances and have resulted in record core diameters of 135 μm and mode field diameter (MFD) of ∼130 μm in passive operation. In order to avoid bend-induced MFD collapse, such rod-type fibers have to be kept straight during operation. However, under high power operation thermallyinduced waveguide changes have been observed in Yb3+ -doped LPF, resulting in substantial fundamental MFD reduction and increased modality [127]. An alternative LMA fiber design is based on the chirallycoupled core (CCC) concept, which provides resonant filtering of HOMs and enables effective SM index-guiding. Single-mode CCC fibers have been produced with core sizes exceeding standard 50 μm [128]. Being resonant thought their length, CCC LMA fibers require tight fabrication tolerances. Finally, LMA MM active fibers can be operated effectively in the SM regime by tailoring the dopant distribution inside the core to provide gain and favor predominantly the FM [129]. Fiber lasers based on gain-guided, index antiguiding mechanism are another interesting approach to achieving LMA operation and power scaling [130]. These waveguides, though, are fundamentally leaky and additional measures should be taken to manage the leaking power during high power operation. 2) Passive Fibers: LMA passive fibers play an important role in the construction of high performance, high power fiber lasers, particularly in delivering efficiently the generated power into the work-piece. In some applications, delivery fibers up to 10–20 m long are required. Optical power LMA delivery fibers should be designed properly to avoid excessive spectral broadening and onset of temporal instabilities due to non-linear interactions, such as stimulated Raman scattering (SRS), stimulated Brillouin scattering (SBS), self-phase modulation (SPM) and four-wave mixing, as well as, beam quality degradation due to modal scrambling. Standard step-index (SI) fibers with core diameters of ∼30 μm and effective areas ∼360 μm2 can be SM at a 5 cm bending radius with NA of ∼0.06, which is considered to be the lowest limit that can be achieved repeatedly and it is manufacturable with current fiber fabrication techniques [131]. When kept straight, SI fibers can maintain single mode operation for diameters below ∼15 μm [12]. A number of different fiber designs have been proposed and experimentally demonstrated, which extend the FM area well beyond the SI capabilities. These fibers are fundamentally multimoded but utilize different techniques to filter out HOMs. An early example is the W-type fiber, which uses a refractive-index dip around the core to drive the second-order mode beyond cutoff into leakage [132] or LMA segmented-cladding fibers, which leak out HOMs [133]. Recently more advanced leakage-channel

0904123

Fig. 13. Nonlinearity enhancement factor as a function of amplifier gain, for L 0 = 15 m and NA = 0.1.

fibers (LCFs) have been demonstrated using a small number of air holes inserted in the silica cladding, providing differential loss for the HOMs. LCFs with core diameters in the range of 170 μm have been demonstrated, with effective areas in excess of 10 000 μm2 [134]. In another approach, modal filtering is achieved by inserting small cores around the main MM core, which are resonant to the HOMs. The HOMs are then leaking out of the main core through evanescent coupling [135]. Lately, state-of-the-art hollow microstructured fibers have been used for high peak power delivery. In such fibers optical nonlinearities are contained effectively, since the vast majority of the power (>99%) is guided in air. Hypocycloid core Kagome lattice microstructured fibers have been used for delivering high beam quality, high peak power 500 fs, 1 mJ pulses over 10 m length, without beam quality degradation. The energy threshold damage was found to be >10 mJ, with output power density after focusing approaching TW/cm2 . This opens up the possibility of using such fibers for practical high peak power delivery [136]. III. NONLINEAR AND OTHER PARASITIC EFFECTS Most of the fiber nonlinearities are χ(3) based and are intensity and fiber length dependent. Hence they become more severe in pulsed, high peak power and CW kW-level operation. Despite the very small nonlinear coefficient in silica (n2 = 3.2 × 10−16 cm2 /W)), due to the high intensities and lengths involved, the nonlinearity enhancement factor (NEF), which compares the strength of the nonlinear interaction in fibers with that of a focused beam in bulk glass (see Appendix B) can take quite large values. Fig. 13 plots the NEF, given by Eqn. (B.3), as a function of amplifier gain, for different V numbers. For λ = 1μ m, a fiber length L0 = 15 m and NA = 0.1, the obtained NEF is ∼105 . This actually makes optical fibers one of the highest nonlinearity media. It is shown that the NEF decreases with gain. This is because the power distribution varies significantly along the length for higher gains. Also, NEF decreases with V number, because in this case the FM effective radius increases. For V > 10, the NEF reduces by about one order of magnitude.

0904123


From Eqn. (B.3) to (B.5), it can be shown that the NEF is inversely proportional to wavelength, and therefore, moving to λ = 2μ m is expected to half the nonlinearity strength. Nonlinear effects are one of the most limiting factors in scaling-up the power in fiber lasers. In general, they transfer energy in unwanted spectral regions and can potentially destabilize laser operation. They can be reduced significantly by special fiber designs and/or appropriate spectral filtering.

A. Stimulated Brillouin and Stimulated Raman Scattering SBS and SRS are related to inelastic nonlinear processes and involve power interactions with acoustic and optical phonons, respectively [137]. 1) Stimulated Raman Scattering: Under controlled conditions and special fiber designs, both effects can be either minimized or used effectively to enhance wavelength coverage of available fiber laser output spectrum. In high peak power pulsed lasers, SRS can be minimized by employing short lengths of phosphosilicate fibers [138]. Fibers with wavelength-selective transmission can suppress the Stokes wave of Raman scattering and result in length-independent nonlinearity threshold, which could be particularly advantageous for high power lasers and fiber beam delivery in material processing applications [139], [140]. Residual backreflections at splices or fiber ends can decrease considerably the SRS threshold [20]. SRS is in general a non-catastrophic effect, resulting in only in power transfer to longer wavelengths. Such spectral broadening can complicate the design of focusing optics and result in effective focal shifts that can compromise processing capabilities. In some cases, the presence of strong forward and backward SRS can destabilize fiber laser cavities. Fig. 14(a) shows the output power overshoot (relaxation oscillation) of a pump-modulated fiber laser. By inserting appropriate spectral filters, the total forward propagating beam can be analyzed into its signal content (centered around 1070 nm determined by FBGs) and the forward propagating SRS (centered around 1130 nm). The SRS threshold is shown to be ∼250 W. A small ripple starts appearing after the first overshoot. Fig. 14(b) shows the output overshoot at higher pump power. In addition to forward signal and SRS, it plots the backward SRS, measured on the HR side of the cavity. It is shown that the first overshoot is terminated abruptly by a sharp, high peak power backward propagating SRS. This is then followed by a secondary relaxation oscillation, modulated at the cavity roundtrip. This behavior is repeatable and predictable, occurring each time there is strong enough backward SRS. 2) Stimulated Brillouin Scattering: Techniques to suppress SBS, while maintaining FM operation, include increasing the mode area with appropriate NA reduction [141], using fibers with tailored acoustic speed profiles [142], increasing the effective linewidth via phase modulation [143]–[145], laser gain competition [146], and using highly doped fibers to absorb the pump light in a short length. Self-heating and strong temperature gradients due to pump absorption can contribute to substantial SBS threshold increase [147]. 11.2 dB suppression of SBS in an Yb3+ -doped, Al/Ge co-doped LMA gain fiber is demonstrated with a ramp-like acoustic index profile exhibiting an acoustic in-

Fig. 14. Output power overshoot (relaxation oscillation) of a pump modulated fiber laser. (a) Total forward power (signal + SRS), Signal and SRS traces resolved, (b) total forward power (signal + SRS), forward signal and backward SRS traces.

dex contrast of 0.09 and acoustic index slope of 0.01/μm [148]. It is shown that SBS can be effectively suppressed by broadening the signal linewidth to a value above 0.07 nm [149]. SBS in an Yb3+ -doped double-clad pulsed fiber amplifier with multi-ns-duration can break-up the original pulse and produce high peak-power sub-pulses. Fig. 15(a) shows three different cases of backward-propagating 1st-Stokes SBS measured at the input of a ns pulsed fiber amplifier. SBS is stochastic in nature and the backward SBS pulses are usually characterized by a sharp (∼10 ns) spike followed by a longer tail. Fig. 15(b) shows the corresponding amplified forward pulses with 200 ns duration and output peak power of ∼15 kW. It is shown that strong backward SBS excitation results in forward pulse distortion [150], as power is transferred into acoustic waves, as well as, generation of forward propagating 2nd Stokes, appearing as superimposed sharp ∼10 ns spikes. Generation of forward propagating 2nd Stokes is usually followed by optical damage and catastrophic fiber failure (see Section IIC). In MM fibers, in addition to normal backward SBS, SBS in a forward direction (FSBS) has been observed, transferring power between LP01 and LP11 forward propagating modes. FSBS is possible because although the overlap between flexural fiber modes and the light is small, the phonon lifetime is much longer than in conventional SBS. Unlike in normal SBS, FSBS does not depend significantly on the laser linewidth, and may also be the first example of a nonlinear effect, which for a given power is actually enhanced by increasing the optical mode area [151]. FSBS can take place in both active and passive fibers and can transfer power from the FM into HOMs and potentially destabilize the output beam.


0904123

Fig. 16.

Fig. 15. (a) Backward-propagating 1st-Stokes SBS measured at the input of a ns pulsed fiber amplifier, (b) corresponding amplified forward pulses with forward propagating second Stokes.

B. SPM and FWM A direct consequence of the Kerr effect is the nonlinear intrapulse phase shift, which results in SPM and equivalent frequency shifts. The SPM-induced spectral broadening depends on the pulse shape and it is more pronounced for pulses with steep leading and trailing edges. SPM is a limiting factor in short-pulse energy scaling when using phase locking or coherent combination of multiple lasers. Four-wave mixing (FWM) in fibers is an elastic χ(3) nonlinear process involving two pump photons, which annihilate to create one Stokes and one anti-Stokes photon with frequencies defined by the energy conservation principle. FWM is a coherent process and its efficiency depends critically on the exact phase matching between the waves involved. In high power fiber lasers and amplifiers the signal beam serves as the FWM pump and increases exponentially along the length. This results in substantial FWM generation despite the phase mismatching [152], [153]. FWM generation is also enhanced in birefringent or MM fibers, since phase matching is greatly facilitated by the fact that the Stokes and anti-Stokes beams can propagate in different fiber modes with the appropriate group velocities [17], [154]. Instead of being always parasitic, SRS and FWM can cooperate and be beneficial in specially designed fibers for certain applications, such as efficient supercontinuum generation. High peak powers enhance the spectral broadening via FWM and Raman shifting and result in record bandwidth and spectral density supercontinuum sources [155]–[157]. The ultimate limit in high power can be set by self-focusing (SF) in fibers [158], [159]. SF is the only nonlinearity that depends on power rather than intensity and, therefore, cannot be

SBS induced damage.

mitigated just by scaling the mode size. For 1060 nm operation, SF in silica fibers occurs at a power of ∼4–5 MW [160] and, therefore, it can only be relevant to ultrashort pulse propagation [161]. Surprisingly, transmission of powers of ∼20 MW, much higher than the widely accepted limit, have been reported using highly MM fibers [162]. However, fiber core design can affect the SF threshold. Numerical results suggest that optical fibers with a strong central dip at the center of the refractive index profile can guide stable fundamental modes at more than 10x the bulk silica critical power for SF [163]. SF threshold increases to ∼6–8 MW with the use of circularly-polarized light [164], [166]. SF threshold has a wavelength squared dependence and, therefore, operating at 2 μm results in quadrupling the aforementioned thresholds. The onset of SF can potentially result in spatial beam collapse and optical damage. C. Optical Damage Optical damage for ns and sub-ns pulses is a catastrophic effect associated usually with electron avalanche effects [164], [165]. Damage initiates if the electron density exceeds 2 × 108 μm−3 , beyond which the plasma frequency approaches the optical frequency and the propagating light is strongly absorbed. The deposited energy is then sufficient to melt or fracture the silica glass. For pulses longer than ∼50 ps the bulk optical damage irradiance is found to be constant at ∼ 4.75 kW/μm2 , which makes the threshold fluence linearly-dependent on the pulse duration. For shorter pulses, the electron avalanche effects evolve slower than the pulse envelope, so that the threshold fluence increases and departs from the above linearity. Preliminary results indicate that Yb3+ doping does not affect appreciably the aforementioned optical damage thresholds [164]. By proper polishing of end-faces, surface damage is measured to be equal to the bulk value [165]. Optical damage of a different type is associated with the onset of strong SBS in pulsed fiber lasers or self Q-switched highly inverted fiber amplifiers. This damage is caused by internal stresses induced by the acoustic waves generated by the SBS material/light interaction. Fig. 16 shows SBS induced damage in the core and cladding a pulsed fiber amplifier. The fiber has turned into white powder over a ∼2–3 cm length, while the coating remains intact. This damage mechanism is different to the optical fuse effect [167], and appears to be similar to the fast optical discharge mechanism observed in fibers [168]. D. Photodarkening High power fiber lasers based on Yb3+ -doped silicate glasses are known to suffer from light-induced optical losses, known as photodarkening (PD). The optical losses are believed to be due

0904123


Fig. 17. Power evolution with time in high-power Yb 3 + -doped claddingpumped fiber lasers. [multimode (MM), single-mode, diode pumped (SM DP), single-mode, tandem pumped (SM - TP), and coherent beam combination (CBC)].

to formation of color centers in the glass matrix, which increase the background loss and reduce the output power. The exact color-center formation mechanisms are still under debate. There have been a number of studies showing that the PD rate and saturated level are dependent on the Yb3+ inversion [169], [170]. The order of the inversion dependence, however, varies between 3.5 [169] and 7 [170]. It has also been observed that photodarkening in LMA fibers is non-uniformly distributed over the fiber cross-section [171]. The PD-induced loss is also nonuniformly distributed along the length of the active fiber [172], following closely a dependence to the calculated Yb3+ inversion to the power of 2. It is shown that increasing (decreasing) the operating temperature results in decrease (increase) of the laser output power, reaching the new equilibria over time scales of ∼200 h [172]. However, the occurrence of PD is entirely dependent on the materials composing the fiber core [173]. The Yb3+ concentration and co-dopants such as aluminum [174], [175], phosphorous [176] or cerium [177] can reduce significantly or even eliminate PD. Photodarkening has also been observed in Tm3+ doped fibers [178], [179]. IV. HIGH POWER FIBER LASERS In the last decade, fiber technology has grown quite diverse and mature and can provide an excellent platform for fabricating robust, high performance laser systems. The core and cladding structures can be tailored appropriately to control the beam modality, optical nonlinearities and scale-up the power. A. Single Fiber, Single-Mode Continuous-Wave (CW) Output In addition to fiber technology advancements, power evolution in fiber lasers with near diffraction-limited output has followed and depended critically on the maturity of the pumping technologies, and their progress from low brightness diodes to combined high-brightness diode modules, and lately to in-band tandem pumping [30]. Fig. 17 shows the power evolution of single mode (SM) near diffraction-limited Yb3+ -doped fiber lasers, when entirely diode pumped (SM-DP) and with the final amplifier in-band tandem pumped (SM-TP). Introduction of high brightness diode pump modules after year 2000 has resulted in a fast increase of

Fig. 18. Brightness enhancement in high-power Yb-doped cladding-pumped fiber lasers. [single-mode (SM), multimode (MM) - direct diode (DD) is shown also for comparison].

SM outputs. It has been predicted that if the fiber’s MFD could be increased arbitrarily, about 36 kW of diffraction-limited power could be obtained from single fiber lasers or amplifiers. This power limit is imposed primarily by thermal and SRS effects, and does not take into account modal instability effects, which can reduce it considerably [180]. As already mentioned, scaling the SM fiber laser power above 3 kW requires in-band (or tandem) pumping to reduce the thermal load on the final power amplifier, which has resulted in SM output of 20 kW [181]. It has been predicted that in-band pumping can extend the SM operation to about 70 kW [182]. Scaling the power to such high SM levels involves very large diameter fibers and stable SM operation will prove quite challenging. It is conceivable that robust fiber lasers can reach ∼25 kW quasi-diffraction-limited SM output. Fig. 17 also includes the case of MM outputs obtained with geometric incoherent combination, currently reaching the 100 kW level [181]. Such power levels promise even higher fiber laser penetration into the industrial and directed energy application space. Fig. 17 finally includes the power evolution of single beam, near diffraction-limited output obtained with coherent combination of SM fiber lasers [183]–[187]. Currently, coherently-combined fiber lasers have demonstrated multi-kW quasi-Gaussian outputs [186], [187]. Coherent combination distributes effectively the optical gain and thermal load among several contributory fiber strands and can break the vicious circle of increased-power/increased-heat-generation/increasednonlinearities and potentially provide high quality output beams with power increased well above the current single fiber strand limits. In addition to raw power scaling, one of the most important characteristics of diode-pumped fiber lasers is the achieved brightness enhancement. The generated laser output beams are characterized by much higher brightness than that of the pump sources. Fig. 18 compares the brightness of SM and MM fiber lasers and the corresponding diode pump modules [188] as a function of power. It is shown that the experimentally observed SM output brightness increase in the range of 10+3 –10+4 is in very close agreement with the theoretical predictions shown in Fig. 6. The SM fiber brightness increases monotonically with the output power, although it is showing signs of saturation.


0904123

Power scaling in direct diode (DD) output, on the other hand, relies on various geometrical beam shaping techniques and the resulting brightness decreases with power. Due to the geometrical incoherent combination, MM fiber laser outputs show a brightness increase ∼1–2 orders of magnitude smaller, almost independent of the power level.

B. Pulsed Fiber Laser Parameter Space Although fiber lasers are ideal for average power scaling, it is generally perceived that they suffer in terms of energy storage and peak power handling. However, even in this front, progress in fiber technology has enabled substantial improvements in pulsed fiber laser performance and has resulted in increased penetration into the industrial and scientific application space. Q-switched fiber lasers have been used extensively in the field of low-cost laser marking [7]. They combine configuration simplicity and substantial pulse energies [189]–[194]. As a practical approximate rule of thumb, the extractable energy from a fiber laser or amplifier is limited to about ten times the saturation energy [190] and can be controlled by fiber design. The pulse duration in Q-switched fiber lasers is directly proportional to the round trip time of the laser cavity. It also depends on the inversion level and it reduces with increasing inversion levels and, therefore, increasing small-signal gain. Q-switched fiber laser has been demonstrated producing pulse durations well below 10 ns by using a short length Yb-doped rod-type photonic crystal fiber as gain medium. Pulse energies up to 0.5 mJ and average powers in excess of 30 W have been obtained in single-transverse mode beam quality, at repetition rates up to 100 kHz [192]. At low repetition rates, below the ytterbium inverse fluorescence lifetime, the generated ASE can reduce the inversion and limit the pulse energies. Optimized pump modulation can minimize the effects of intra-pulse ASE and maximize the extractable energy [193], [194]. MOPAs based on a diode-seeded nanosecond fiber system offer adaptive pulse shape control [195], [196] that can cover an extremely large range of pulse duration (from ps to CW) and repetition rates (from pulse-on-demand to MHz). They combine the fast dynamics and turn-on characteristics of semiconductor lasers and the high gain, high average power capabilities of fiber amplifiers, resulting in high performance pulsed laser systems with energies and beam qualities suitable for a number of diverse applications, such as marking and material micro-processing [197], [198]. Fig. 19 summarizes the progress in peak power, pulse energy and average power achieved by nanosecond pulsed fiber lasers within the last decade. The main results are categorized in terms of beam quality: single-mode (SM–M 2 < 1.5), low-moded (LM–M 2 ∼ 3) and multimoded (MM–M 2 ∼ 6–8). Most of the record results presented in Fig. 19 have been obtained using large core rod-type fibers and SM to LM output beams. Q-switched 60 ns pulses with 26 mJ pulse energy and near diffraction-limited beam quality (M 2 < 1.3) with average output power of 130 W and peak power of 500 kW is achieved, using a large-pitch fiber with a core diameter of 135 μm [199]. A micro-chip seed, Yb-doped fiber MOPA produced 1-ns-long, 4.3 mJ pulses, with average power of 42 W, peak power of

Fig. 19.

Nanosecond pulsed fiber laser performance parameter space.

4.5 MW and near-Gaussian, single-transverse-mode profile of M 2 ∼ 1.3, using a 100 μm-core rod-like PCF used as the final amplifier [200]. Fig. 19 shows that high performance nanosecond pulsed fiber lasers with SM and LM output beams have shown output powers below 250 W. In order to circumvent this limitation spectral beam combination has been used to achieve 1.1 kW, 5 ns pulsed laser [201]. Spectral and coherent beam combination (CBC) will be required to extend the SM/LM nanosecond fiber laser performance to the high average/high energy parameter space region (highlighted in Fig. 19). Such beam combination techniques will be necessary to avoid modal instability issues, likely to be encountered in this regime (see discussion below). Ultrashort pulse lasers have opened up new scientific and industrial application areas, such as time-resolved material and chemical studies, nonlinear microscopy, metrology and precision material micro-machining. Compared to solid-state crystal counterparts, fiber lasers are characterized by broad emission spectra and offer themselves for ultrafast tens-of-fs operation [14], [202]–[205]. Chirp and nonlinear propagation in fibers can also be combined to achieve even shorter pulses [206]. Lately, significant power scaling in superfast pulse fiber lasers has been achieved based on the powerful chirped-pulse amplification (CPA) technique [207] and special fibers, such as the ones using rod-type PCF fiber technology [13], [204], [205]. Compared to diode-pumped solid-state crystal and thin-disc lasers, fiber ultrashort pulse lasers offer superior thermo-mechanical behavior and more robust operation. They offer the potential for highly integrated and passively cooled ultrashort pulse sources. Fig. 20 summarizes the progress in pulse energy and average power achieved ultrafast (ps and fs) pulsed fiber lasers within the last decade. High average powers, in excess of 800 W, and moderate pulse energies (Ep ≤ 10 μJ) have been demonstrated [204]. This was achieved by using 27 μm) MFD pixilated core [120] and 500 μm outer diameter JAC fibers. At the other extreme, appreciably high energies (>2 mJ) and moderate average powers (>10 W) with record (∼4 GW) peak power have

0904123


Fig. 21. Transverse mode instability threshold versus nominal core diameter. (PCF-LPF#1: [211]- [214], DMF#1-#3: [215], PCF-B1: [216], PCFB2: [217], PCF-SAT: [218], SI-MC: [204], (SI-NS): [210], SI & SI-GT: [219], PM25: [220]). Fig. 20.

Ultrafast pulsed fiber laser parameter space.

been achieved [208], using large pitch PCF fibers with 105 μm MFD. Scaling up the average power requires special fibers with increasingly large diameters. However, exceeding 100 W in the high pulse energy regime (Ep ≤ 10 μJ) [209] or 1 kW in the lower energy regime (Ep ≤ 10 μJ) [204], delineated by the dashed line, the power fiber amplifier operation is severely limited by TMIs [204], [211], resulting in significant output power variations and beam pointing drift. The limit is established experimentally and it is related to the fiber effective core diameters. This currently appears to be a hard limit and intensive research is underway to understand the root cause and develop robust solutions to the modal instability effects [210]–[229]. C. Transverse Mode Instabilities In high power LMA fiber amplifiers, TMI manifests itself as sharp and rapid output beam profile deterioration above an output power threshold. For near single fundamental-mode input excitation, the output beam shows large content of and strong competition with HOMs (dominantly LP11 mode), after a certain threshold has been reached. A number of research groups have recently reported on TMI effects in PCF and LPF high power Yb3+ -doped fiber amplifiers [211]–[218]. Lately, TMI has been observed also in standard solid-core LMA fiber amplifiers [219], [220]. Fig. 21 plots the TMI threshold power as a function of the active fiber nominal diameter. The highest TMI thresholds to date has been obtained with actively cooled, step index fiber of 22 μm [210] and ∼30 μm core diameter (SI-MC) [204]. The fibers had micro-structured doped core to achieve low NA and was bent to preferentially attenuate HOMs. Fig. 21 includes also results obtained with short length, straight rod-type PCFs and LPFs (PCF-LPF#1 & #2: [211]–[214], DMF#1-#3: [215]), as well as, longer bendable PCFs (PCF-B1: [216], PCF-B2: [217], PCF-SAT: [218]). It also includes more conventional step-index

fibers, with and without gain tailoring (SI and SI-GT: [219]), as well as, polarization-maintaining step-index fibers (PM25: [220]). PM25 is monolithic, fully-spliced amplifier, in contrast with all the other configurations, which are free-standing and end-pumped. Fig. 21 shows that the TMI threshold generally decreases with the nominal core diameter, irrespective of the fiber type used. TMI threshold, however, has been observed to be affected by a number of other amplifier characteristics. In the case of DMF [215], it is shown that HOM excess leakage results in approximately double the TMI threshold. Also, in the case of SI-GT [219], gain tailoring results in substantial (∼ x3) TMI threshold increase. However, gain tailoring is not as effective in the case of PCF-GT [214]. In the case of PCF-SAT [218], the TMI threshold has been shown to increase substantially by efficient fiber cooling. Finally, in the case of PM25 polarizationmaintaining fiber it is observed that increasing the input power and pumping the amplifier off the absorption peak results in almost double the TMI threshold. Interestingly, in this case, a similar non-PM fiber shows no TMI instability up to 1 kW level [220]. It should be also remarked that an all-fiber, splicedup and coiled amplifier with core diameter of 20 μm showed no signs of TMI for >2 kW output power [230]. To the best of our knowledge, so far there has been no TMI observed in fiber amplifiers with core diameter smaller than 20 μm. Finally, It should be mentioned that due to lack of experimental details, it is not clear if all the observed TMI effects follow the same evolution patterns [213], or are all due to the same root cause. Different theoretical models have been proposed for the root cause of the observed TMI effects [221]–[229]. All models consider thermo-optically induced refractive-index gratings as the main mechanism of forward mode coupling. The instability has been attributed to either stimulated thermal Rayleigh scattering (STRS) [221], [223]–[227] or other thermal mode coupling effects [222], [228], [229]. So far, the proposed models have had different degrees of success in predicting mode coupling and instabilities. However, to the best of our knowledge, there has been limited success to quantitatively predict instability


0904123

TABLE I COMPARISON OF DIFFERENT HIGH POWER LASER TECHNOLOGIES.

Fig. 22. to date.

Fiber laser wavelength coverage and maximum output power achieved

evolution and dynamics. This is not surprising, given the lack of experimental details and other uncertainties regarding published data. Specially designed experiments are required to prove or disprove proposed theories. VI. INDUSTRIAL FIBER LASERS AND APPLICATIONS V. OTHER FIBER LASERS Fiber lasers can cover an extended range of wavelengths by simply doping the core with different active dopants. Fig. 16 shows schematically the wavelength ranges offered by dopants such as Nd3+ , [231], [232] Er3+ /Yb3+ [233], [234] and Tm3+ [235]. Power scaling in Nd3+ and Er3 +/Yb3 + doped fiber lasers has been severely hampered by the relative large quantum defect and excessive thermal management requirements. Tm3+ doped fiber lasers operate around the eye-safe 2 μm region and have been scaled up to kW level and appear to be promising for new directed energy and industrial applications [236]. A monolithic, robustly single-mode, resonantly cladding-pumped Ho3+ -doped fiber laser producing more than 400 W of output power in the 2.05–2.15 μmwavelength range [237]. Using nonlinear processes such as SRS, high power lasers emitting in the spectral regions shown in Fig. 22 can be used as pumps and, combined with properly designed and optimised fibers, can offer substantial power in almost any spectral region in the 1–2.5 μm span. Fiber lasers have also been used as seeds to produce high performance supercontinuum sources [238]. CW supercontinuum generation extending to the visible spectral region has been demonstrated by pumping photonic crystal fibers at 1.07 μm with a 400 W single mode CW Ytterbium fiber laser. The continuum spans over 1300 nm with average powers up to 50 W and spectral power densities over 50 mW/nm [157]. High-energy pulsed supercontinuum spanning the 450–1750 nm region with energy spectral density in excess of 1 nJ/nm in the visible, suitable for STED microscopy, has also been generated [156]. Fiber distributed-feedback (DFB) lasers [239]–[241] can provide high purity, single frequency, single polarization [242], low phase noise seeds ideal for advanced high power MOPA configurations, sensors [243] and other applications [244]. It should be mentioned that in the highest power laser MOPA system, demonstrated to date in the world at the National Ignition Facility, the only laser used is actually a fiber DBF laser [245].

Industrial high power fiber lasers are almost exclusively based on all-fiber monolithic configurations, exploiting the excellent power scaling capabilities of fiber amplifiers in MOPA configurations. In such monolithic configurations, a high power all-fiber laser seed is followed usually by one matched, lowgain and well saturated fiber amplifier [23]–[30]. Additionally, hybrid high power fiber laser systems have been demonstrated, using free-space optics for pump coupling and laser cavities with mirrors butt-coupled or directly deposited onto the fiber facets [22]. All-fiber MOPA configurations offer the possibility of using multiple pump power injection points and therefore distribute evenly the pump absorption and thermal load, providing servicefree, reliable industrial laser systems. Table I shows a comparison of the wall-plug efficiency (WPE), expected lifetime, maintenance requirements and fiber delivery capabilities for the main industrial high power laser technologies. It is shown fiber lasers outperform all other technologies combining record >30% WPE, 100k hours lifetime (defined by the single-emitter (SE) diode pumps) and maintenance free operation. Fig. 23 compares the typical beam quality, quantified by the beam-parameter product (BPP = ω0 θ0 ) variation with output power for the most common laser applications in material processing and manufacturing to date. It also superimposes the BPP and power requirements for the main materialprocessing laser applications. The contours show parameters averaged over different operational conditions and materials. These applications are based primarily on thermal processes, such as heating, melting and vaporization. In addition to replacing traditional mechanical or chemical techniques, lasers have also enabled a number of novel processes. Laser cutting, for example, allows repeatable high-precision patterns at high speeds that cannot be produced via conventional methods. Also use of lasers enables welding of dissimilar materials, like steel and aluminum, which is of growing interest to shipbuilding and car industries and known to be impossible in conventional welding.

0904123


come more challenging to achieve stable focal position of the focused beam at the work-piece, because of the time dependent thermal lensing and optical distortions in the transmitting optics inside the laser processing head [188], [246]. It is rather ironic that although eliminating the thermal lensing from the laser cavity is one of the major contributors to scaling-up the diffractionlimited fiber laser output, this deleterious effect “sneaks” back into the processing head optics. To gain the full potential and make efficient use of high power fiber lasers with diffractionlimited beam quality new processing heads have been developed [188], [247], [248]. VII. SUMMARY—FUTURE PROSPECTS Fig. 23. BPP and average power requirements for laser applications & BPP versus average output power for main industrial lasers [4].

In automotive industry, welding car bodies, transmission and engine components, air bags, exhaust systems, etc., are now made robotically using laser systems. In healthcare, lasers are used for welding deep brain stimulator implants, pacemakers and prosthetics. In electronics industry, for drilling and cutting of printed circuit boards. In photovoltaics for scribing, drilling and cutting of Si-wafer, ablation of conduction or dielectric layers of thin film solar and crystalline Si solar cells. More recently in additive manufacturing, 3-D rapid prototyping and manufacturing by selective sintering, melting and 3-D cladding directly from CAD files is enabled by lasers. Rapid prototyping has evolved from polymer components to tool-free rapid manufacturing of high quality metallic parts using materials, such as titanium, aluminum and cobalt chrome powders. So far most of the industrial applications are based on lasers operating predominantly in CW or relatively long pulse mode. Recently, advances in laser technology have resulted in industryworthy ultrashort laser systems capable of efficient material processing. Femtosecond pulses can extend the laser processing capabilities into materials inaccessible by traditional lasers. For example, transparent materials can be processed efficiently by focusing fs pulses tightly to induce nonlinear absorption through a combination of athermal effects, such as multiphoton absorption, tunneling ionization, and avalanche ionization. As a result, the induced structural changes are confined into tiny volumes with nm precision and are ideal for 3-D micromachining. This area of highly nonlinear matter/light interaction is still in its infancy and is expected to take fiber laser material processing to a new level, with a number of novel applications expected in the near future. One of the main attributes of high power fiber lasers is their superior beam quality at high powers. For the same collimated beam size, higher beam quality radiation result in smaller spot size at the work-piece. Alternatively, for the same spot size at the work-piece, higher beam quality requires smaller and therefore lighter focusing beam optics. This results in lighter processing heads and higher processing speeds. Finally, for the same beam size and focusing optics, as well as, same spot size, beams with higher beam quality can be focused further away enabling remote material processing [188]. However, with the development of high-power, highbrightness near-diffraction-limited fiber laser sources it has be-

Fiber lasers have come of age and are currently fast increasing their share in the industrial applications market. They uniquely combine high average powers, unparalleled beam quality, small footprint, and record efficiencies. They gradually replace conventional laser technologies offering substantially lower cost of ownership, higher processing speeds in existing applications while enabling new ones. In this paper, we have summarized the fundamental properties and reviewed the latest developments in high power ytterbiumdoped fiber lasers. The review has been focused primarily on the main fiber laser configurations, used in industrial applications, have considered issues related to cladding pumping. Special attention has been placed on pump combination techniques and the parameters that affect the brightness enhancement observed in high power fiber lasers. The review also included the major limitations imposed by fiber nonlinearities and other parasitic effects, such as optical damage, TMI and photodarkening. The paper finally summarized the power evolution in continuouswave and pulsed ytterbium-doped fiber lasers and highlighted their impact on material processing and other industrial applications. Following the spectacular progress in their performance so far, future innovations in materials and fiber designs are expected to continue pushing the performance boundaries with new radical fiber laser solutions. So far, the tremendous success of fiber lasers has been almost entirely based on Yb3+ -doped fibers operating around 1 μm. However, moving forward extending the output beam wavelength into the mid-infrared (mid-IR) will be beneficial for a large number of existing or enable novel new applications [235], [249]. For industrial material processing applications, such as plastic welding, or glass processing, fiber laser sources in the mid-IR with substantial power (>100 W) will be required. Processing glass will require robust laser sources in the 3–5 μm range. At present, there are no industrial-grade, fiber-based lasers in this spectral region. Emission in this spectral region relies entirely on ZBLAN or possibly chalcogenide glasses [235], the power handling capabilities of which have not been proven yet. Further power scaling with diffraction limited outputs, well beyond the current single-fiber performance, can be achieved by spectral (SBC) and/or CBC of high power SM fiber lasers [182], [185]. SBC and CBC distribute spatially the thermal load and intensity and can effectively mitigate thermal and nonlinear effects, which set the hard limits to the power generated and


0904123

transmitted in currently used fibers. In addition to power scaling, CBC and SBC increase the output beam spatial brightness. SBC though is limited by the amplification bandwidth of the active medium and results in spectral brightness deterioration, which might complicate the processing head design. Four 2 kW fiber lasers have been spectrally combined to provide 8.2 kW of output power [250]. The beam quality was retained to M 2 < 1.5 up to 2.5 kW and degraded to M 2 ∼ 3.5 at full power due to the onset of TMI. CBC has been already demonstrated by tiling eight SM fiber lasers side-by-side in the near field (tiled aperture) to provide a record 4 kW of diffraction-limited beam (M 2 = 1.25) [186]. Using a single diffractive optical elements (filled aperture) five SM fiber lasers have been combined coherently into one beam with M 2 = 1.1, exceeding that of the contributory lasers [187]. Power scaling in CBC is achieved by increasing the number of tiled contributory fiber lasers. So far, a maximum of 64 fiber lasers have been combined successfully combined coherently [251], making CBC an extremely powerful technique for future fiber laser power scaling. SBC and CBC can also be combined for multidimensional power scaling [252]. In addition to average power scaling, research is now concentrated into novel techniques for scaling the pulse energy and peak power in ultrafast laser systems, using recently demonstrated promising techniques such as dividedpulse amplification [253]–[255] and/or the stack-and-dump concept [256]. Currently, these are areas of intensive research and new exciting results are expected in the near future. Finally, fiber lasers offer themselves for massive “parallelism” and can go beyond the classic MOPA configurations into schemes such as the coherent amplifier network (ICAN). Such radical concepts can potentially produce pulses with energies of >10 J at repetition rates of several kHz, as required for the next-generation particle accelerators [257]. Given the size, power requirements and expected cost, practical implementation of such future coherent amplified network concepts can only be realized by the fiber laser technology, which can provide 10 s of kW of diffraction-limited beams, with record wall-plug efficiencies (>30%) robustly in small foot-print and low cost. APPENDIX A BEAM BRIGHTNESS The brightness (or radiance) of a beam (B) is defined as the beam power (P ) per unit area (A) and unit solid angle (Ω), namely [99], [259]:

For rectangular cross-sections [110], A = dx dy and

θx θy Ω = 4 sin−1 sin sin ≈ θx θy 2 2

where dx and dy are the lengths and θx , θy are the divergence full angles in the two orthogonal directions. Again, brightness is given in terms of beam quality parameters as π 2 P P P = = . dx dy θ x θ y 16 (BPPx BPPy ) 4 Mx2 My2 λ2 (A.4) There are two important theorems that govern brightness in a passive optical system. First, assuming that both object and image spaces have the same index of refraction, the brightness theorem states that the brightness of beam produced by an imaging system cannot be greater than the original source brightness. The brightness is preserved only when the system is lossless. The underlying principle is conservation of energy, or conservation of number of rays. The second theorem states that the brightness of a collection of mutually incoherent beams cannot be higher than the brightness of the brightest beam. These two theorems imply that there is an upper limit to the brightness achieved by a combined pump module, which defines to large extend the efficiency of the various cladding pumping schemes. The above theorems are sometimes expressed in terms of e´ tendue, which is defined as B=

E = n2 A Ω

(A.1)

For circular cross-sections A = πr2 and Ω = πN A2 , where r is the radius and NA the numerical aperture. The brightness can also be given in terms of beam quality as B=

P P = . π 2 BPP2 (M 2 λ)2

APPENDIX B NONLINEARITY ENHANCEMENT FACTOR The NEF is a figure of merit that compares the strength of the nonlinear interaction in fibers with that of a focused beam in bulk silica. For a Gaussian beam of power P0 and focused waist radius ω0 , the (intensity) x (effective length) product is given by [258]: P0 λ

(B.1)

where the effective length is equal to Rayleigh length. A quasiGaussian beam with waist radius ω0 , propagating in a fiber amplifier of length L0 and gain G = Pout /Pin = exp(γL0 ), where Pout = P0 , is characterized by (intensity) x (effective length) product

(A.2)

(A.5)

where n is the surrounding medium refractive index. Etendue describes the light gathering power or acceptance of an optical system. Finally, the spectral brightness or spectral brilliance is essentially the brightness per unit optical bandwidth, expressed in W/(μm2 sr Hz).

ILbulk = P . B= AΩ

(A.3)

ILam p = 0

L0

Iin eγ z dz = I0

G−1 γG

(B.2)

0904123


where I0 = P0 πω02 = GIin and γ is the gain coefficient. The NEF is then defined as NEF =

λ G−1 ILam p L0 . = ILbulk πω02 G ln G

(B.3)

In the quasi-Gaussian approximation, the fundamental fiber mode is given by [100]: 1.619 2.879 ω0 ≈ r0 0.65 + 3/2 + (B.4) V6 V and

r0 = λ

V 2πNA

.

(B.5)

ACKNOWLEDGMENT The authors would like to thank helpful discussions and fruitful collaboration over the years with colleagues and coworkers in SPI (Dr. S. R. Norman, Dr. M. P. Varnham, Dr. M. K. Durkin, Dr. F. Ghiringhelli, and Dr. L. Walker) and the ORC (Prof. D. N. Payne, Prof. J. Nilsson, Prof. W. A. Clarkson, Prof. J. K. Sahu, and Prof. D. J. Richardson). REFERENCES [1] E. Snitzer, “Proposed fiber cavities for optical masers,” J. Appl. Phys., vol. 32, pp. 36–39, 1961. [2] C. J. Koester and E. Snitzer, “Amplification in a fiber laser,” Appl. Opt., vol. 3, pp. 1182–1186, 1964. [3] T. H. Maiman, “Stimulated optical radiation in ruby,” Nature, vol. 187, pp. 493–494, 1960. [4] A. E. Willner, R. L. Byer, C. J. Chang-Hasnain, S. R. Forrest, H. Kressel, H. Kogelnik, G. J. Tearney, C. H. Townes, and M. N. Zervas, “Optics and photonics: Key enabling technologies,” Proc. IEEE, vol. 100, pp. 1604– 1643, 2012. [5] A. E. Siegman, Lasers. Mill Valley, CA, USA: Univ. Science, 1986. [6] H. Injeyan and G. D. Goodno, High Power Laser Handbook. New York, NY, USA: McGraw-Hill, 2011. [7] Strategies Unlimited, “The worldwide market for lasers,” Mountain View, CA, USA, 2013. [8] E. Snitzer, “Glass lasers,” Appl. Opt., vol. 5, pp. 1487–1499, 1966. [9] L. D. DeLoach, S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Evaluation of absorption and emission properties of Yb3 + doped crystals for laser applications,” IEEE J. Quantum Electron., vol. 29, no. 4, pp. 1179–1191, Apr. 1993. [10] O. G. Okhothikov, Fiber Lasers. Weinheim, Germany: Wiley, 2012. [11] V. Ter-Mikirtychev, Fundamentals of Fiber Lasers and Amplifiers, vol. 181. New York, NY, USA: Springer (Springer Series in Optical Sciences), 2014. [12] D. J. Richardson, J. Nilsson, and W. A. Clarkson, “High power fiber lasers: Current status and future perspectives,” J. Opt. Soc. Amer. B, vol. 27, pp. B63–B92, 2010. [13] J. Limpert, F. Roser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tunnermann, “The rising power of fiber lasers and amplifiers,” J. Sel. Topics Quantum Electron., vol. 13, pp. 537–545, 2007. [14] L. Jintong, L. Dan, and D. Yitang, “A review of fiber lasers,” China Commun., vol. 9, pp. 1–15, 2012. [15] J. L. Archabault and S. G. Grubb, “Fiber gratings in lasers and amplifiers,” J. Lightw. Technol., vol. 15, no. 8, pp. 1378–1390, Aug. 1997. [16] M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, and S. Barcelos, “Moving fibre/phase mask-scanning beam technique for enhanced flexibility in producing fibre gratings with uniform phase mask,” Electron. Lett., vol. 31, no. 17, pp. 1488–1490, 1995. [17] J. Limpert, S. Hofer, A. Liem, H. Zellmer, A. Tunnermann, S. Knoke, and H. Voelckel, “100-W average-power, high-energy nanosecond fiber amplifier,” Appl. Phys. B, vol. 75, pp. 477–479, 2002.

[18] S. Bohme, S. Fabian, T. Schreiber, R. Eberhardt, and A. Tunnermann, “End cap splicing of photonic crystal fibers with outstanding quality for high power applications,” Proc. SPIE, vol. 8244, 824406, 2012. [19] Y. Jeong, J. K. Sahu, D. N. Payne, and J. Nilsson, “Ytterbium-doped large-core fiber laser with 1.36 kW continuous-wave output power,” Opt. Exp., vol. 12, pp. 6088–6092, 2004. [20] C.-H. Liu, B. Ehlers, F. Doerfel, S. Heinemann, A. Carter, K. Tankala, J. Farroni, and A. Galvanauskas, “810 W continuous-wave and singletransverse-mode fibre laser using 20 μ mcore Yb-doped double-clad fibre,” Electron. Lett., vol. 40, pp. 1471–1472, 2004. [21] J. Nilsson, W. A. Clarkson, R. Selvas, J. K. Sahu, P. W. Turner, S. U. Alam, and A. B. Grudinin, “High-power wavelength tunable cladding-pumped rare-earth-doped silica fiber lasers,” Opt. Fiber Technol., vol. 10, pp. 5–30, 2004. [22] J. D. Minelly, L. Spinelli, R. Tumminelli, S. Govorkov, D. Anthon, E. Pooler, R. Pathak, D. Roh, D. Grasso, D. Schleuning, B. Perilloux, and P. Zambon, “All-glass kW fibre laser end-pumped by MCCP-cooled diode stacks,” in Proc. 12th Eur. Quantum Electron. Conf. Lasers ElectroOpt. Eur., 2011, p. 1. [23] V. Gapontsev, D. Gapontsev, N. Platonov, O. Shkurikhin, V. Fomin, A. Mashkin, M. Abramov, and S. Ferin, “2 kW CW Ytterbium fiber laser with record diffraction-limited brightness,” in Proc. Conf. Lasers Electro-Opt. Eur., 2005, p. 508. [24] S. Norman, M. N. Zervas, A. Appleyard, P. Skull, D. Walker, P. Turner, and I. Crowe, “Power scaling of high power fiber lasers for micromachining and materials processing applications,” Proc. SPIE, vol. 6102, p. 61021P, 2006. [25] S. Norman and M. N. Zervas, “Fiber lasers prove attractive for industrial applications,” Laser Focus World, vol. 43, no. 8, pp. 93–96, 2007. [26] D. Gapontsev, “6 kW CW single mode ytterbium fiber laser in all-fiber format,” Proc. 21st Annu. Solid State Diode Laser Technol. Rev., p. 258, 2008. [27] W. Rath, “Lasers for industrial production processing: Tailored tools with increasing flexibility,” in Proc. SPIE, 2012, vol. 8239, 823908. [28] D. A. V. Kliner, “4-kW fiber laser for metal cutting and welding,” Proc. SPIE, vol. 7914, 791418, 2011. [29] M. N. Zervas, “High power fiber lasers: From lab experiments to real world applications,” in Proc. AIP Conf. Emerging Trends Novel Mater. Photon., 2010, vol. 1288, pp. 63–66. [30] M. O’Connor and B. Shiner, “High power fiber lasers for industry and defense,” in High Power Laser Handbook, H. Injeyan and G. D. Goodno, Eds. New York, NY, USA: McGraw-Hill, 2011. [31] E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B. C. McCollum, “Double-clad, offset core Nd fiber laser,” presented at the Opt. Fiber Commun. Conf., New Orleans, LA, 1988, Paper PD5. [32] H. Po, E. Snitzer, R. Tuminelli, L. Zenteno, F. Hakimi, N. M. Cho, and T. Haw, “Double clad high brightness Nd fiber laser pumped by GaAlAs phased array,” presented at the Opt. Fiber Commun. Conf., Houston, TX, 1989, Paper PD7. [33] N. A. Mortensen, “Air-clad fibers: Pump absorption assisted by chaotic wave dynamics?,” Opt. Exp., vol. 15, pp. 8989–8996, 2007. [34] M. N. Zervas, A. Marshall, and J. Kim, “Effective absorption in claddingpumped fibers,” Proc. SPIE, vol. 7914, p. 79141T, 2011. [35] M. H. Muendel, “Optimal inner cladding shapes for double-clad fiber lasers,” presented at the Conf. Lasers Electro-Opt., Washington,, DC, USA, 1996, p. 209. [36] A. Liu and K. Ueda, “The absorption efficiency of circular, offset, and rectangular double-clad fibers,” Opt. Commun., vol. 132, pp. 511–518, 1996. [37] A. Liu, J. Song, K. Kouichi, and K. Ueda, “Effective absorption and pump loss of double-clad fiber lasers,” Proc. SPIE, vol. 2986, pp. 30–38, 1997. [38] P. Leproux, S. Fevrier, V. Doya, P. Roy, and D. Pagnoux, “Modeling and optimization of double-clad fiber amplifiers using chaotic propagation of the pump,” Opt. Fiber Technol., vol. 6, pp. 324–339, 2001. [39] V. Doya, O. Legrand, and F. Mortessagne, “Optimized absorption in a chaotic double-clad fiber amplifier,” Opt. Lett., vol. 26, pp. 872–874, 2001. [40] D. Kouznetsov, J. Moloney, and E. Wright, “Efficiency of pump absorption in double-clad fiber amplifiers—Part I: Fiber with circular symmetry,” J. Opt. Soc. Amer. B, vol. 18, pp. 743–749, 2001. [41] D. Kouznetsov and J. Moloney, “Efficiency of pump absorption in double-clad fiber amplifiers—Part II: Broken circular symmetry,” J. Opt. Soc. Amer. B, vol. 19, pp. 1259–1263, 2002.


[42] J. J. Morehead and M. H. Muendel, “Nearly circular pump guides,” Proc. SPIE, vol. 7914, 79142Y, 2011. [43] J. K. Sahu, C. C. Renaud, K. Furusawa, R. Selvas, J. A. Alvarez-Chavez, D. J. Richardson, and J. Nilsson, “Jacketed air-clad cladding pumped ytterbium-doped. Fibre laser with wide turning range,” Electron. Lett., vol. 37, pp. 1116–1117, 2001. [44] W. J. Wadsworth, R. M. Percival, G. Bouwmans, J. C. Knight, T. A. Birks, T. D. Hedley, and P. S. J. Russell, “Very high numerical aperture fibers,” IEEE Photon. Technol. Lett., vol. 16, no. 3, pp. 843– 845, Mar. 2004. [45] R. Selvas, J. K. Sahu, L. B. Fu, J. N. Jang, J. Nilsson, A. B. Grudinin, K. H. Ylä-Jarkko, S. U. Alam, P. W. Turner, and J. Moore, “Highpower, low-noise, Yb-doped, cladding-pumped, three-level fiber sources at 980 nm,” Opt. Lett., vol. 28, pp. 1093–1095, 2003. [46] M. Aslund, S. D. Jackson, J. Canning, A. Teixeira, and K. LyytikainenDigweed, “The influence of skew rays on angular losses in air-clad fibres,” Opt. Commun., vol. 262, pp. 77–81, 2006. [47] A. Liu and K. Ueda, “Propagation losses of pump light in rectangular double-clad fibers,” Opt. Eng., vol. 35, pp. 3130–3134, 1996. [48] D. A. V. Kliner, J. P. Koplow, L. Goldberg, A. L. G. Carter, and J. A. Digweed, “Polarization-maintaining amplifier employing doubleclad bow-tie fiber,” Opt. Lett., vol. 26, pp. 184–186, 2001. [49] C. Pare, “Influence of inner cladding shape and stress-applying parts on the pump absorption of a double-clad fiber amplifier,” Proc. SPIE, vol. 5260, pp. 272–277, 2003. [50] D. Gloge, “Bending loss in multimode fibers with graded and ungraded core index,” Appl. Opt., vol. 11, pp. 2506–2513, 1972. [51] D. Marcuse, “Coupled power equations for lossy fibers,” Appl. Opt., vol. 17, pp. 3232–3237, 1978. [52] J. Nilsson, S. U. Alam, J. A. Alvarez-Chavez, P. W. Turner, W. A. Clarkson, and A. B. Grudinin, “High power and tunable operation of erbium-ytterbium co-doped cladding-pumped fiber lasers,” IEEE J. Quantum Electron., vol. 39, no. 8, pp. 987–994, Aug. 2003. [53] A. Tunnermann, T. Schreiber, and J. Limpert, “Fiber lasers and amplifiers: An ultrafast performance evolution,” Appl. Opt., vol. 49, pp. F71– 78, 2010. [54] V. Filippov, Y. Chamorovskii, J. Kerttula, K. Golant, M. Pessa, and O. G. Okhotnikov, “Double clad tapered fiber for high power applications,” Opt. Exp., vol. 16, pp. 1929–1944, 2008. [55] X. P. Cheng, P. Shum, J. Zhang, and M. Tang, “Analysis of nonlinear effective absorption coefficient of double cladding fiber,” presented at the IEEE Region Conf. TENCON, Hong Kong, Nov. 2006. [56] C. L. Bonner, T. Bhutta, D. P. Shepherd, and A. C. Tropper, “Double-clad structures and proximity coupling for diode-bar-pumped planar waveguide lasers,” IEEE J. Quantum Electron., vol. 36, no. 2, pp. 236–242, Feb. 2000. [57] D. P Shepherd, S. J Hettrick, C. Li, J. I. Mackenzie, R. J. Beach, S. C. Mitchell, and H. E. Meissner, “High-power planar dielectric waveguide lasers,” J. Phys. D, Appl. Phys., vol. 34, pp. 2420–2432, 2001. [58] H. X. Kang, H. Zhang, P. Yan, D. S. Wang, and M. Gong, “An endpumped Nd:YAG planar waveguide laser with an optical to optical conversion efficiency of 58%,” Laser Phys. Lett., vol. 5, pp. 879–881, 2008. [59] T. Y. Fan, “Efficient coupling of multiple diode laser arrays to an optical fiber by geometric multiplexing,” Appl. Opt., vol. 30, pp. 630–632, 1991. [60] D. J. DiGiovanni and A. J. Stentz, “Tapered fiber bundles for coupling light into and out of cladding-pumped fiber devices,” U.S. Patent 5 864 644 1999. [61] A. Kosterin, V. Temyanko, M. Fallahi, and M. Mansuripur, “Tapered fiber bundles for combining high-power diode lasers,” Appl. Opt., vol. 43, pp. 3893–3900, 2004. [62] L. Goldberg, B. Cole, and E. Snitzer, “V-groove side-pumped 1.5 μm fibre amplifier,” Electron. Lett., vol. 33, pp. 2127–2129, 1997. [63] G. Canat, J. C. Mollier, J. P Bouzinac, G. M. Williams, B. Cole, L. Goldberg, Y. Jaouën, and G. Kulcsar, “Dynamics of high-power erbium–ytterbium fiber amplifiers,” J. Opt. Soc. Amer. B, vol. 22, pp. 2308–2318, 2005. [64] E. Snitzer, H. Ho, R. P. Tumminelli, and F. Hakimi, “Optical fiber lasers and amplifiers,” U.S. Patent 4 815 079, 1989. [65] Q. Xiao, P. Yan, S. Yin, J. Hao, and M. Guo, “100 W ytterbium-doped monolithic fiber laser with fused angle-polished side-pumping configuration,” Laser Phys. Lett., vol. 8, pp. 125–129, 2011. [66] V. P. Gapontsev and I. Samartsev, “Coupling arrangement between a multimode light source and an optical fiber through an intermediate optical fiber length,” U.S. Patent 5 999 673, 1999.

0904123

[67] P. Ou, P. Yan, M. Gong, W. Wei, and Y. Yuan, “Studies of pump light leakage out of couplers for multi-coupler side-pumped Yb-doped doubleclad fiber lasers,” Opt. Commun., vol. 239, pp. 421–428, 2004. [68] A. B. Grudinin, J. Nilsson, P. W. Turner, C. C. Renaud, W. A. Clarkson, and D. N. Payne, “Single clad coiled optical fiber for high power lasers and amplifiers,” presented at the Conf. Lasers Electro-Opt., Baltimore, MD, USA, 1999, Paper CPD26. [69] A. B. Grudinin, D. N. Payne, P. W. Turner, J. Nilsson, M. N. Zervas, M. Ibsen, and M. K. Durkin, “Multi-fibre arrangements for high power fiber lasers and amplifiers,” U.S. Patent 6 826 335, 2000. [70] P. Polynkin, V. Temyanko, M. Mansuripur, and N. Peyghambarian, “Efficient and scalable side pumping scheme for short high-power optical fiber lasers and amplifiers,” IEEE Photon. Technol. Lett., vol. 16, no. 9, pp. 2024–2026, Sep. 2004. [71] Y. Wang, “Heat dissipation in kilowatt fiber power amplifiers,” IEEE J. Quantum Electron., vol. 40, no. 6, pp. 731–740, Jun. 2004. [72] J. R. Leger and W. C. Goltsos, “Geometrical transformation of linear diode-laser arrays for longitudinal pumping of solid-state lasers,” IEEE J. Quantum Electron., vol. 28, no. 4, pp. 1088–1100, Apr. 1992. [73] S. R. Karlsen, R. K. Price, M. Reynolds, A. Brown, R. Mehl, S. Patterson, and R. J. Martinsen, “100-W, 105-μm, 0.15 NA fiber coupled laser diode module,” Proc. SPIE, vol. 7198, 719829, 2009. [74] JDSU Product Catalogue, JDS Uniphase Corporation, CA , USA, 2013. [75] Y. Xiao, F. Brunet, M. Kanskar, M. Faucher, A. Wetter, and N. Holehouse, “1-kilowatt CW all-fiber laser oscillator pumped with wavelength-beamcombined diode stacks,” Opt. Exp., vol. 20, pp. 3296–3301, 2012. [76] B. Sévigny, P. Poirier, and M. Faucher, “Pump combiner loss as a function of input numerical aperture power distribution,” Proc. SPIE, vol. 7195, 719523, 2009. [77] A. Wetter, M. Faucher, M. Lovelady, and F. Séguina, “Tapered fusedbundle splitter capable of 1 kW CW operation,” Proc. SPIE, vol. 6453, 645301, 2007. [78] Q. Xiao, P. Pan, J. He, Y. Wang, X. Zhang, and M. Gong, “Tapered fused fiber bundle coupler capable of 1 kW laser combining and 300 W laser splitting,” Laser Phys., vol. 21, pp. 1415–1419, 2011. [79] H. –S. Seo, J. T. Ahn, B. J. Park, J.H. Song, and W. Chung, “Efficient pump beam multiplexer based on single-mode fibers,” Jpn. J. Appl. Phys., vol. 51, 010203, 2012. [80] S. U. Alam, A. T. Harker, R. J. Horley, F. Ghiringhelli, M. P. Varnham, P. W. Turner, M. N. Zervas, and S. R. Norman, “All-fibre, high power, cladding-pumped 1565 nm MOPA pumped by high brightness 1535 nm pump sources,” presented at the Conf. Lasers Electro-Opt., San Jose, CA, USA, 2008, Paper CWJ4. [81] V. Gapontsev, V. Fomin, D. Gapontsev, and V. Ivshin, “Advances in multi-kW fiber lasers,” presented at the Advanced Laser Appl. Conf. Expo., Michigan, MI, USA, Sep. 2006. [82] J. Zhu, P. Zhou, Y. Ma, X. Xu, and Z. Liu, “Power scaling analysis of tandem-pumped Yb-doped fiber lasers and amplifiers,” Opt. Exp., vol. 19, pp. 18645–18654, 2011. [83] M. H. Muendel, R. Farrow, K. H. Liao, D. Woll, J. Luu, C. Zhang, J. Morehead, J Segall, J. Gregg, K. Tai, B. Kharlamov, H. Yu, and L. Myers, “Fused fiber pump and signal combiners for 4-kW Ytterbium fiber laser,” Proc. SPIE, vol. 7914, p. 791431, 2011. [84] S. B. Poole, D. N. Payne, and M. E. Fermann, “Fabrication of low-loss optical fibres containing rare-earth ions,” Electron. Lett., vol. 21, no. 17, pp. 737–738, 1985. [85] R. J. Mears, L. Reekie, S. B. Poole, and D. N. Payne, “Neodymium doped silica single-mode fibre lasers,” Electron. Lett., vol. 21, no. 17, pp. 738–740, 1985. [86] R. J. Mears, L. Reekie, S. B. Poole, and D. N. Payne, “Low-threshold tunable CW and Q-switched fibre laser operating at 1.55 μm,” Electron. Lett., vol. 22, no. 3, pp. 159–160, 1986. [87] M. E. Fermann, D. C. Hanna, D. P. Shepherd, P. J. Suni, and J. E. Townsend, “Efficient operation of an Yb-sensitised Er fiber laser at 1.56 mm,” Electron. Lett., vol. 24, pp. 1135–1136, 1988. [88] D. C. Hanna, R. M. Percival, I. R. Perry, R. G. Smart, P. J. Suni, and A. C. Tropper, “Yb-doped monomode fibre laser: broadly tunable operation from 1.010 μm to 1.62 μm and three-level operation at 974 nm,” J. Modern Opt., vol. 37, pp. 329–331, 1987. [89] J. Suni, J. E. Townsend, and A. C. Tropper, “Continuous-wave oscillation of a monomode thulium-doped fiber laser,” Electron. Lett., vol. 24, no. 19, pp. 1222–1223, 1988. [90] D. C. Hanna, R. M. Percival, R. G. Smart, J. E. Townsend, and A. C. Tropper, “Continuous-wave oscillation of holmium-doped silica fiber laser,” Electron. Lett., vol. 25, no. 9, pp. 593–594, 1989.

0904123


[91] P. Barua, E. H. Sekiya, K. Saito, and A. J. Ikushima, “Influences of Yb3 + ion concentration on the spectroscopic properties of silica glass,” J. Non-Crystalline Solids, vol. 354, pp. 4760–4764, 2008. [92] Y. Qiao, L. Wen, B. Wu, J. Ren, D. Chen, and J. Qiu, “Preparation and spectroscopic properties of Yb-doped and Yb–Al-codoped high silica glasses,” Mater. Chemistry Phys., vol. 107, pp. 488–491, 2008. [93] H. M. Pask, R. J. Carman, D. C. Hanna, A. C. Tropper, C. J. Mackechnie, P. R. Barber, and J. M. Dawes, “Ytterbium-doped silica fiber lasers: Versatile sources for the 1–1.2 μm region,” IEEE J. Sel. Topics Quantum Electron., vol. 1, no. 1, pp. 2–13, Apr. 1995. [94] M. J. Weber, J. E. Lynch, D. H. Blackburn, and D. J. Cronin, “Dependence of the stimulated emission cross section of Yb3 + on host glass composition,” IEEE J. Quantum Electron., vol. QE-19, no. 10, pp. 1600– 1608, Oct. 1983. [95] F. Auzel and P. Goldner, “Towards rare-earth clustering control in doped glasses,” Opt. Mater., vol. 16, pp. 93–103, 2001. [96] S. D. Jackson and T. A. King, “Theoretical modelling of Tm-doped silica fiber lasers,” J. Lightw. Technol., vol. 17, no. 5, pp. 948–956, May 1999. [97] S. D. Jackson, “Cross relaxation and energy transfer upconversion processes relevant to the functioning of 2 μm Tm3 + -doped silica fibre lasers,” Opt. Commun., vol. 230, pp. 197–203, 2004. [98] A. E. Siegman, “How to (maybe) measure laser beam quality,” in DPSS Lasers: Applications and Issues, M. W. Dowley, Ed. Washington, DC, USA: OSA, 1998, pp. 184–199. [99] T.S. Ross and W.P. Latham, “Appropriate measures and consistent standard for high energy laser beam quality,” J. Directed Energy, vol. 2, pp. 22–58, 2006. [100] D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell System Tech. J.,, vol. 56, no. 5, pp. 703–718, 1977. [101] D. Gloge, “Optical power flow in multimode fibers,” Bell System Tech. J., vol. 51, pp. 1767–1783, 1972. [102] S. Saghafi and C. J. R. Sheppard, “The beam propagation factor for higher order Gaussian beams,” Opt. Commun., vol. 153, pp. 207–210, 1998. [103] Y. Jeong, A. J. Boyland, J. K. Sahu, S. Chung, J. Nilsson, and D. N. Payne, “Multi-kilowatt single-mode Ytterbium-doped large-core fiber laser,” J. Opt. Soc. Korea, vol. 13, pp. 416–422, 2009. [104] A. E. Siegman and S. W. Townsend, “Output beam propagation and beam quality from multimode stable-cavity laser,” IEEE J. Quantum Electron., vol. 29, no. 4, pp. 1212–1217, Apr. 1993. [105] Y. Shamir, Y. Sintov, E. Shafir, and M. Shtaif, “Beam quality output of a few-modes fiber seeded by an off-center single-mode fiber source,” Opt. Lett., vol. 34, pp. 1795–1797, 2009. [106] S. Wielandy, “Implications of higher-order mode content in large mode area fibers with good beam quality,” Opt. Exp., vol. 15, pp. 15402–15408, 2007. [107] D. Gloge, “Optical power flow in multimode fibers,” Bell Syst. Tech. J., vol. 51, pp. 1767–1783, 1972. [108] M. N. Zervas, “High power Ytterbium-doped fiber lasers: Fundamentals and applications,” Int. J. Mod. Phys. B, vol. 28, 1442009, 2014. [109] Z. Jiang and J. R. Marciante, “Impact of transverse spatial-hole burning on beam quality in large-area Yb-doped fibers,” J. Opt. Soc. Amer. B, vol. 25, pp. 247–254, 2008. [110] J. F. Seurin, G. Xu, Q. Wang, B. Guo, R. Van Leeuwen, A. Miglo, P. Pradhan, J. D. Wynn, V. Khalfin, and C. Ghosh, “High-brightness pump sources using 2D VCSEL arrays,” Proc. SPIE, vol. 7615, 76150F, 2010. [111] H. Yoda, P. Polynkin, and M. Mansuripur, “Beam quality factor of higher order modes in a step-index fiber,” J. Lightw. Technol., vol. 24, no. 3, pp. 1350–1355, Mar. 2006. [112] M. E. Fermann, “Single-mode excitation of multimode fibers with ultrashort pulses,” Opt. Lett., vol. 23, pp. 52–54, 1998. [113] Y. Jung, Y. Jeong, G. Brambilla, and D. J. Richardson, “Adiabatically tapered splice for selective excitation of the fundamental mode in a multimode fiber,” Opt. Lett., vol. 34, pp. 2369–2371, 2009. [114] H. Zimer, M. Kozak, A. Liem, F. Flohrer, F. Doerfel, P. Riedel, S. Linke, R. Horley, F. Ghiringhelli, S. Demoulins, M. N. Zervas, J. Kirchhof, S. Unger, S. Jetschke, T. Peschel, and T. Schreiber, “Fibers and fiberoptic components for high power fiber lasers,” Proc. SPIE, vol. 7914, 791414, 2011. [115] J. P. Koplow, D. A. V. Kliner, and L. Goldberg, “Single-mode operation of a coiled multimode fiber amplifier,” Opt. Lett., vol. 25, pp. 442–444, 2000. [116] R. T. Schermer, “Mode scalability in bent optical fibers,” Opt. Exp., vol. 15, pp. 15674–15701, 2007.

[117] Z. Li, J. Zhou, W. Wang, B. He, Y. Xue, and Q. Lou, “Limitations of coiling technique for mode controlling of multimode fiber lasers,” presented at the CLEO/Pacific Rim, Shangai, China, 2009. [118] B. Sevigny, X. Zhang, M. Garneau, M. Faucher, Y. K. Lize, and N. Holehouse, “Modal sensitivity analysis for single-mode operation in large-mode area fiber,” Proc. SPIE, vol. 6873, 68730A, 2008. [119] S. A. Cerqueira, Jr, “Recent progress and novel applications of photonic crystal fibers,” Rep. Prog. Phys., vol. 73, 024401, 2010. [120] W. J. Wadsworth, R. M. Percival, G. Bouwmans, J. C. Knight, and P. S. J. Russell, “High power air-clad photonic crystal fibre laser,” Opt. Exp., vol. 11, pp. 48–53, 2003. [121] G. Canat, S. Jetschke, S. Unger, L. Lombard, P. Bourdon, J. Kirchhof, V. Jolivet, A. Dolfi, and O. Vasseur, “Multifilament-core fibers for high energy pulse amplification at 1.5 μm with excellent beam quality,” Opt. Lett., vol. 33, pp. 2701–2703, 2008. [122] G. Canat, R. Spittel, S. Jetschke, L. Lombard, and P. Bourdon, “Analysis of the multifilament core fiber using the effective index theory,” Opt. Exp., vol. 18, pp. 4644–4654, 2010. [123] F. Di Teodoro, M. K. Hemmat, J. Morais, and E. C. Cheung, “High peak power operation of a 100 μm-core Yb-doped rod-type photonic crystal fibre amplifier,” Proc. SPIE, vol. 7580, 758006, 2010. [124] P. S. J. Russell, “Photonic crystal fibers,” Science, vol. 299, pp. 358–362, 2003. [125] J. Limpert, F. Stutzki, F. Jansen, H. J. Otto, T. Eidam, C. Jauregui, and A. Tunnermann, “Yb-doped large-pitch fibres: effective single-mode operation based on higher-order mode delocalisation,” Light: Sci. Appl., vol. 1, no. 4, pp. 1–5, 2012. [126] R. Dauliat, D. Gaponov, A. Benoit, F. Salin, K. Schuster, R. Jamier, and P. Roy, “Inner cladding microstructuration based on symmetry reduction for improvement of singlemode robustness in VLMA fiber,” Opt. Exp., vol. 21, pp. 18927–18936, 2013. [127] F. Jansen, F. Stutzki, H. J. Otto, T. Eidam, A. Liem, C. Jauregui, J. Limpert, and A. Tunnermann, “Theramally induced waveguide changes in active fibers,” Opt. Exp., vol. 20, pp. 3997–4008, 2012. [128] C-H. Liu, G. Chang, N. Litchinitser, D. Guertin, N. Jacobsen, K. Tankala, and A. Galvanauskas, “Chirally coupled core fibers at 1550-nm and 1064-nm for effectively single-mode core size scaling,” presented at the Conf. Lasers Electro-Opt., Baltimore, MD, USA, 2007, Paper CTuBB3. [129] J. R. Marciante, “Gain filtering for single-spatial-mode operation of large-mode-area fibre amplifiers,” IEEE J. Sel. Topics Quantum Electron., vol. 15, no. 1, pp. 30–36, Jan. 2009. [130] V. Sudesh, T. Mccomb, Y. Chen, M. Bass, M. Richardson, J. Ballato, and A. E. Siegman, “Diode-pumped 200 μm diameter core, gain-guided, index-antiguided single mode fiber laser,” Appl. Phys. B, vol. 90, pp. 369– 372, 2008. [131] M. J. Li, X. Chen, A. Liu, S. Gray, J. Wang, D. T. Walton, and L. A. Zenteno, “Limit of effective area for single-mode operation in step-index large mode area laser fibers,” J. Lightw. Technol., vol. 27, no. 15, pp. 3010–3016, Jan. 2009. [132] S. Kawakami and S. Nishida, “Characteristics of a doubly clad optical fiber with a low-index inner cladding,” IEEE J. Quantum Electron., vol. 10, no. 12, pp. 879–887, Dec. 1974. [133] V. Rastogi and K. S. Chiang, “Propagation characteristics of a segmented cladding fiber,” Opt. Lett., vol. 26, pp. 491–493, 2001. [134] L. Dong, T. W. Wu, H. A. McKay, L. Fu, J. Li, and H. G. Winful, “Allglass large-core leakage channel fibers,” IEEE J. Sel. Topics Quantum Electron., vol. 15, no. 1, pp. 47–53, Jan. 2009. [135] J. M. Fini, “Design of solid and microstructure fibers for suppression of higher-order modes,” Opt. Exp., vol. 13, pp. 3477–3490, 2005. [136] B. Beaudou, F. Gerôme, Y. Y. Wang, M. Alharbi, T. D. Bradley, G. Humbert, J.-L. Auguste, J.-M. Blondy, and F. Benabid, “Millijoule laser pulse delivery for spark ignition through kagome hollow-core fiber,” Opt. Lett., vol. 37, pp. 1430–1432, 2012. [137] G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. New York: Academic, 2001. [138] B. Morasse, E. Gagnon, J. Arsenault-Roy, and J.-P. De Sandro, “High peak power single-mode amplification using highly doped double cladding Ytterbium phosphosilicate fiber,” in presented at the Workshop Specialty Opt. Fibers Appl., Sigtuna, Sweden, 2013, Paper F2.19. [139] A. J. Kim, P. Dupriez, C. Codemard, J. Nilsson, and J. K. Sahu, “Suppression of stimulated Raman scattering in a high power Yb-doped fiber amplifier using a W-type core with fundamental mode cut-off,” Opt. Exp., vol. 14, pp. 5103–5113, 2006.


[140] X. Ma, I. N. Hu, and A. Galvanauskas, “Propagation-length independent SRS threshold in chirally-coupled-core fibers,” Opt. Exp., vol. 19, pp. 22575–22581, 2011. [141] D. Taverner, D. J. Richardson, L. Dong, J. E. Caplen, K. Williams, and R. V. Penty, “158-μJ pulses from a single-transverse-mode, large-modearea erbium-doped fiber amplifier,” Opt. Lett., vol. 22, pp. 378–380, 1997. [142] S. Gray, D. T. Walton, X. Chen, J. Wang, M. J. Li, A. Liu, A. B. Ruffin, J. A. Demeritt, and L. A. Zenteno, “Optical fibers with tailored acoustic speed profiles for suppressing stimulated Brillouin scattering in highpower, single-frequency sources,” IEEE J. Sel. Topics Quantum Electron., vol. 15, no. 1, pp. 37–46, Jan. 2009. [143] L. Yingfan, L. Zhiwei, D. Yongkang, and L. Qiang, “Research on stimulated Brillouin scattering suppression based on multi-frequency phase modulation,” Chin. Opt. Lett., vol. 7, pp. 29–31, 2009. [144] D. Brown, M. Dennis, and W. Torruellas, “Improved phase modulation for SBS mitigation in kW-class fiber amplifiers,” presented at the SPIE Photon. West, San Francisco, CA, USA, Jan. 2011. [145] J. Edgecumbe, T. Ehrenreich, C.-H. Wang, K. Farley, J. Galipeau, R. Leveille, D. Björk, I. Majid, and K. Tankala, “kW class, narrowlinewidth, counter pumped fiber amplifiers,” Solid State Diode Laser Tech. Rev., vol. 17, 2010. [146] I. Dajani, C. Zeringue, C. Lu, C. Vergien, L. Henry, and C. Robin, “Stimulated Brillouin scattering suppression through laser gain competition: Scalability to high power,” Opt. Lett., vol. 35, pp. 3114–3116, 2010. [147] Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency Ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Topics Quantum Electron., vol. 13, no. 3, pp. 546–551, May/Jun. 2007. [148] M. D. Mermelstein, M. J. Andrejco, J. Fini, A. Yablon, C. Headley, III, D. J. DiGiovanni, and A. H. McCurdy, “11.2 dB SBS gain suppression in a large mode area Yb-doped optical fiber,” Proc. SPIE, vol. 6873, 68730N, 2008. [149] Z. Zhang, X. Zhou, Z. Sui, J. Wang, H. Li, Y. Liu, and Y. Liu, “Numerical analysis of stimulated inelastic scatterings in ytterbium-doped doubleclad fiber amplifier with multi-ns-duration and multi-hundred-kW peakpower output,” Opt. Commun., vol. 282, pp. 1186–1190, 2009. [150] R. Su, P. Zhou, H. Lu, X. Wang, C. Luo, and X. Xu, “Numerical analysis on impact of temporal characteristics of SBS for nanosecond laser in an optical fiber,” Opt. Commun., vol. 316, pp. 86–90, 2014. [151] P. S. J. Russell, D. Culverhouse, and F. Farahi, “Theory of forward stimulated Brillouin scattering in dual-mode single-core fibers,” IEEE J. Quantum Electron., vol. 27, no. 3, pp. 836–842, Mar. 1991. [152] C. D. Brooks and F. Di Teodoro, “1 mJ energy, 1 MW peak power, 10 W average-power spectrally narrow, diffraction-limited pulses from a photonic-crystal fiber amplifier,” Opt. Exp., vol. 13, pp. 8999–9002, 2005. [153] J. P. Feve, P. E. Schrader, R. L. Farrow, and D. A. V. Kliner, “Fourwave mixing in nanosecond pulsed fiber amplifiers,” Opt. Exp., vol. 15, pp. 4646–4662, 2007. [154] R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron., vol. 18, no. 7, pp. 1062–1072, Jul. 1982. [155] M. E. Fermann and I. Hartl, “Fiber laser based hyperspectral sources,” Laser Phys. Lett., vol. 6, pp. 11–21, 2009. [156] P. J. Almeida, P. Dupriez, J. Clowes, E. Bricchi, M. Rusu, and A. B. Grudinin, “Ultrafast fiber lasers and nonlinear generation of light,” presented at the 11th Int. Conf. Transparent Opt. Netw., Azores, Portugal, 2009, Paper We.C5.2. [157] J.C. Travers, A.B. Rulkov, B.A. Cumberland, S.V. Popov, and J.R. Taylor, “Visible supercontinuum generation in photonic crystal fibers with a 400 W continuous wave fiber laser,” Opt. Exp., vol. 16, pp. 14435– 14447, 2008. [158] R.Y. Chiao, E. Garmire, and C.H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett., vol. 13, pp. 479–482, 1964. [159] G. Fibich and A.L. Gaeta, “Critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett., vol. 25, pp. 335–337, 2000. [160] R. L. Farrow, G. R. Hadley, A. V. Smith, and D. A. V. Kliner, “Numerical modeling of self-focusing beams in fiber amplifiers,” Proc. SPIE, vol. 6453, 645309, 2007. [161] M. Y. Chen, Y. C. Chang, and A. Galvanauskas, “High-energy and high peak-power nanosecond pulse generation with beam quality control in 200-μm core highly multimode Yb-doped fiber amplifiers,” Opt. Lett., vol. 30, pp. 358–360, 2005.

0904123

[162] T. Schmidt-Uhlig, P. Karlitschek, G. Marowsky, and Y. Sano, “New simplified coupling scheme for the delivery of 20 MW Nd:YAG laser pulses by large core optical fibers,” Appl. Phys. B, vol. 72, pp. 183–186, 2001. [163] A. D. Yablon and J. Jasapara, “Fiber designs for exceeding the bulkmedia self-focusing threshold,” Proc. SPIE, vol. 6453, 64531D, 2007. [164] A. V. Smith, B. T. Do, G. R. Hadley, and R. L. Farrow, “Optical damage limits to pulse energy from fibers,” IEEE J. Sel. Topics Quantum Electron., vol. 15, no. 1, pp. 153–158, Jan. 2009. [165] A. V. Smith and B. T. Do, “Bulk and surface laser damage of silica by picosecond and nanosecond pulses at 1064 nm,” Appl. Opt., vol. 47, pp. 4812–4832, 2008. [166] D. N. Schimpf, T. Eidam, E. Seise, S. Hadrich, J. Limpert, and A. Tunnermann, “Circular versus linear polarization in laser-amplifiers with Kerr-nonlinearity,” Opt. Exp., vol. 17, pp. 18774–18781, 2009. [167] R. Kashyap and K. J. Blow, “Observation of catastrophic self-propelled self-focusing in optical fibres,” Electron. Lett., vol. 24, no. 1, pp. 47–49, 1988. [168] A. Bufetov, A. A. Frolov, V. P. Efremov, M. Ya. Schelev, V. I. Lozovoi, V. E. Fortov, and E. M. Dianov, “Fast optical discharge propagation through optical fibres under kW-range laser radiation,” in Proc. 31st Eur. Conf. Opt. Commun., 2005, vol. 6, pp. 39–40. [169] S. Jetschke, S. Unger, U. Röpke, and J. Kirchhof, “Photodarkening in Yb doped fibers: Experimental evidence of equilibrium states depending on the pump power,” Opt. Exp., vol. 15, no. 22, pp. 14838–14843, 2007. [170] J. Koponen, M. Söderlund, H. Hoffman, D. Kliner, and J. Koplow, “Photodarkening measurements in large mode area fibers,” Proc. SPIE, vol. 6453, 64531E, 2006. [171] M. Hotoleanu, J. Koponen, T. Kokki, and M. Laurila, “Experimental verification of spatial distribution of photodarkening in LMA Yb-doped fibers,” presented at the Conf. Lasers Electro-Opt., San Jose, CA, USA, 2008, Paper CFS3. [172] M. N. Zervas, F. Ghiringhelli, M. K. Durkin, and I. Crowe, “Distribution of photodarkening-induced loss in Yb-doped fiber amplifiers,” Proc. SPIE, vol. 7914, 79140L, 2011. [173] S. Jetschke, S. Unger, A. Schwuchow, M. Leich, and J. Kirchhof, “Efficient Yb laser fibers with low photodarkening by optimization of the core composition,” Opt. Exp., vol. 16, pp. 15540–15545, 2008. [174] S. Jetschke, S. Unger, M. Leich, and J. Kirchhof, “Photodarkening kinetics as a function of Yb concentration and the role of Al codoping,” Appl. Opt., vol. 51, pp. 7758–7764, 2012. [175] B. Morasse, S. Chatigny, E. Gagnon, C. Hovington, J.-P. Martin, and J-P. deSandro, “Low photodarkening single cladding ytterbium fibre amplifier,” Proc. SPIE, vol. 6453, 64530H, 2007. [176] M. Engholm and L. Norin, “Preventing photodarkening in ytterbiumdoped high power fiber lasers; correlation to the UV-transparency of the core glass,” Opt. Exp., vol. 16, pp. 1260–1268, 2008. [177] M. Engholm, P. Jelger, F. Laurell, and L. Norin, “Improved photodarkening resistivity in ytterbium-doped fiber lasers by cerium codoping,” Opt. Lett., vol. 34, pp. 1285–1287, 2009. [178] M. M. Broer, D. M. Krol, and D. J. DiGiovanni, “Highly nonlinear nearresonant photodarkening in a thulium-doped aluminosilicate glass fiber,” Opt. Lett., vol. 18, no. 10, pp. 799–801, 1993. [179] W. S. Brocklesby, A. Mathieu, R. S. Brown, and J. R. Lincoln, “Defect production in silica fibers doped with Tm3 + ,” Opt. Lett., vol. 18, no. 24, pp. 2105–2107, 1993. [180] J. W. Dawson, M. J. Messerly, R. J. Beach, M. Y. Shverdin, E. A. Stappaerts, A. K. Sridharan, P. H. Pax, J. E. Heebner, C. W. Siders, and C. P. J. Barty, “Analysis of the scalability of diffraction-limited fiber lasers and amplifiers to high average power,” Opt. Exp., vol. 16, pp. 13240–13266, 2008. [181] B. Shiner, “The impact of fiber laser technology on the world wide material processing market,” presented at the CLEO: Appl. Technol., San Jose, CA, USA, 2013, Paper AF2J.1. [182] J. Zhu, P. Zhou, Y. Ma, X. Xu, and Z. Liu, “Power scaling analysis of tandem-pumped Yb-doped fiber lasers and amplifiers,” Opt. Exp., vol. 19, pp. 18645–18654, 2011. [183] C. X. Yu and T. Y. Fan, “Beam combining,” in High Power Laser Handbook, H. Injeyan and G. D. Goodno, Eds. New York: McGraw-Hill, 2011. [184] T. J. Wagner, “Fiber laser beam combining and power scaling progress, air force research laboratory laser division,” Proc. SPIE, vol. 8237, 823718, 2012.

0904123


[185] Z. Liu, P. Zhou, X. Xu, X. Wang, and Y. Ma, “Coherent beam combining of high power fiber lasers: Progress and prospects,” Sci. China: Technol. Sci., vol. 56, pp. 1597–1606, 2013. [186] C. X. Yu, S. J. Augst, S. M. Redmond, K. C. Goldizen, D. V. Murphy, A. Sanchez-Rubio, and T. Y. Fan, “Coherent combining of a 4 kW, eight-element fiber amplifier array,” Opt. Lett., vol. 36, pp. 2686–2688, 2011. [187] S. M. Redmond, D. J. Ripin, C. X. Yu, S. J. Augst, T. Y Fan, P. A. Thielen, J. E. Rothenberg, and G. D. Goodno, “Diffractive coherent combining of a 2.5 kW fiber laser array into a 1.9 kW Gaussian beam,” Opt. Lett., vol. 37, pp. 2832–2835, 2012. [188] E. Beyer, A. Mahrle, M. Lutke, J. Standfuss, and F. Bruckner, “Innovation in high power fiber laser applications,” Proc. SPIE, vol. 8237, 823717, 2012. [189] Y. Wang and C.Q. Xu, “Actively Q-switched fiber lasers: Switching dynamics and nonlinear processes,” Progress Quantum Electron., vol. 31, pp. 131–216, 2007. [190] C. C. Renaud, H. L. Offerhaus, J. A. Alvarez-Chavez, J. Nilsson, W. A. Clarkson, P. W. Turner, D. J. Richardson, and A. B. Grudinin, “Characteristics of Q-switched cladding pumped ytterbium-doped fiber lasers with different high-energy fiber designs,” IEEE J. Quantum Electron., vol. 37, no. 2, pp. 199–206, Feb. 2001. [191] M.-Y. Chen, Y.-C. Chang, A. Galvanauskas, P. Mamidipudi, R. Changkakoti, and P. Gatchell, “27-mJ nanosecond pulses in M 2 = 6.5 beam from a coiled highly multimode Yb-doped fiber amplifier,” presented at the Conf. Lasers Electro-Opt., San Francisco, CA, USA, 2004, Paper CTuS4. [192] J. Limpert, N. Deguil-Robin, S. Petit, I. Manek-Honninger, F. Salin, P. Rigail, C. Honninger, and E. Mottay, “High power Q-switched Ybdoped photonic crystal fiber laser producing sub-10 ns pulses,” Appl. Phys. B, vol. 81, pp. 19–21, 2005. [193] T. Wei, Z. Tan, J. Li, and J. Zhua, “Theoretical and experimental study of the pump pulse width optimization of the Yb-doped fiber amplifier,,” Optik—Int. J. Light Electron. Opt., vol. 124, pp. 2459–2462, 2013. [194] C. Zheng, H. T. Zhang, W. Y. Cheng, M. Liu, P. Yan, and M. L. Gong, “11-mJ pulse energy wideband Yb-doped fiber laser,” Opt. Commun., vol. 285, pp. 3623–3626, 2012. [195] K. T. Vu, A. Malinowski, D. J. Richardson, F. Ghiringhelli, L. M. B. Hickey, and M. N. Zervas, “Adaptive pulse shape control in a diode-seeded nanosecond fiber MOPA system,” Opt. Exp., vol. 14, pp. 10996–11001, 2006. [196] A. Malinowski, P. Gorman, C. A. Codemard, F. Ghiringhelli, A. J. Boyland, A. Marshall, M. N. Zervas, and M. K. Durkin, “Highpeak-power, high-energy, high-average-power pulsed fiber laser system with versatile pulse duration and shape,” Opt. Lett., vol. 38, pp. 4686– 4689, 2013. [197] M. N. Zervas, M. Durkin, F. Ghiringhelli, K. Vysniauskas, L. Hickey, A. Gillooly, P. Turner, and B. Kao, “High peak power, high rep-rate pulsed fibre laser for marking applications,” Proc. SPIE, vol. 6102, 61020Q, 2006. [198] R. Horley, S. Norman, and M. N. Zervas, “Progress and development in fibre laser technology,” Proc. SPIE, vol. 6738, 67380K, 2007. [199] F. Stutzki, F. Jansen, A. Liem, C. Jauregui, J. Limpert, and A. Tünnermann, “26 mJ, 130 W Q-switched fiber-laser system with neardiffraction-limited beam quality,” Opt. Lett., vol. 37, no. 6, pp. 1073– 1075, 2012. [200] C. D. Brooks and F. Di Teodoro, “Multimegawatt peak-power, singletransverse-mode operation of a 100 mm core diameter, Yb-doped rod-like photonic crystal fiber amplifier,” Appl. Phys. Lett., vol. 89, pp. 111–119, 2006. [201] O. Schmidt, C. Wirth, I. Tsybin, T. Schreiber, R. Eberhardt, J. Limpert, and A. Tünnermann, “Average power of 1.1 kW from spectrally combined, fiber-amplified, nanosecond-pulsed sources,” Opt. Lett., vol. 34, pp. 1567–1569, 2009. [202] M. E. Fermann and I. Hartl, “Ultrafast fiber laser technology,” J. Sel. Topics Quantum Electron., vol. 15, pp. 191–206, 2009. [203] A. Tunnermann, T. Schreiber, and J. Limpert, “Fiber lasers and amplifiers: An ultrafast performance evolution,” Appl. Opt., vol. 49, pp. F71– F78, 2010. [204] T. Eidam, S. Hanf, E. Seise, T. V. Andersen, T. Gabler, C. Wirth, T. Schreiber, J. Limpert, and A. Tunnermann, “Femtosecond fiber CPA system emitting 830 W average output power,” Opt. Lett., vol. 35, pp. 94– 96, 2010. [205] C. Jauregui, J. Limpert, and A. Tunnermann, “High-power fibre lasers,” Nature Photon., vol. 7, pp. 861–867, 2013.

[206] X. Chen, A. Jullien, A. Malvache, L. Canova, A. Borot, A. Trisorio, C. G. Durfee, and R. Lopez-Martens, “Generation of 4.3 fs, 1 mJ laser pulses via compression of circularly polarized pulses in a gas-filled hollow-core fiber,” Opt. Lett., vol. 34, pp. 1588–1590, 2009. [207] D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun., vol. 56, no. 3, pp. 219–221, 1985. [208] T. Eidam, J. Rothhardt, F. Stutzki, F. Jansen, S. Hädrich, H. Carstens, C. Jauregui, J. Limpert, and A. Tünnermann, “Fiber chirped-pulse amplification system emitting 3.8 GW peak power,” Opt. Exp., vol. 19, pp. 255–260, 2011. [209] F. Röser, T. Eidam, J. Rothhardt, O. Schmidt, D. N. Schimpf, J. Limpert, and A. Tünnermann, “Millijoule pulse energy high repetition rate femtosecond fiber chirped-pulse amplification system,” Opt. Lett., vol. 32, no. 24, pp. 3495–3497, 2007. [210] C. Wirth, T. Schreiber, M. Rekas, I. Tsybin, T. Peschel, R. Eberhardt, and A. Tunnermann, “High-power linear-polarized narrow linewidth photonic crystal fiber amplifier,” Proc. SPIE, vol. 7580, 75801H, 2010. [211] T. Eidam, C. Wirth, C. Jauregui, F. Stutzki, F. Jansen, H. J. Otto, O. Schmidt, T. Schreiber, J. Limpert, and A. Tunnermann, “Experimental observations of the threshold-like onset of mode instabilities in high power fibre amplifiers,” Opt. Exp., vol. 19, pp. 13218–13224, 2011. [212] F. Jansen, F. Stutzki, H.-J. Otto, T. Eidam, A. Liem, C. Jauregui, J. Limpert, and A. Tünnermann, “Thermally induced waveguide changes in active fibers,” Opt. Exp., vol. 20, pp. 3997–4008, 2012. [213] H.-J. Otto, F. Stutzki, F. Jansen, T. Eidam, C. Jauregui, J. Limpert, and A. Tünnermann, “Temporal dynamics of mode instabilities in high power fiber lasers and amplifiers,” Opt. Exp., vol. 20, pp. 15710–15722, 2012. [214] T. Eidam, S. Hädrich, F. Jansen, F. Stutzki, J. Rothhardt, H. Carstens, C. Jauregui, J. Limpert, and A. Tünnermann, “Preferential gain photoniccrystal fiber for mode stabilization at high average powers,” Opt. Exp., vol. 19, pp. 8656–8661, 2011. [215] M. Marko Laurila, M. Jørgensen, K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Distributed mode filtering rod fiber amplifier delivering 292 W with improved mode stability,” Opt. Exp., vol. 20, pp. 5742–5753, 2012. [216] N. Haarlammert, O. de Vries, A. Liem, A. Kliner, T. Peschel, T. Schreiber, R. Eberhardt, and A. Tünnermann, “Build up and decay of mode instability in a high power fiber amplifier,” Opt. Exp., vol. 20, pp. 13274–13283, 2012. [217] M. Karow, H. Tünnermann, J. Neumann, D. Kracht, and P. Weßels, “Beam quality degradation of a single-frequency Yb-doped photonic crystal fiber amplifier with low mode instability threshold power,” Opt. Lett., vol. 37, pp. 4242–4244, 2012. [218] B. G. Ward, C. Robin, and I. Dajani, “Origin of thermal modal instabilities in large mode area fiber amplifiers,” Opt. Exp., vol. 20, pp. 11407– 11422, 2012. [219] D. Engin, W. Lu, H. Verdun, and S. Gupta, “High power modal instability measurements of very large mode area (VLMA) step index fibers,,” Proc. SPIE, vol. 8733, 87330J, 2013. [220] K. Brar, J. Henrie, S. Courtney, M. Savage-Leuchs, R. Afzal, and E. Honea, “Threshold power and fiber-degradation-induced modal instabilities in high-power fiber amplifiers based on large-mode-area fibers,” Proc. SPIE, vol. 8961, 89611R, 2014. [221] A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Exp., vol. 19, pp. 10180–10192, 2011. [222] C. Jauregui, T. Eidam, H.-J. Otto, F. Stutzki, F. Jansen, J. Limpert, and A. Tunnermann, “Physical origin of mode instabilities in high-power fiber laser systems,” Opt. Exp., vol. 20, pp. 12912–12925, 2012. [223] A. V. Smith and J. J. Smith, “Steady-periodic method for modelling mode instability in fiber amplifiers,” Opt. Exp., vol. 21, pp. 2606–2623, 2013. [224] A. V. Smith and J. J. Smith, “Increasing mode instability thresholds of fiber amplifiers by gain saturation,” Opt. Exp., vol. 21, pp. 15168–15182, 2013. [225] K. R. Hansen, T. T. Alkeskjold, J. Broeng, and J. Lægsgaard, “Theoretical analysis of mode instability in high-power fiber amplifiers,” Opt. Exp., vol. 21, pp. 1944–1971, 2013. [226] L. Dong, “Stimulated thermal Rayleigh scattering in optical fibers,” Opt. Exp., vol. 21, pp. 2642–2656, 2013. [227] I.-N. Hu, C. Zhu, C. Zhang, A. Thomas, and A. Galvanauskas, “Analytical time-dependent theory of thermally-induced modal instabilities in high power fiber amplifiers,” Proc. SPIE, vol. 8601, 860109, 2013.


[228] S. Naderi, I. Dajani, T. Madden, and C. Robin, “Investigations of modal instabilities in fiber amplifiers through detailed numerical simulations,” Opt. Exp., vol. 21, pp. 16111–16129, 2013. [229] B. G. Ward, “Modeling of transient modal instability in fiber amplifiers,” Opt. Exp., vol. 21, pp. 12053–12067, 2013. [230] L. Huang, W. Wang, J. Leng, S. Guo, X. Xu, and X. Cheng, “Experimental investigation on evolution of the beam quality in a 2-kW high power amplifier,” IEEE Photon. Tech. Lett., vol. 26, no. 1, pp. 33–36, Jan. 2014. [231] H. Zellmer, U. Willamowski, A. Tunnermann, H. Welling, S. Unger, V. Reichel, H.-R. Muller, T. Kirchhof, and P. Albers, “High-power cw neodymium-doped fiber laser operating at 9.2 W with high beam quality,” Opt. Lett., vol. 20, pp. 578–80, 1995. [232] D. B. S. Soh, S. Yoo, J. Nilsson, J. K. Sahu, K. Oh, S. Baek, Y. Jeong, C. Codemard, P. Dupriez, J. Kim, and V. Philippov, “Neodymium-doped cladding-pumped aluminosilicate fiber laser tunable in the 0.9 μm wavelength range,” IEEE J. Quantum Electron., vol. 40, no. 9, pp. 1275–1282, Sep. 2004. [233] J. K. Sahu, Y. Jeong, D. J. Richardson, and J. Nilsson, “A 103 W erbium– ytterbium co-doped large-core fiber laser,” Opt. Commun., vol. 227, pp. 159–163, 2003. [234] Y. Jeong, S. Yoo, C. A. Codemard, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, P. W. Turner, L. Hickey, A. Harker, M. Lovelady, and A. Piper, “Erbium:Ytterbium codoped large-core fiber laser with 297-W continuous-wave output power,” J. Sel. Topics Qantum Electron., vol. 13, pp. 573–579, 2007. [235] S. D. Jackson, “Towards high-power mid-infrared emission from a fibre laser,” Nature Photon., vol. 6, pp. 423–431, 2012. [236] P. F. Moulton, G. A. Rines, E. V. Slobodtchikov, K. F. Wall, G. Frith, B. Samson, and A. L. G. Carter, “Tm-doped fiber lasers: Fundamentals and power scaling,” J. Sel. Topics Quantum Electron., vol. 15, pp. 85–92, 2009. [237] A. Hemming, N. Simakov, J. Haub, and A. Carter, “Power scaling of resonantly pumped holmium-doped fibre lasers,” in Proc. 23rd Annu. Solid State Diode Laser Technol. Rev., Jun. 2013, pp. 24–27. [238] G. Genty, S. Coen, and J. M. Dudley, “Fiber supercontinuum sources (Invited),” J. Opt. Soc. Amer. B, vol. 24, pp. 1771–1785, 2007. [239] J. T. Kringlebotn, J. L. Archambault, L. Reekie, and D. N. Payne, “Er3+:Yb3+-codoped fiber distributed-feedback laser,” Opt. Lett., vol. 19, pp. 2101–2103, 1994. [240] M. Sejka, P. Varming, J. Hubner, and M. Kristensen, “Distributed feedback Er3+-doped fibre laser,” Electron. Lett., vol. 31, pp. 1445–1446, 1995. [241] K. Yelen, M. N. Zervas, and L. M. B. Hickey, “Fiber DFB lasers with ultimate efficiency,” J. Lightw. Technol., vol. 23, no. 1, pp. 32–43, Jan. 2005. [242] M. N. Zervas, “Twisted hi-bi fiber distributed-feedback lasers with controllable output state of polarization,” Opt. Lett., vol. 38, pp. 1533–1535, 2013. [243] O. Hadeler, M. Ibsen, and M. N. Zervas, “Distributed-feedback fiber laser sensor for simultaneous strain and temperature measurements operating in the radio-frequency domain,” Appl. Opt., vol. 40, pp. 3169–3175, 2001. [244] M. N. Zervas, “Fiber DFB lasers,” in Optical Fiber Telecommunications VIA, I. P. Kaminow, T. Li, and A. E. Willner, Eds. New York: Academic, 2013. [245] D. F. Browning and G. V. Erbert, “Distributed feedback fiber laser: The heart of the national ignition facility,” National Technical Information Science, Alexandria, VA, USA, Tech. Rep. CRL-ID-155446, 2003. [246] F. Abt, A. Hess, and F. Dausinger, “Temporal behaviour of the focal shift of beam forming optics for high power single mode lasers,” presented at the 27th Int. Congr. Appl. Lasers Electro-Opt., CA, USA, 2008, pp. 561–568, Paper #1302. [247] H. Zimer, R. Niedrig, and B. Wedel, “Beam delivery systems and processing heads for 1 μm high brightness laser cutting systems,” Proc. SPIE, vol. 8239, 82390V, 2012. [248] C. Thiel, R. Weber, J. Johannsen, and T. Graf, “Stabilization of a laser welding process against focal shift effects using beam manipulation,” Phys. Procedia, vol. 41, pp. 209–215, 2013. [249] P. Zhou, X. Wang, Y. Ma, H. Lu, and Z. Liu, “Review of recent progress on mid-infrared fiber lasers,” Laser Phys., vol. 22, pp. 1744–1751, 2012. [250] C. Wirth, O. Schmidt, I. Tsybin, T. Schreiber, R. Eberhardt, J. Limpert, A Tünnermann, K. Ludewigt, M. Gowin, E. ten Have, and M. Jung, “High average power spectral beam combining of four fiber amplifiers to 8.2 kW,” Opt. Lett., vol. 36, no. 16, pp. 3118–3120, 2011.

0904123

[251] J. Bourderionnet, C. Bellanger, J. Primot, and A. Brignon, “Collective coherent phase combining of 64 fibers,” Opt. Exp., vol. 19, no. 18, pp. 17053–17058, 2011. [252] X. Wang, J. Leng, P. Zhou, Y. Ma, X. Xu, and Z. Liu, “1.8-kW simultaneous spectral and coherent combining of three-tone nine channel all-fiber amplifier array,” Appl. Phys. B, vol. 107, pp. 785–790, 2012. [253] L. J. Kong, L. M. Zhao, S. Lefrancois, D. G. Ouzounov, C. X. Yang, and F. W. Wise, “Generation of megawatt peak power picosecond pulses from a divided-pulse fiber amplifier,” Opt. Lett., vol. 37, pp. 253–255, 2012. [254] M. Kienel, A. Klenke, T. Eidam, M. Baumgartl, C. Jauregui, J. Limpert, and A. Tunnermann, “Analysis of passively combined divided-pulse amplification as an energy-scaling concept,” Opt. Exp., vol. 21, pp. 29031– 29042, 2013. [255] A. Klenke, M. Kienel, T. Eidam, S. Hadrich, J. Limpert, and A. Tunnermann, “Divided-pulse nonlinear compression,” Opt. Lett., vol. 38, pp. 4593–4595, 2013. [256] S. Breitkopf, T. Eidam, L. von Grafenstein, A. Klenke, H. Carstens, S. Holzberger, I. Pupeza, E. E. Fill, T. Schreiber, J. Limpert, F. Krausz, and A. Tunnermann, “Non-steady-state enhancement cavities using pulse-dumping as power scaling concept of femtosecond lasers,” presented at the Adv. Solid State Lasers, Paris, France, 2013, Paper AW2A.3. [257] G. Mourou, B. Brocklesby, T. Tajima, and J. Limpert, “The future is fibre accelerators,” Nature Photon., vol. 7, pp. 258–261, 2013. [258] G.P. Agrawal, Nonlinear Fiber Optics, 3rd ed. New York: Academic, 2001. [259] G. Brooker, Modern Classical Optics. New York, NY, USA: Oxford Univ. Press, 2003.

Michalis N. Zervas received the graduate degree from the University of Thessaloniki, Greece, in 1984, the M.Sc. degree in applied and modern optics (with distinction), and the Ph.D. degree in fiber optics from the University of Reading, Reading, Berkshire, U.K., in 1985 and the University College London in 1989, respectively. He joined the Optoelectronics Research Centre, University of Southampton, in 1991 as a Research Fellow and was promoted to a Research Lecturer in 1995 and a Professor in 1999. His research interests include advanced optical fiber amplifier configurations, high-power fiber lasers, fiber DFB lasers, Bragg grating theory and devices, surface-plasmon effects and devices, optical microresonators, and nonlinear fiber optics. He is a co-founder of Southampton Photonics, Inc., a University of Southampton spin-off manufacturing high-power fiber lasers, where he is currently serving as a Chief Scientist. He has published more than 300 papers in scientific journals and conference proceedings and holds 20 patents.

Christophe A. Codemard received the graduate de´ gree from Ecole Nationale Supérieure Des Sciences Appliquées et de Technologie, Lannion, France, in optoelectronics in 1999 and the Ph.D. degree from the Optoelectronics Research Centre, Southampton University, U.K., in 2002 that he completed in 2007. He worked for Point Source Ltd. and Southampton Photonics Ltd. as a Development Engineer in 1999 and 2000, respectively. After a year as a Senior Development Engineer at SPI Laser working on high power laser from January 2006 to April 2007, he joined the ORC as a Research Fellow in the High Power Fiber Laser group until January 2010. Subsequently, he joined Fianium Ltd. as an Engineering Manager and then as the Head of Laser Development. He then joined SPI Laser Ltd., where he currently leads the Advanced Laser Laboratory. His main research interests include high power rare-earth doped fiber lasers and amplifiers, pulsed fiber lasers, nonlinear effects and numerical simulations. He has published more than 100 papers in scientific journals and conference proceedings.