Mid-Infrared Fiber Lasers

Mid-Infrared Fiber Lasers Markus Pollnau1 and Stuart D. Jackson2 1

2

Advanced Photonics Laboratory, Institute for Biomedical Imaging, Optics and Engineering, Swiss Federal Institute of Technology 1015 Lausanne, Switzerland [email protected] Optical Fibre Technology Centre, Australian Photonics CRC. The University of Sydney 206 National Innovation Centre, Australian Technology Park Eveleigh NSW 1430, Australia [email protected]

Abstract. The current state of the art in mid-infrared fiber lasers is reviewed in this chapter. The relevant fiber-host materials such as silicates, fluorides, chalcogenides, and ceramics, the fiber, pump, and resonator geometries, and the spectroscopic properties of rare-earth ions are introduced. Lasers at transitions ranging from 1.9 to 4 µm occurring in the rare-earth ions Tm3+ , Ho3+ , and Er3+ and their population mechanisms are discussed on the basis of the fundamental spectroscopic properties of these ions. Continuous-wave, fundamental-mode power levels ranging from a few mW near 4 µm up to ≈ 10 W near 2 µm have been demonstrated in recent years. Power-scaling methods and their limitations, the possibilities to optimize the population mechanisms and increase the efficiencies of these lasers, as well as the prospects of future mid-infrared fiber lasers in a number of rare-earth ions at transitions in the wavelength range beyond 3 µm and extending to 5 µm are described.

1

Introduction

Since the introduction of the double-clad fiber more than a decade ago and with the recent technological advances in the fields of fiber fabrication and beam-shaped high-power diode lasers, the performance of diode-pumped fiber lasers has steadily improved. Today, fiber lasers can compete with their corresponding bulk crystalline systems in certain applications, especially when transverse-fundamental-mode, continuous-wave (CW) laser operation at output powers in the milliwatt to multiwatt range is required. The increased recent interest in fiber lasers emitting at mid-infrared wavelengths between 2 and 3 µm primarily relates to the high potential of these wavelengths for applications in laser microsurgery. Due to the high absorption of water in the spectral region at 2.7–3.0 µm, high-quality laser cutting or ablation has been demonstrated in biological tissues. In addition, laser wavelengths near 2 µm could be suitable for tissue welding. A number of other potential laser applications in the mid-infrared spectral region, e.g. environmental trace-gas I. T. Sorokina, K. L. Vodopyanov (Eds.): Solid-State Mid-Infrared Laser Sources, Topics Appl. Phys. 89, 219–255 (2003) c Springer-Verlag Berlin Heidelberg 2003

www.cadfamily.com EMail:[email protected] The document is for study only,if tort to your rights,please inform us,we will delete

220

Markus Pollnau and Stuart D. Jackson

detection, are currently becoming increasingly important. In all these applications fiber lasers may find their niches. The high development costs of fabricating fibers with sufficiently low losses in the mid-infrared spectral region has impeded the necessary research efforts in the field of mid-infrared fiber lasers. The currently available fiber materials that are suitable as host materials for specific rare-earth-doped fiber lasers in the spectral region 2–5 µm will be introduced in Sect. 2. More than any other idea, the invention of the double-clad fiber geometry has accelerated the output-power scaling and hence the success of fiber lasers. The various aspects of the fiber, pump, and resonator geometries will be described in Sect. 3. A significant number of spectroscopic investigations has led to a better understanding of the population mechanisms of rare-earth-doped laser systems. The fundamental spectroscopic properties of rare-earth ions in solid-state host materials will be reviewed in Sect. 4. Equipped with this general information, the performance of the most important mid-infrared fiber laser transitions in the wavelength range 2–3 µm can be understood in detail. Sect. 5 will be devoted to the Tm3+ fiber lasers at 1.9 and 2.3 µm, whereas the Ho3+ fiber lasers at 2.1 and 2.9 µm will be discussed in Sect. 6. An impressive example of the variety of population mechanisms and operational regimes in a single system is the Er3+ 2.7 µm fiber laser transition that will be investigated in Sect. 7. At wavelengths beyond 3 µm, it becomes increasingly difficult to find suitable host materials for actively doped laser systems. This statement holds true for glass fibers in the same way as for crystalline materials. The prospects of future midinfrared fiber lasers in this wavelength range will be discussed in Sect. 8. Besides general introductions to the different topics of lasers [1,2] that include many aspects relevant also to mid-infrared fiber lasers, a comprehensive introduction to the field of rare-earth-doped fiber lasers can be found in [3].

2

Fiber Materials

The choice of the fiber material involves a number of considerations: the maximum phonon energy, the environmental durability, the draw ability, the rare-earth solubility, and the purity of the starting materials. The maximum phonon energy of the glass sets the overall infrared transparency range of the fiber and the multiphonon relaxation rates which influence the quantum efficiency. The multiphonon relaxation rates for the common fiber glasses as a function of the energy gap between energy levels are shown in Fig. 1. The optical transparency range relates to both the size of the band gap and also the infrared absorption cut-off, hence to the vibrational frequency ν of the anion–cation bonds of the glass. For an ordered structure, (1) ν = (1/2π) k/M ,


-1

Multiphonon Relaxation Rate (s )

Mid-Infrared Fiber Lasers 10

12

10

11

10

10

221

-1

Borate (1400 cm ) -1

Phosphate (1200 cm )

9

10

8

10

-1

Silicate (1100 cm )

7

10

-1

Germanate (900 cm )

6

10

-1

Tellurite (700 cm )

5

10

4

-1

10

ZBLA (500 cm )

3

10

2

10

1

10

-1

GLS (350 cm )

2000

3000

4000

5000

6000

7000

-1

Energy Gap (cm )

Fig. 1. Calculated and measured multiphonon relaxation rates as a function of the energy gap between energy levels for glasses with different maximum phonon energies. (Data taken from [4,5])

where M = m1 m2 /(m1 + m2 ) is the reduced mass for two bodies m1 , m2 vibrating with an elastic restoring force k. While for disordered structures like glass, this is not an accurate expression, nevertheless, it does highlight the important contributions to the glass transparency. The relative cation– anion bond strength is intimated by the field strength Z/r2 , where Z is the valence state of the cation or anion and r is the ionic radius. Generally, glasses composed of large anions and cations with low field strengths display high transparency in the mid-infrared spectral region. The important physical properties of the popular glasses used for optical fibers are shown in Table 1. Table 1. Properties of popular fiber materials Fiber material

Max. phonon energy (cm−1 )

Silica ZBLAN GLS

1100 [4] 550 [7] 425 [5]

2.1

Infrared Propagation losses transparency (λ at minimum) ( µm) (dB/km) < 2.5 < 6.0 < 8.0

0.2 (1.55 µm) 0.05 (2.55 µm) 0.5 (3.50 µm)

Thermal conductivity (W/K m) 1.38 [6] 0.7–0.8 [8] 0.43–0.5 [9]

Silicates

This glass is perhaps the most important material used for optical fiber production [3,10], however, the maximum phonon energy is high (≈ 1100 cm−1 ) and has so far limited the emission wavelength of mid-infrared fiber lasers using this material to ≈ 2.2 µm [11]. Silica is robust and involves the very effec-


222


tive modified chemical vapor deposition (MCVD) technique for fiber fabrication. Reducing the OH− content in the glass, which has two main absorption peaks in the range 1.3–2.0 µm [12], improves the near-to-mid-infrared utility. Rare-earth ions such as Nd3+ and Er3+ which have high field strengths have low solubility in silicate glass which can lead to clustering and micro-scale phase separation. 2.2

Fluorides

The use of fluoride glasses, especially the heavy-metal fluorides [13,14], as host materials for mid-infrared fiber lasers has found wide acceptance. The most common form of heavy-metal fluoride glass is the fluorozirconate (ZrF4 ) composition and the most widespread fluoride fiber material is ZBLAN [15], a mixture of 53 mol.% ZrF4 , 20 mol.% BaF2 , 4 mol.% LaF3 , 3 mol.% AlF3 , and 20 mol.% NaF. Since it can be readily drawn into single-mode optical fiber [16] it is particularly important to mid-infrared fiber lasers [17]. The large atomic weight of the zirconium atom combined with relatively weak bonding provides a maximum phonon energy for ZBLAN of ≈ 550 cm−1 and allows for high infrared transparency up to ≈ 6 µm. Multiphonon relaxation, however, becomes significant for transitions at wavelengths longer than ≈ 3 µm. Compared to silica, ZBLAN has a lower damage threshold and a lower level of inhomogeneous spectral-line broadening (Sect. 4.1) because the rareearth ion is placed in sites of a less perturbed network. The crystal-field strength is also comparatively weaker [18]. An overview of the spectroscopic properties of rare-earth ions doped into ZBLAN has been given in [7]. 2.3

Chalcogenides

Chalcogenides are composed of the chalcogen elements S, Se and Te [19,20,21]. They are environmentally durable, have a low toxicity and have reasonably large glass forming regions. When the rare-earth ions are doped into these glasses [22], the radiative transition probabilities and, therefore, the absorption and emission cross-sections are high as a result of the high refractive index (≈ 2.6) of the glass and the high degree of covalency of the rare-earth ion with the surrounding medium. Maximum phonon energies of 300–450 cm−1 produce low rates of multiphonon relaxation, see Fig. 1, and therefore high quantum efficiencies. The low thermal conductivity, see Table 1, is however an important factor to be considered in the design of chalcogenide-based lasers. Of the large number of rare-earth chalcogenides studied for luminescent emission, the most important glasses are the sulfide glasses GaLaS (GLS) [23] and GeGaS [24] because of the reasonably high rare-earth solubility. 2.4

Ceramics

Studies into the use of ceramics as host materials for the rare earths have recently made a lot of progress [25]. These ceramics are composed of nano-


Mid-Infrared Fiber Lasers

223

crystallites of materials such as Y3 Al5 O12 (YAG) and can be produced in a simple and cost-efficient process at relatively low temperatures. This allows the fabrication of materials with very high melting points [26] that are difficult to grow by other techniques such as the Czochralski method [27]. This class of materials is also available in fiber geometry [28]. Ceramic fibers combine the characteristics of crystalline materials such as high absorption and emission cross-sections, large thermal conductivity, and even the possibility of doping with transition-metal ions [28] with the convenience of guiding the pump and signal light in a fiber. Currently, the losses of these fibers are comparatively high, but further improvement can be expected.

3

Fiber, Pump, and Resonator Geometries

The light oscillating in a fiber-laser resonator can be either free running or deliberately modulated depending on whether CW or pulsed output, respectively, is desired. Consequently, a large number of techniques for pulsed operation including Q-switching and mode locking of fiber lasers have been explored. These techniques have been investigated intensively for the common laser transitions at 1 µm in Nd3+ and Yb3+ and at 1.5 µm in Er3+ , and are usually described in combination with these lasers. The small fiber size limits the peak power through the damage-threshold intensity (propagating power per core area) and, hence, crystalline lasers in bulk geometries or optical parametric processes are often preferred when high-energy short pulses are needed. This argument accounts especially for mid-infrared ZBLAN-based fiber lasers, because these fibers possess a lower damage threshold compared to silica fibers. The description of mid-infrared fiber lasers is, therefore, confined to CW operation and specific techniques for pulsed operation of fiber lasers are not discussed in this chapter. In an analogous way to the optical excitation of bulk gain media, doped optical fibers can be either end pumped (core pumped) or side pumped (cladding pumped). The former method is less scalable since it relies on the use of expensive high-beam-quality pump sources because core areas are usually < 100 µm2 . On the other hand, the larger cladding area (> 104 µm2 ) allows for high-power diode-array pumping [29,30,31,32,33]. The obvious simplicity of the core-pumping method negates further explanation and we will concentrate on the cladding-pumping technique: one of the most important developments in fiber-laser technology. 3.1

Fiber Designs for Cladding Pumping

In the design of fibers for cladding pumping, the core of the fiber is generally made to guide a single-transverse LP01 mode. The shape of the multimode pump cladding, see Fig. 2, however, remains somewhat flexible and can be shaped with a number of considerations in mind. The pump cladding,


224

Markus Pollnau and Stuart D. Jackson Jacket

Outer cladding

(a)

(b)

Pump cladding

(c)

Core

(d)

Fig. 2. Principal double-clad fiber geometries which include (a) circular shaped pump cladding with axially positioned core, (b) circular shaped pump cladding with off-axially positioned core, (c) rectangular shaped pump cladding and (d) D-shaped pump cladding

which in turn is surrounded by a low-refractive-index transparent polymer or glass, provides a high numerical aperture (NA) of 0.3–0.55 for the pump cladding. There are three main double-clad-fiber layouts: circular, circular with offset core, and rectangular as shown schematically in Fig. 2. Maximum pump-light absorption sees the core near the outer edge of the circular pump cladding [34] because a portion of the launched light is skew to the fiber axis and produces an inner caustic and never crosses the central region of the pump cladding. Scrambling these skew rays by bending [35] or by using a graded and slightly elliptical pump cladding [36] increases the pumpabsorption efficiency as does spatially varying refractive-index fluctuations in inhomogeneous pump claddings [37]. Inner caustics can be avoided by rectilinearly shaping the pump cladding [38] which has the ancillary advantage of matching the shape of diode-array output. The overall absorption coefficient of the fiber is reduced by the ratio of the core area to the area of the pump cladding [34]. The propagation losses for the rectangular-shaped pump cladding are higher and the effective numerical aperture lower as compared to the circular shape [39]; however, in certain cases higher dopant concentrations can provide shorter fiber lengths that also lead to reduced nonlinear effects. A D-shaped or truncated circular pump cladding [40], see Fig. 2d, is also effective while being easier to make than rectangular preforms. The circular-multimode pump cladding may also have the gain medium distributed in a ring around the edge of the pump cladding either discretely or continuously in multi-core [41] and M-profile [42] arrangements, respectively. The effective absorption coefficient is now further increased while maintaining high-beam-quality output. A large-mode-area core [43] can also increase the effective absorption coefficient of the fiber. Recently, double-clad pump schemes have been demonstrated also with holey fibers [44]. These structures offer the additional advantage of singlemode guiding over a broad spectral range [45].



3.2

225

Fiber-Laser Resonators

Typical free-running fiber-laser resonators are shown schematically in Fig. 3. In the simplest resonator, see Fig. 3a, the pump light passes through a dichroic mirror that is highly reflective for the oscillating laser light. Fresnel reflection at the cleaved output end facet of the fiber can provide sufficient feedback for laser oscillation; however, with an output-coupler mirror – and pump retroreflector – placed at the output end of the fiber the optical efficiency can be maximized. In an alternative arrangement, the pump light can be launched into the output end of the fiber, see Fig. 3b. A dichroic mirror oriented at 45◦ to the fiber axis extracts the laser output and a broadband highly reflecting mirror is placed at the rear fiber end. To scale the output power, each end of the fiber can be pumped, see Fig. 3c. Periodic V-grooves [46] or prism coupling [47] along the fiber to distribute the pump access allow one to further scale the output power and are useful for pumping fiber ring resonators. Spectrally combining the output from a number of separate fiber lasers is also a promising power-scaling technique [48,49,50]. The highest reported fiberlaser output powers of 110 W in a singly Yb3+ -doped fiber [51] and 150 W in a Nd3+ ,Yb3+ -codoped fiber [52] have been obtained using arrangements as shown schematically in Fig. 3c. Bragg gratings can substitute the fiber-butted mirror if spectrally well-defined output is required. (a)

Output

Pump Fiber M (b)

Pump

M Fiber M Output

(c)

M Pump

Pump Fiber M Output

Fig. 3. Schematic diagram of resonators used for free-running fiber lasers with (a) a single-end co-propagating pump, (b) a single-end counter-propagating pump and (c) dual end pumps. M represents the mirror


226

3.3


Thermal Issues

As higher pump powers become available from laser-diode systems, it is generally recognized that thermal and thermo-optical issues set limitations to the power scalability of end-pumped bulk-laser systems. Owing to the unfavorable temperature dependence of thermal and thermo-optical parameters [53], the large heat load in the crystal leads, firstly, to a significant temperature increase in the rod, secondly, to strong thermal lensing with pronounced spherical aberrations, and ultimately, to rod fracture in a high-average-power end-pumped system. Due to its geometry, the fiber provides potentially high pump- and signalbeam intensities without the drawbacks of significant thermal and thermooptical effects. Its large surface-area-to-volume ratio means that the heat generated from multiphonon relaxation in the core is dissipated effectively by radiation and convection from the outer surface of the fiber. This is especially true for single-clad, core-pumped single-mode fibers where this ratio is highest [54]. Double-clad fibers have a relatively smaller surface-area-tovolume ratio and thermal issues need to be taken into account [6,55,56]. Thermal management will be required when very high output powers are desired. In particular, for high-power mid-infrared operation, thermal management may be very important because of the decreased quantum efficiency and the consequently higher amount of heat dissipation.

4 Spectroscopic and Laser Properties of Rare-Earth Ions The structure of a glass is less well defined as compared to a crystalline material. The local variation of the chemical environment of active ions in a glass has a number of consequences. Most important, the active ions may undergo chemical reactions during the fabrication process and be incorporated in the host in several oxidation states with different spectroscopic properties. Oxidation states other than the desired one may act as impurities that introduce undesired optical effects such as parasitic pump absorption, the reabsorption of oscillating laser light, the lifetime quenching of the laser ion, and the trapping of the excitation energy. A stable oxidation state of the optically active ion is thus highly desirable. The necessity of a stable oxidation state excludes a number of transition-metal ions from the list of suitable dopants in glass environments. This is one of the possible reasons why examples of transitionmetal-ion-doped lasers in glass hosts are rare. On the other hand, most of the rare-earth ions prefer to stabilize in the trivalent oxidation state and are, therefore, suitable candidates as glass and fiber dopants. This chapter will, therefore, concentrate on the rare-earth ions as active dopants of fiber lasers.



4.1

227

Spectra of Rare-Earth Ions in Glasses

The optical transitions of lanthanide (rare-earth) ions in the visible and infrared spectral region occur within the 4f subshell. This subshell is shielded by the outer 5s and 5p subshells and the influence of the host material is relatively small compared to, e.g., the 3d transitions in transition-metal ions. The electronic structure of trivalent rare-earth ions derives from the perturbation of the 4f energy level in the central-field approximation by the noncentrosymmetric electron–electron interaction, the spin–orbit interaction, and the crystal-field splitting (Stark effect); see the example of the energy-level scheme of Er3+ in Fig. 4. The spin–orbit multiplets are commonly denoted by their 2S+1 LJ terms in Russell–Saunders coupling, although the 4f electrons of lanthanide ions exhibit intermediate coupling and the total angular momenta J of the spin–orbit multiplets are linear combinations of the total orbital angular momenta L and total spins S. Single crystal-field (Stark) transitions between two spin–orbit multiplets cannot be distinguished in glasses at ambient temperature, because inhomogeneous spectral-line broadening occurs due to the local variation of the ligand electric field. Also homogeneous (lifetime) broadening mechanisms are relevant in a number of glasses. This spectral-line broadening makes glasses the preferred hosts when broadband,

4 11

4f Er3+

2 4 4

H S

F

4

I

4

F3/2 4

F7/2 F5/2 2 H11/2 4

S3/2

4

F9/2

4

I9/2

4

I11/2

4

I13/2

CentralNonSpinField Centrosym. Orbit Approx. Splitting Splitting 4

I15/2

CrystalField Splitting

Fig. 4. Energy-level scheme of trivalent erbium indicating the splitting of the 4f 11 configuration in the centralfield approximation by the noncentrosymmetric electron–electron interaction, the spin–orbit interaction, and the Stark splitting by the local electric field of the host material (indicated only for selected spin–orbit multiplets)


228


continuous tunability of lasers is desired. On the other hand, the spectralline broadening leads to lower absorption and emission cross-sections for the same transition in glasses compared to single-crystalline hosts. The reduced cross-sections lead to generally higher pump threshold of laser transitions in glasses, a fact that is compensated in fiber geometry because a high pump confinement is achieved over the whole fiber length. 4.2

Intraionic Processes

Generally, the probability of an allowed electric-dipole transition is seven orders of magnitude larger than that of an allowed magnetic-dipole transition. Since electric-dipole transitions within the 4f subshell are parity forbidden, the intensities of radiative transitions in rare-earth ions are weak and the radiative lifetimes of the emitting states are long, typically in the ms range. Mixing of the 4f states with higher-lying (typically 5d) electronic states of opposite parity at ion sites without inversion symmetry, however, means that electric-dipole transitions become partially allowed and are usually the dominant transitions between 4f electronic states. The oscillator strengths f and integrated absorption and emission cross-sections σ of these spin–orbit multiplet-to-multiplet transitions can be calculated with the help of the semiempirical Judd–Ofelt theory [57,58]. If the degree of inhomogeneous spectralline broadening is relatively small and the absorption and emission spectra remain structured, as is the case for ZBLAN, the cross-sections σ(λ) at individual wavelengths that are relevant to pump absorption and stimulated emission of narrow laser lines must be determined experimentally. Besides ground-state absorption (GSA), excited-state absorption (ESA) of pump photons, see Fig. 5a, can play a significant role in fiber lasers, specifically in the case of high-intensity core pumping. An experimental example will be given later in Sect. 7.1. Since the absorption increases exponentially with the absorption coefficient α(λP ) = N σ(λP ), ESA becomes relevant for the population dynamics of a laser when (a) the ESA and GSA cross-sections σ(λP ) are comparable at the pump wavelength λP and (b) the population density N of the excited state in which the second pump-absorption step originates becomes a significant fraction of the density of ions in the ground state, i.e., a large degree of ground-state bleaching must be present for ESA to play a significant role. A radiative transition from an excited state i to a lower-lying state j is characterized by the radiative rate constant Aij . If the decay occurs to several lower-lying states, the overall radiative rate constant Ai is the sum of all individual rate constants. The branching ratio of each radiative transition is defined as βij = Aij /Ai . Radiative decay of excited states is in competition with nonradiative decay by interaction with vibrations of the host material, called multiphonon relaxation. The rate constant of a multiphonon relaxation process decreases exponentially with the energy gap to the next lower-lying state and with the order of the process, i.e., the number of phonons required



(a)

229

(b) 2

2

Pump (ESA) 1

1 Pump (GSA)

Pump

0

0 Ion

Donor Ion

Acceptor Ion

(c)

(d)

2

2 Laser

1

Acceptor Ion

Laser

1 Pump

Pump

0

0 Sensitizing Ion A

Laser Ion B

Laser Ion A

(e)

(f)

2

2

1

1 Pump

Pump

0

Quenching Ion B

Pump

0 Donor Ion

Acceptor Ion

Donor Ion

Acceptor Ion

Fig. 5. Intra- and interionic processes in fiber lasers: (a) excited-state absorption (ESA); (b) energy migration; (c) sensitization and (d) quenching of a laser ion by an ion of a different type; (e) cross-relaxation and (f ) energy-transfer upconversion


230


to bridge the energy gap [59,60]. This fact is illustrated in Fig. 1 for different glasses. The rate constant of multiphonon relaxation increases with host temperature. The measurable luminescence lifetime τi of an excited state i is the inverse of the sum of the overall radiative rate constant Ai and the rate constant of multiphonon relaxation, Wi . The radiative quantum efficiency is defined as η = Ai /(Ai + Wi ). The influence of multiphonon relaxations is stronger in oxides as compared to fluorides because of the smaller atomic mass m2 of the anion and the larger elastic restoring force k, see (1), due to stronger covalent bonds in oxides [3], both resulting in larger maximum phonon energies in oxides. A brief example: The luminescence lifetime of the 4 I11/2 upper laser level of the erbium 3 µm laser (Sect. 7) is partly quenched by multiphonon relaxation. Typically, nonradiative decay becomes dominant if five or less phonons are required to bridge the energy gap. With an energy gap between the 4 I11/2 and the next lower lying 4 I13/2 levels of ≈ 3400–3500 cm−1 , radiative decay prevails for phonon energies below ≈ 600 cm−1 , roughly the maximum phonon energy of ZBLAN, see Table 1. Fluorides are, therefore, preferred over oxides as host materials for most of the mid-infrared laser transitions. Like absorption, the strength of a stimulated-emission process is characterized by the emission cross-section σ(λL ) of the laser transition. From a simple analysis, for one resonator round-trip of oscillating laser photons, the product τ σ(λL ) with τ the luminescence lifetime of the upper laser level, is identified as a “figure of merit” for a possible laser transition. The larger this product, the lower is the expected pump threshold of the laser transition. This “figure of merit”, however, does not take into account the numerous parasitic effects that can occur in the population dynamics of a laser system, such as pump ESA, reabsorption of laser photons, and energy-transfer processes. It is often these parasitic processes that lead to surprising performance characteristics – as likely in the negative as in the positive sense – and make the interpretation of rare-earth-doped solid-state lasers challenging. Examples will be discussed in Sects. 5–7. 4.3

Interionic Processes

In addition to intraionic excitation and decay mechanisms, radiative energy transfer due to reabsorption of emitted photons by other active ions in the sample and nonradiative energy-transfer processes due to multipole– multipole or exchange interactions between neighboring active ions can occur. Radiative energy transfer leads to an increase in the luminescence lifetime. Among the nonradiative energy-transfer processes, most common is the electric dipole–dipole interaction, which can occur as a direct [61] or phononassisted [62] energy transfer. A direct energy transfer requires spectral resonance between the involved emission and absorption transitions whereas an indirect transfer can also be nonresonant, i.e., an existing energy gap between the emission and absorption transitions involved in the transfer is bridged by



231

one or several phonons. A process that leads to phonon emission has typically a higher probability than a process requiring phonon absorption. Since the electrostatic field of an electric dipole decreases with distance r as r−3 , the probability of an energy transfer between two such dipoles exhibits a strong distance sensitivity of r−6 . Therefore, nonradiative energy transfer occurs predominantly between neighboring active ions. An obvious possibility of an energy-transfer process is shown in Fig. 5b. An excited ion transfers its excitation to a nearby ion of the same type. If this process occurs consecutively between a number of similar ions and the energy is thus transferred over a larger distance, it is called energy migration. Quenching of the luminescence lifetime of an excited state by energy transfer to impurities is often accelerated by energy migration among the excited donor ions [63]. Figure 5 displays further energy-transfer processes that typically occur in rare-earth-doped solid-state lasers. Rare-earth ions of a different type can be deliberately co-doped into the host material in order to influence the laser properties of the lasing ions. Efficient excitation by means of absorption and energy transfer of pump light from sensitizing ions to the upper laser level of the lasing ions, see Fig. 5c, can be exploited when the lasing ions do not sufficiently absorb the pump light at the desired pump wavelength or the dopant concentration of the lasing ions is limited because, e.g., the laser transition terminates in the ground-state multiplet. Similarly, the transfer of excitation from the lower laser level of the lasing ions to nearby quenching ions, see Fig. 5d, is desirable when the lifetime of the lower laser level is extremely long. The low relaxation rate from the lower laser level would otherwise lead to accumulation of excitation in this level, which can result in self-terminating laser behavior and/or bleaching of the ground-state population density and, consequently, decreased GSA. Energy-transfer processes that have both ions in excited states before or after the energy transfer are shown in Fig. 5e,f. In the former case, an excited ion transfers part of its excitation to a nearby ion in its ground state. This process is called cross-relaxation. Its rate increases with the average number of non-excited neighboring ions, i.e., with dopant concentration. Therefore, cross-relaxation leads to concentration quenching of the measured luminescent decay time of the initial excited state involved in the transfer process. In the inverse process – called energy-transfer upconversion (ETU) – excitation is transferred from one to another excited ion, see Fig. 5f. After the absorption of two low-energy pump photons, ETU leads to a single excitation of higher energy and a single high-energy photon may be emitted from the second excited state. In the presence of fast energy migration among the active ions, the excitation is spatially diffused and all these energy-transfer processes can be described by rate-equation analysis using a rate term W Nd Na that comprises a macroscopic energy transfer probability W and the population densities Nd


232


and Na of the initial states of the donor and acceptor ions, respectively [64]. This model, however, is usually not applicable at low dopant concentrations where energy migration is weak. In addition, a number of authors reported on active-ion clusters in fiber materials, see, e.g., [65,66,67,68]. This or any other non-uniform distribution of active ions complicates the analysis of the influence of energy-transfer processes on the performance of rare-earth-doped fiber lasers, as ions within such clusters are more susceptible to interionic processes than isolated ions. In the simplest approach, this distinction defines two different classes of ions that exhibit different population dynamics [69]. 4.4

Overview of Mid-Infrared Fiber Lasers

The relevant parameters of the fiber lasers with the highest output powers reported as of the end of 2001 for each mid-infrared transition are summarized in Table 2. As can be seen, most of the realized mid-infrared fiber lasers used ZBLAN as the host material, because silica glasses, on the one hand, have maximum phonon energies that are too high and hence a transparency that is too low in the wavelength region beyond ≈ 2.2 µm and chalcogenide glasses, on the other hand, are only at the beginning of their career as fiber-laser host materials. The transitions included in Table 2 will be discussed in detail in the following sections of this chapter. Table 2. Mid-infrared fiber lasers Ion Tm3+ Ho3+ Tm3+ Er3+ Ho3+ Ho3+ Er3+ Ho3+

Fiber host

λPump (nm)

λLaser ( µm)

Silica ZBLAN ZBLAN ZBLAN ZBLAN ZBLAN ZBLAN ZBLAN

787 805 790 792 1150 532 653 890

1.9 2.1 2.3 2.7 2.9 3.22 3.45 3.95

Transition 3

F4 → 3 H6 I7 → 5 I8 3 H4 → 3 H5 4 I11/2 → 4 I13/2 5 I6 → 5 I7 5 S2 → 5 F5 4 F9/2 → 4 I9/2 5 I5 → 5 I6 5

Output power 14 W 8.8 W 22 mW 1.7 W 1.3 W 11 mW 8 mWb) 11 mWb)

Slope Eff. a) 46 % 36 % 7% 17 % 30 % 2.8 % 3% 3.7 %

Ref. [70] [71] [72] [73] [74] [75] [76] [77]

a)

The values of the slope efficiency are given versus incident, launched, or absorbed pump power as stated by the authors and are not necessarily comparable to each other b) Operation with the fiber cooled below ambient temperature



233

5 Thulium-Doped Fiber Lasers at 1.9–2.0 µm and 2.3–2.5 µm The use of the Tm3+ ion for mid-infrared fiber laser applications has been widespread mainly as a result of the convenient absorption band near 0.79 µm which allows for AlGaAs diode laser pumping. The primary luminescent transitions of Tm3+ relevant to mid-infrared laser emission are the 3 F4 → 3 H5 transition at ≈ 2.3 µm and the 3 H4 → 3 H6 ground-state transition at ≈ 1.9 µm, see the energy-level scheme in Fig. 6. The 3 F4 level is excited by the 0.79 µm pump wavelength. 5.1

Three-Level Lasers at 1.9–2.0 µm

The first explorations into fiber lasers utilizing the 1.9 µm ground-state transition related to the dye-laser pumping at 797 nm of a Tm3+ -doped silica fiber laser [79]. Overlap of the main absorption band with the emission wavelength of AlGaAs diode lasers quickly resulted in diode-laser pumping of these fiber lasers based on either silica [80] or fluoride [81] glass hosts. A useful phononassisted cross-relaxation process, (3 F4 , 3 H6 ) → (3 H4 , 3 H4 ), can transform one absorbed pump photon into two excitations in the 3 H4 upper laser level of the 2 µm transition [82], see Fig. 6. The efficient room-temperature CW operation of Tm3+ -doped diode-pumped bulk crystalline lasers [83] is largely due to this self-quenching process. This process is highly dependent upon the overall concentration of Tm3+ ions and competition by multiphonon relaxation from the 3 F4 level. High concentrations of Tm3+ in low-phonon-energy glasses enable full exploitation of this beneficial phenomenon. The significantly stronger multiphonon relaxation and corresponding shorter lifetime of the 3 F4 level in silica (≈ 20 µs) means that the cross-relaxation process is significantly weaker in silica as compared to fluoride glass. The large degree of Stark splitting of the 3 H6 ground state provides the 3 H4 → 3 H6 transition with a very broad emission spanning ≈ 400 nm in 3

τ3 = 1.5 ms

F4 Laser 2.3 µm NR

CR

3

H5 NR

3

τ1 = 6.8 ms

H4 GSA

Laser 2.0 µm

3

H6 Tm3+

Fig. 6. Partial energy-level scheme of Tm3+ displaying the measured lifetimes when doped into fluoride glass [78]. NR and CR represent nonradiative decay and cross-relaxation, respectively


234


many hosts and represents one of the broadest luminescent transitions available from any rare-earth ion. The broad emission spectrum produces a large degree of wavelength tunability [84]. Since the Tm3+ 1.9 µm transition can be favorably operated in silica fiber (with its higher peak-power damage threshold compared to ZBLAN fiber), pulses in the range of 190–500 fs have been obtained in additive-pulse [85] or passive [86] mode-locking from this broad emission spectrum. The smaller emission cross-section and the three-level nature of the laser transition usually resulted in relatively higher pump thresholds as compared to the standard Nd3+ -doped fiber lasers. Reabsorption from the ground state of the Tm3+ ions has to be overcome because the groundstate multiplet is the lower laser level. Reducing the population of the higher Stark levels of the ground state by way of cooling the fiber causes emission at shorter wavelengths. Tunability to longer wavelengths can be obtained by variation of the fiber length because of the increased level of reabsorption by the ground state with longer lengths of fiber [87]. Early power-scaling experiments involved the use of the convenient 1.064 µm Nd3+ :YAG laser which pumped the short wavelength side of the 3 H5 level [88]. Pumping the long wavelength side of the 3 H5 level with a high-power 1.319 µm Nd3+ :YAG laser also yields efficient output [89]. Inband pumping of the transition at 1.57 µm in silica [90] and at 1.58–1.60 µm in fluoride glass [91,92] has also been demonstrated. Whilst theoretical modeling of Tm3+ -doped silica fiber lasers [93] confirms that inband pumping is the most efficient pump method for silica based fiber lasers because of the high Stokes efficiency, nevertheless, the wide availability of high-power AlGaAS diode lasers means that diode-cladding-pumped systems in both standing-wave [87,70] and ring-resonator [94] arrangements are perhaps the most practical ways of producing high output power, see Fig. 7. Currently, the Tm3+ -doped silica fiber laser is probably the most mature of the midinfrared fiber-laser systems primarily because of the robustness and convenience offered by the silica glass host. While less efficient than Tm3+ -doped fluoride fiber lasers, the comparatively higher pump threshold relevant to Tm3+ -doped silica fiber lasers is easily provided for by currently available high-power diode-laser pump sources. The maximum output power from highpower Tm3+ -doped fiber lasers is still currently an order of magnitude lower than comparable diode-pumped crystalline systems [95]. 5.2

Four-Level Lasers at 2.3–2.5 µm

The increased quantum efficiency of the 3 F4 level when Tm3+ ions are doped into a ZBLAN host offers a greater range of emission wavelengths. Besides lasers at shorter wavelengths such as ≈ 1.47 µm (3 F4 → 3 H4 ) and ≈ 0.8 µm (3 F4 → 3 H6 ), the mid-infrared four-level CW laser at ≈ 2.3 µm (3 F4 → 3 H5 ) [96,97,72] is of interest, see Fig. 6. Deliberately designing the fiber to have a relatively low Tm3+ -ion concentration reduces cross-relaxation and hence severe lifetime quenching of the 3 F4 level. The lifetime of the lower


Mid-Infrared Fiber Lasers 3+

14

1.8 wt.% Tm

12

3.6 mol.% Tm , 0.4 mol.% Ho

3+

Output Power (W)

235

3+

3+

2.2 wt.% Tm 10 8 6 4 2 0 0

10

20

30

40

50

Incident Pump Power (W)

Fig. 7. Measured output powers from diode-cladding-pumped fiber lasers using 1.8 wt.% Tm3+ -doped silica [86], 2.2 wt.% Tm3+ -doped silica [70], and 3.6 mol.% Tm3+ , 0.4 mol.% Ho3+ -doped fluoride glass [71]

laser level of the 3 F4 → 3 H5 transition is quite short and leads to a low pump threshold and broad tunability which can extend from 2.25 µm to 2.5 µm [78]. Simultaneous lasing on the 3 H4 → 3 H6 transition at 1.9 µm produces a two-color fiber laser [98]. Applications requiring highly efficient output or multi-mid-infrared-wavelength output will benefit from the use of Tm3+ -doped ZBLAN fibers.

6

Holmium-Doped Fiber Lasers at 2.1 µm and 2.9 µm

The use of the Ho3+ ion as the active dopant for fiber lasers opens up a number of very useful mid-infrared transitions. In this section, we will concentrate on the 5 I7 → 5 I8 ground-state transition at ≈ 2.1 µm and the 5 I6 → 5 I7 transition at ≈ 2.9 µm, see the energy-level scheme in Fig. 8. One of the significant shortcomings of Ho3+ , however, is the lack of GSA transitions [99] that overlap with convenient high-power pump sources. As a result, many of the early demonstrations of Ho3+ -doped room-temperature crystalline CW lasers [82] involved sensitizing with Tm3+ in order to access the convenient absorption bands and the practical cross-relaxation process Tm3+ provides. Energy migration amongst the Tm3+ ions and a suitable Tm3+ :Ho3+ concentration ratio ensures that efficient energy transfer to Ho3+ takes place [100,101], see Fig. 8. The results of a recent spectroscopic study of Ho:YAG [102] suggest that the cross-relaxation process (5 I5 , 5 I8 ) → (5 I7 , 5 I7 ) and the related ETU process will probably be important in some highly Ho3+ -doped fibers; however, the cross-relaxation process (5 I6 , 5 I8 ) → (5 I7 , 5 I7 ) and its related ETU process seem to have a negligible effect on the overall population dynamics.


236

Markus Pollnau and Stuart D. Jackson 5

S2

Laser 3.2 µm

5

F5

5

I4

3

F4

3

H5

5

I5

Laser CR 3.9 µm ET

3

H4

5

I6

Laser 2.9µm

5

I7

Laser 2.1 µm

GSA

3

H6

6.1

5

Tm3+

Ho3+

I8

Fig. 8. Partial energy-level scheme of Ho3+ with Tm3+ sensitizer. ET represents energy transfer

Three-Level Lasers at 2.1 µm

As is the case with the ground-state transition of the Tm3+ ion discussed above, the 5 I7 → 5 I8 ground-state transition has been the most widely explored laser transition of Ho3+ . The first fiber laser configuration making use of this transition employed ZBLANP glass (a variant of ZBLAN) and argonion pumping [103]. A year later, this was followed by a demonstration of an argon-ion-pumped Ho3+ -doped silica fiber laser [104]. In both cases, the fiber was singly doped with Ho3+ , the output power < 1 mW, and each needed a relatively high pump power to reach laser threshold. Improvements in the output power and efficiency have been made recently with Yb3+ -doped silica fiber laser pumping of the 5 I6 level [105]; however, the output power has only increased to 280 mW. As mentioned above, a practical method of efficiently generating laser emission on the 5 I7 → 5 I8 transition is to co-dope Ho3+ laser ions with Tm3+ sensitizer ions. The first demonstration of a fiber laser operating with the Tm3+ , Ho3+ system occurred in 1991 [106] when 250 mW was generated at a slope efficiency of 52 % from a Ti:sapphire-pumped fluoride fiber laser. A year later [107], this work was followed by an increase in the Tm3+ concentration to improve the cross-relaxation and resulted in a higher slope efficiency being obtained. Demonstration of a Tm3+ , Ho3+ -doped silica fiber laser soon followed [108,109]; however, owing to lower Tm3+ concentrations and strong multiphonon relaxation of the 3 F4 level which forces weaker cross-relaxation, significantly lower slope efficiencies were measured, especially when pumped at 1.064 µm [11]. To date, the highest output power from a fiber laser operating on the 5 I7 → 5 I8 transition has been produced by a diode-cladding-pumped Tm3+ , Ho3+ -doped fluoride fiber laser [71], see



237

Fig. 7. In an analogous way to recent demonstrations in bulk laser systems [110,111], tandem-pumping Ho3+ with a separate Tm3+ laser operating at 1.9 µm may also prove effective in fibers, because it similarly exploits the cross-relaxation process between Tm3+ ions but avoids any ETU between Ho3+ ions in the 5 I7 upper laser level and excited Tm3+ ions [112]. 6.2

Four-Level Lasers at 2.9 µm

As a result of the infrared absorption cut-off of silica and the strong multiphonon relaxation quenching of mid-infrared transitions of rare-earth ions in this host, four-level fiber lasers operating on the 5 I6 → 5 I7 transition at ≈ 2.9 µm have to date only involved fluoride glass as the host material. The lifetime of the 5 I7 level is longer than the lifetime of the 5 I6 level and hence the 2.9 µm transition can be self-terminating. The first demonstration of a fiber laser using this transition [113] produced only ≈ 13 mW when pumped at a wavelength of 640 nm. High-power cascade lasing at 2.9 µm and 2.1 µm has been employed recently to extend the output power and to remove bottlenecking at the 5 I7 level [114]. With direct pumping of the upper laser level, 1.3 W of output power has been measured from this laser scheme [74]. Sensitizing Ho3+ with Yb3+ ions, see the energy-level scheme in Fig. 9, in order to exploit the more favorable absorption features of Yb3+ has been used in diode-pumped crystalline lasers for the generation of both 2.1 µm [115] and 2.9 µm [116] output. When sensitizing with Yb3+ ions, Ho3+ -doped silica fiber lasers at 2.1 µm may produce significantly more output because Yb3+ can be doped to quite high levels in silica thus ensuring strong absorption and sufficient energy transfer to Ho3+ . Similarly, a Yb3+ -sensitized Ho3+ -doped ZBLAN fiber will also be diode-laser pumpable and may efficiently provide high-power 2.9 µm output without the costly requirement of an intermediate laser system. Initial spectroscopic results look encouraging [117]. ET

5

I5

2

F5/2

5

τ2 = 3.5 ms GSA

I6

Laser 2.9 µm

5

I7

τ1 = 12 ms

Laser 2.1 µm 2

F7/2

5

Yb3+

Ho3+

I8

Fig. 9. Partial energy-level scheme of Ho3+ with Yb3+ sensitizer displaying the measured lifetimes of Ho3+ when doped into fluoride glass host [114]


238

7


Erbium-Doped Fiber Lasers at 2.7–2.8 µm

The first observation of coherent emission near 3 µm from erbium ions was reported in 1967 [118]. In 1983, the first CW lasing near 3 µm was obtained [119]. The first erbium 3 µm fiber laser was demonstrated in 1988 [120]. Although the lifetime of the 4 I13/2 lower laser level exceeds that of the 4 I11/2 upper laser level, CW lasing can be obtained on this four-level-laser transition in ZBLAN without employing special techniques to depopulate the 4 I13/2 lower laser level, because the lower laser level is not fed significantly by luminescent decay or multiphonon relaxation from the upper laser level [121]. In addition, the Stark splitting of the laser levels contributes to population inversion, because the laser transition occurs between a low-lying Stark component of the upper and a high-lying Stark component of the lower laser level [122]. During the relaxation oscillations at the onset of lasing, a red-shift of the lasing wavelength is often observed in erbium 3 µm laser systems [123,124,125], because the excitation energy is accumulated in the long-lived 4 I13/2 lower laser level and the character of the lasing process changes from four-level to three-level lasing [122]. For the same reason, the tunability range of a 3 µm CW laser [126] is narrowed and red-shifted with increasing pump power. Depending on the erbium concentration and fiber geometry, the 3 µm fiber laser has been operated in a number of different regimes that will be discussed in the following sections. 7.1

Excited-State Absorption and Cascade Lasing

Pump ESA has a major influence on the performance of low-doped, corepumped erbium 2.7 µm ZBLAN fiber lasers. Pumping at 980 nm directly into the upper laser level provides the highest Stokes efficiency of ηSt = λp /λl = 35 % [127]. However, ESA at 980 nm from the 4 I11/2 upper laser level [128] is detrimental to lasing and must be avoided. Experimentally, the best pump wavelength [129] is near 792 nm. This wavelength is at the peak of ESA from the 4 I13/2 lower laser level [130], as can be seen from the measured GSA and ESA cross-sections in Fig. 10a. The reason for the strong influence of this ESA is that depletion of the lower laser level by ESA favorably results in a redistribution of its population density and overcomes the bottleneck that results from the long lower-level lifetime. Slope efficiencies obtained in this way were < 15 %. Moreover, a saturation of the output power at 2.7 µm was observed, regardless of the pump wavelength, and the highest reported output powers were in the 20 mW region [131,132]. The output power saturated, because the excitation of the metastable 4 S3/2 level (lifetime ≈ 580 µs [133]) led to inversion with respect to the 4 I13/2 level. A second laser transition at 850 nm repopulated the 4 I13/2 lower laser level of the 2.7 µm transition, see Fig. 10b, causing the 2.7 µm laser to saturate at low output powers [129].



(a)

(b) 24

4

4I15/2 4I13/2 4I11/2

-22

cm2]

20

σ ESA [10

239

F7/2 H11/2 4 S3/2 2

τ5 = 580 µs Laser Laser 1.7µm 850nm

16 12

4

F9/2

4

I9/2

4

I11/2

ESA

8 4 0 780

790

800

810

820

830

τ2 = 6.9 ms Laser 2.7µm

840

Wavelength [nm] 4

τ1 = 9.0 ms

I13/2

GSA

4

I15/2 Er3+

Fig. 10. (a) Absorption cross-sections in ZBLAN:Er3+ near 800 nm: GSA 4 I15/2 → 4 I9/2 and ESA 4 I13/2 → 2 H11/2 , 4 I11/2 → 4 F3/2 , and 4 I11/2 → 4 F5/2 . (Data taken from [130].) (b) Partial energy-level scheme of erbium indicating the processes relevant to the ZBLAN:Er3+ cascade laser: Lower loop with GSA to 4 I9/2 , multiphonon relaxation, laser transition at 2.7 µm, luminescent decay, and upper loop with ESA to 2 H11/2 , thermal relaxation, laser transition at 1.7 µm, multiphonon relaxation, laser transition at 2.7 µm. Competitive lasing at 850 nm is suppressed in the cascade regime

Significant improvement in the performance of this laser system was obtained by deliberately operating a third laser transition 4 S3/2 → 4 I9/2 at 1.7 µm, thereby suppressing the competitive laser at 850 nm and recycling the excitation energy accumulated in the 4 S3/2 level into the upper laser level, see the energy-level scheme in Fig. 10b. The slope efficiency of the 2.7 µm transition increased significantly to 23 % [134], close to the Stokes-efficiency limit of 29 % under 800-nm pumping. An output power of 150 mW was demonstrated experimentally [134]. This cascade lasing regime represents the best option for dopant concentrations of typically 0.1 mol% (≈ 1.6×1019 cm−3 ) at which ESA is important. Also a three-transition-cascade lasing regime with additional lasing at the transition 4 I13/2 → 4 I15/2 near 1.6 µm was demonstrated [135], but no further improvement was obtained. 7.2

Lifetime Quenching by Pr3+ Co-Doping

In ZBLAN fibers with higher dopant concentrations of typically 1–5 mol% (≈ 1.6–8 × 1020 cm−3 ) and with the double-clad geometry, ESA is much less


240


important, because the reduced pump intensity with low-brightness diode lasers leads to smaller excitation densities. The relatively high fabrication costs of ZBLAN double-clad fibers means that pre-calculation and optimization of the expected device performance on the basis of the available spectroscopic parameters becomes an important tool. Currently, the most successful approach towards a high-power erbium 2.7 µm fiber laser is co-doping of the fiber with Pr3+ [73]. This idea was reported already in [131,136,137] and was proposed for the double-clad fiber laser in [138]. In this approach, the Er3+ 2.7 µm transition is operated as a simple four-level laser, see the energy-level scheme in Fig. 11a: The 4 I13/2 lower laser level is depopulated by the energy-transfer process ET1 to the Pr3+ co-dopant and fast decay to the ground state by multiphonon relaxation within Pr3+ . This energy-transfer process is much more efficient than the energy-transfer process ET2 from the 4 I11/2 upper laser level to the Pr3+ co-dopant, because the oscillator strength in Pr3+ is much higher for the transition involved in the former process [133]. The relatively weak lifetime quenching of the upper laser level affects the pump threshold, but it does not influence the slope efficiency. The strong lifetime quenching of the 4 I13/2 lower laser level and the fact that the 4 I11/2 population density is clamped to laser threshold significantly reduces ground-state bleaching and excitation of the laser levels, thus making the influence of ESA negligible, but similarly preventing energy recycling by ETU [139]. Like in the cascade-lasing regime (Sect. 5.2), each pump photon can at best produce one laser photon in the Er3+ , Pr3+ -co-doped system. The theoretical limit of the slope efficiency is given by the Stokes efficiency, which is 29 % under 800-nm pumping. Experimentally, a slope efficiency of 17 % and an output power of 1.7 W were obtained [73], see Fig. 11b. Other researchers [140] reported output powers of 660 mW. Since ESA from both laser levels is negligible, the system can alternatively be pumped near 980 nm, which provides the highest possible Stokes efficiency of 35 %. In this way, the experimental slope efficiency could be increased to 25 % [141]. The fiber that was used in these experiments contained an erbium concentration of 3.5 mol.%. 7.3

Energy Recycling by Energy-Transfer Upconversion

Energy-transfer processes between erbium ions govern the population mechanisms of highly erbium-doped laser systems. In the energy-level scheme of Fig. 12a, the important ETU and cross-relaxation processes are introduced. The ETU process (4 I13/2 , 4 I13/2 ) → (4 I15/2 , 4 I9/2 ) leads to a fast depletion of the lower laser level. Half of the ions that undergo this process are upconverted to the 4 I9/2 level and, by subsequent multiphonon relaxation, are recycled to the 4 I11/2 upper laser level from where they can each emit a second laser photon, for a single pump-photon absorption. For a large number of ions participating in this process, the quantum efficiency ηq = nl /np of


Mid-Infrared Fiber Lasers (a)

241

(b)

4

2

F7/2 H11/2 4 S3/2 1

D2

4

F9/2

4

I9/2

4

I11/2

ET2 1

G4

Output Power [W]

2

1

0 0

ET1 4

3

F4 F3 3 F2 3 H6

I13/2

2

4

6

8

10

12

Launched Pump Power [W]

3

Laser GSA

3

H5

3

4

H4

I15/2 Er

3+

3+

Pr

Fig. 11. (a) Partial energy-level scheme of erbium indicating the processes relevant to the ZBLAN:Er3+ lifetime-quenching laser: GSA at 980 nm to the 4 I11/2 upper laser level (or at 790 nm to the 4 I9/2 pump level and subsequent multiphonon relaxation to 4 I11/2 ), laser transition to the 4 I13/2 lower laser level, and relaxation to the ground state via energy transfer ET1 to the Pr3+ co-dopant. The energy transfer ET2 from the 4 I11/2 upper laser level to the Pr3+ co-dopant is weak. (b) Output power at 2.7 µm under 792-nm pumping (Data taken from [73])

pump photons np converted to laser photons nl increases from 1 to 2 [122]. In a simple rate-equation system which includes the processes shown in Fig. 12a the slope efficiency is given by [142] ln (1 − T ) b2 W22 ηsl = ηSt , (2) 2 − 12 ln [(1 − T ) (1 − L)] b2 W11 with T , the transmission of the outcoupling mirror, L, the internal resonator losses, and bi and Wii , the Boltzmann factors and ETU parameters of the upper (i = 2) and lower (i = 1) laser levels, respectively. If ETU occurs only from the lower laser level, i.e., W22 = 0, we obtain a factor-of-two increase in slope efficiency from (2). The slope efficiency is reduced, however, by the resonator losses, the nonperfect mode overlap, and the ETU process from the upper laser level in the case of W22 > 0. Energy recycling by ETU is the most efficient way to operate a CW erbium laser near 3 µm. The highest slope efficiency obtained experimentally is currently 50 % in LiYF4 :15 % Er3+ [143]. Quasi-CW excitation reduces the


242


(a)

(b)

F7/2 H11/2 4 S3/2 2

ETU2 4

F9/2

4

I9/2

4

I11/2

4

I13/2

CR

ETU1

W [10 -17 cm3s -1], Ratio

4

10 9 8 7 6 5 4 3 2 1 0

W11 W22 Ratio

0

ETU1

4

5

10

15

Erbium Conc. [10 20 cm-3]

ETU2

CR

I15/2 Er3+

Fig. 12. (a) Partial energy-level scheme of erbium indicating ETU1 from 4 I13/2 , ETU2 from 4 I11/2 , and cross-relaxation (CR) from the thermally coupled 4 S3/2 and 2 H11/2 levels. (b) Macroscopic parameters of ETU1 from 4 I13/2 (W11 ) and ETU2 from 4 I11/2 (W22 ) and the ratio W11 /W22 in ZBLAN:Er3+ bulk glasses. (Data taken from [133])

slope efficiency, because the lower laser level is less populated and ETU is less efficient in this case [144]. The parameters Wii of both ETU processes in ZBLAN bulk glasses [133] versus Er3+ concentration are shown in Fig. 12b. The criterion for optimization of the slope efficiency in (2) is maximizing the ratio W11 /W22 . For Er3+ concentrations of > 2–3 mol% at which ETU processes become important, this ratio is ≈ 3, see the dashed line in Fig. 12b, a more favorable value than reported for LiYF4 :Er3+ [145]. Energy recycling by ETU at high Er3+ concentrations [146] might lead to output powers at 3 µm on the order of 10 W. So far, two research groups tried to exploit energy recycling [147,148], however the slope efficiencies in these experiments did not exceed the slope efficiencies obtained in Er3+ ,Pr3+ -co-doped fibers pumped at corresponding pump wavelengths [73,141].

8

Fiber Lasers at Wavelengths Beyond 3 µm

Generating wavelengths longer than 3 µm from fiber lasers is a task which tests the limits of current glass technology. The need for lower phonon ener-



243

gies has to be balanced with acceptable mechanical, chemical, and thermal properties. Since the highly developed ZBLAN glass is only useful for laser transitions up to 3–3.5 µm, glasses such as the chalcogenides [149] will need to fill the gap. It is because these glasses have to be drawn into low-loss fiber which has prevented long-wavelength emission to the extent that is possible in crystalline-based solid-state lasers [150]. Creating efficient and high power mid-infrared fiber lasers with output wavelengths > 3 µm is at the forefront of current fiber-laser research efforts. 8.1

ZBLAN Fiber Lasers at 3.22 µm, 3.45 µm, and 3.95 µm

The operation of lasers at the longer wavelengths of 3.22 µm [75] and 3.95 µm [151] has been obtained from Ho3+ -doped ZBLAN fiber and at 3.45 µm [76] from Er3+ -doped ZBLAN fiber. It was, however, necessary to cool the ZBLAN fiber for the 3.45 µm and 3.95 µm transitions. These two laser transitions span five or six maximum phonon energies in ZBLAN, therefore the lifetime of the upper laser level for each of these transitions is short and engenders an increase in the pump threshold compared to other ZBLAN fiber lasers operating at the shorter mid-infrared wavelengths. In addition, the lower laser levels of these transitions possess quite long lifetimes and some saturation of the output power has been observed [77]. This problem (while it can be mitigated with cascaded lasing), combined with the use of inconvenient pump sources has impeded the full utilization of these laser transitions. The 3.95 µm wavelength emitted from the cooled ZBLAN fiber laser is currently the longest laser wavelength that has been generated from a fiber laser. A laser transition that has as yet not been realized but might work well in ZBLAN fibers is the 6 H13/2 → 6 H15/2 transition at 3.0–3.4 µm in Dy3+ . 8.2

Future Mid-Infrared Fiber Lasers

As mentioned above, fiber lasers operating on laser transitions which have wavelengths > 3 µm will need to use glasses which have very low phonon energies. While rare-earth-doped heavy-metal oxides [152] have been studied for 2–3 µm mid-infrared emission, up to now, there has been no report of laser action for a fiber laser comprised of such a glass. Heavy-metal oxides do not seem to be suitable for lasers at wavelengths beyond 3 µm, because their maximum phonon energies are comparable to fluoride glasses and are too high for laser transitions beyond 3 µm. The chalcogenide glasses have, by contrast, been doped with a number of rare-earth ions including Ho3+ [153], Tm3+ [154], Tb3+ [154], Dy3+ [155], Pr3+ [156], and Er3+ [157,158] for studies into > 3-µm mid-infrared luminescence, see Table 3. Fiber-laser action has been reported, however, only for an Nd3+ -doped GLS glass operating at a wavelength of ≈ 1 µm [159]. Recent demonstrations of fabricating Bragg gratings [160], single-mode fiber [161] and holey fiber [162] with chalcogenide glass highlight the utility of this glass


244


Table 3. Examples of luminescent transitions investigated as candidates for midinfrared lasers in sulfide fibers Ion 3+

Dy Tm3+ Ho3+ Dy3+ Tb3+ Ho3+

λLaser ( µm) 3.2 3.8 3.9 4.3 4.8 4.9

Transition 6

6

H13/2 → H15/2 3 H5 → 3 H4 5 I5 → 5 H6 6 H11/2 → 6 H13/2 7 F5 → 7 F6 5 I4 → 5 I5

Ref. [155] [154] [153] [155] [154] [153]

for fiber-based applications; however, the purity and toxicity of the starting materials and the difficulty of making ultra-low loss fiber currently impede the widespread use of chalcogenide glass for mid-infrared fiber-laser applications. Once these obstacles have been overcome, future > 3-µm fiber lasers will most likely involve the rare-earth ions Pr3+ , Nd3+ , Dy3+ , and Ho3+ doped into chalcogenide glass because most of the important mid-infrared transitions relevant to these ions can be accessed with pump-photon wavenumbers < 10 000 cm−1 . Judicious choice of the overall dopant-ion concentration and the use of particular sensitizer and quenching ions will enable the production of efficient > 3 µm output some time in the future.

9

Conclusions

On our journey through the forest of the various established and yet to be demonstrated mid-infrared fiber lasers, we have found that the shorter the wavelength, the better is the laser performance. When we approach longer wavelengths in the mid-infrared spectrum, we find that the quality and durability of the required low-phonon-energy fibers decline, Stokes and slope efficiencies decrease, whereas the thermal problems increase. The assumption that due to its large surface-to-volume ratio, the fiber geometry might avoid all thermal problems has been questioned by several recent high-power fiberlaser experiments in the near- and mid-infrared spectral region. All the above phenomena are not much different from the situation found in crystalline lasers. Nevertheless, there remain distinct differences between these two host categories. When flexibility of the resonator design, short pulses, and high peak powers are required, the fiber shows some disadvantages. On the other hand, fiber lasers are preferred when high beam quality or low pump threshold combined with medium CW output power are desired. The low pump threshold is an invaluable advantage when cascade-laser operation is required to depopulate the long-lived terminating level of one laser transition by a second laser transition. The comparatively low dopant concentrations that are useful in fiber lasers due to the long interaction lengths can minimize energy dissipation by interionic processes but, equally true, limit the exploitation of



245

these processes as a tool to optimize the population mechanisms of a certain laser system. Although still a great challenge with respect to the fabrication process, chalcogenide-glass fibers have the potential to revolutionize CW midinfrared lasers in the wavelength range between 3–5 µm.

References 1. A. E. Siegman: Lasers (University Science Books, Mill Valley, CA 1986) 220 2. O. Svelto: Principles of Lasers, 3rd ed. (Plenum Press, New York 1989) 220 3. M. J. F. Digonnet (Ed.): Rare-Earth-Doped Fiber Lasers and Amplifiers, 2nd ed. (Marcel Dekker, New York 2001) 220, 221, 230 4. R. Reisfeld, M. Eyal: Possible ways of relaxations for excited states of rare earth ions in amorphous media, J. Phys. (Paris) 46, C349 (1985) 221 5. T. Schweizer: Rare-earth-doped gallium lanthanum sulphide glasses for midinfrared fibre lasers, Dissertation, University of Hamburg, Germany (1998) 221 6. D. C. Brown, H. J. Hoffman: Thermal, stress, and thermo-optic effects in high average power double-clad silica fiber lasers, IEEE J. Quantum Electron. 37, 207 (2001) 221, 226 7. L. Wetenkamp: Charakterisierung von laseraktiv dotierten Schwermetallfluorid-Gl¨ asern und Faserlasern, Dissertation, Technical University of Braunschweig, Germany (1991) 221, 222 8. S. M. Lima, T. Catunda, R. Lebullenger, A. C. Hernandes, M. L. Baesso, A. C. Bento, L. C. M. Miranda: Temperature dependence of thermo-optical properties of fluoride glasses determined by thermal lens spectrometry, Phys. Rev. B 60, 15173 (1999) 221 9. S. M. Lima, T. Catunda, M. L. Baesso, L. D. Vila, Y. Messaddeq, E. B. Stucchi, S. J. L. Ribeiro: Thermal-optical properties of Ga:La:S glasses measured by thermal lens technique, J. Non-Cryst. Solids 247, 222 (1999) 221 10. B. J. Ainslie, S. P. Craig, S. T. Davey: The absorption and fluorescence spectra of rare earth ions in silica-based monomode fiber, J. Lightwave Technol. 6, 287 (1988) 221 11. S. D. Jackson, T. A. King: CW operation of a 1.064 µm pumped Tm-Ho-doped silica fiber laser, IEEE J. Quantum Electron. 34, 1578 (1998) 221, 236 12. O. Humbach, H. Fabian, U. Grzesik, U. Haken, W. Heitmann: Analysis of OH absorption bands in synthetic silica, J. Non-Cryst. Solids 203, 19 (1996) 222 13. D. C. Tran, G. H. Sigel, Jr., B. Bendow: Heavy metal fluoride glasses and fibers: a review, J. Lightwave Technol. 2, 566 (1984) 222 14. P. W. France, M. G. Drexhage, J. M. Parker, M. W. Moore, S. F. Carter, J. V. Wright: Fluoride Glass Optical Fibres (Blackie, Glasgow 1990) 222 15. S. T. Davey, P. W. France: Rare earth doped fluorozirconate glasses for fibre devices, BT Technol. J. 7, 58 (1989) 222 16. M. Monerie, F. Alard, G. Maze: Fabrication and characterisation of fluorideglass single-mode fibres, Electron. Lett. 21, 1179 (1985) 222 17. L. Wetenkamp, G. F. West, H. T¨ obben: Optical properties of rare earth-doped ZBLAN glasses, J. Non-Cryst. Solids 140, 35 (1992) 222 18. Y. D. Huang, M. Mortier, F. Auzel: Stark level analysis for Er3+ -doped ZBLAN glass, Opt. Mater. 17, 501 (2001) 222


246


19. P. N. Kumta, S. H. Risbud: Rare-earth chalcogenides – an emerging class of optical materials, J. Mat. Sci. 29, 1135 (1994) 222 20. J. S. Sanghera, J. Heo, J. D. Mackenzie: Chalcohalide glasses, J. Non-Cryst. Solids 103, 155 (1988) 222 21. L. D. DeLoach, R. H. Page, G. D. Wilke, S. A. Payne, W. F. Krupke: Transition metal-doped zinc chalcogenides: Spectroscopy and laser demonstration of a new class of gain media, IEEE J. Quantum Electron. 32, 885 (1996) 222 22. L. B. Shaw, B. Cole, P. A. Thielen, J. S. Sanghera, I. D. Aggarwal: Mid-wave IR and long-wave IR laser potential of rare-earth doped chalcogenide glass fiber, IEEE J. Quantum Electron. 48, 1127 (2001) 222 23. Y. D. West, T. Schweizer, D. J. Brady, D. W. Hewak: Gallium lanthanum sulphide fibers for infrared transmission, Fiber Integrated Opt. 19, 229 (2000) 222 24. J. Heo, Y. B. Shin: Absorption and mid-infrared emission spectroscopy of Dy3+ in Ge-As (or Ga)-S glasses, J. Non-Cryst. Solids 196, 162 (1996) 222 25. J. R. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Misawa, M. Prabhu, J. Xu, K. Ueda, H. Yagi, T. Yanagitani, A. A. Kaminskii, A. Kudryashov: 72 W Nd:Y3 Al5 O12 ceramic laser, Appl. Phys. Lett. 78, 3586 (2001) 222 26. J. Lu, J. Lu, T. Murai, K. Takaichi, T. Uematsu, K. Ueda, H. Yagi, T. Yanagitani, T. Works, A. A. Kaminskii: Optical properties and highly efficient laser oscillation of Nd:Y2 O3 ceramics, in CLEO Europe, OSA Tech. Digest (Opt. Soc. Am., Washington, DC 2002), p. 60 223 27. G. Huber, V. Peters, K. Petermann: New solid-state lasers based on rare-earth doped sesquioxide crystals, in CLEO Europe 2000, OSA Tech. Digest (Opt. Soc. Am., Washington, DC 2000) p. 386 223 28. B. N. Samson, P. A. Tick, N. F. Borrelli: Efficient neodymium-doped glassceramic fiber laser and amplifier, Opt. Lett. 26, 145 (2001) 223 29. H. Po, E. Snitzer, R. Tumminelli, L. Zenteno, F. Hakimi, N. M. Cho, T. Haw: Doubly clad high brightness Nd fiber laser pump by GaAlAs phased array, in Proc. Optical Fibre Communication Conf. (1989) paper PD7 223 30. H. Po, J. D. Cao, B. M. Laliberte, R. A. Minns, R. F. Robinson, B. H. Rockney, R. R. Tricca, Y. H. Zhang: High power neodymium-doped single transverse mode fibre laser, Electron. Lett. 29, 1500 (1993) 223 31. I. N. Duling III, W. K. Burns, L. Goldberg: High-power superfluorescent fiber source, Opt. Lett. 15, 33 (1990) 223 32. J. D. Minelly, W. L. Barnes, R. I. Laming, P. R. Morkel, J. E. Townsend, S. G. Grubb, D. N. Payne: Diode-array pumping of Er3+ /Yb3+ co-doped fiber lasers and amplifiers, IEEE Photonics Technol. Lett. 5, 301 (1993) 223 33. H. M. Pask, J. L. Archambault, D. C. Hanna, L. Reekie, P. S. J. Russell, J. E. Townsend, A. C. Tropper: Operation of cladding-pumped Yb3+ -doped silica fibre lasers in 1 µm region, Electron. Lett. 30, 863 (1994) 223 34. A. Liu, K. Ueda: The absorption characteristics of circular, offset, and rectangular double-clad fibers, Opt. Commun. 132, 511 (1996) 224 35. H. Zellmer, U. Willamowski, A. T¨ unnermann, H. Welling, S. Unger, V. Reichel, H.-R. M¨ uller, T. Kirchhof, P. Albers: High-power CW neodymiumdoped fiber laser operating at 9.2 W with high beam quality, Opt. Lett. 20, 578 (1995) 224 36. A. Ankiewicz, W. L. R. Perera, P. L. Chu, D. A. C. C. Jayasinghe: Use of graded elliptical cladding for efficient pumping of doped fiber cores, Opt. Commun. 133, 82 (1997) 224



247

37. D. Kouznetsov, J. V. Moloney, E. M. Wright: Efficiency of pump absorption in double-clad fiber amplifiers. I. Fiber with circular symmetry, J. Opt. Soc. Am. B 18, 743 (2001) 224 38. M. H. Muendel: Optimal inner cladding shapes for double-clad fiber lasers, in CLEO 9, OSA Tech. Digest Ser. (Opt. Soc. Am., Washington, DC 1996), p. 209 224 39. A. Liu, K. Ueda: Propagation losses of pump light in rectangular double-clad fibers, Opt. Eng. 35, 3130 (1996) 224 40. V. Doya, O. Legrand, F. Mortessagne: Optimized absorption in a chaotic double-clad fiber amplifier, Opt. Lett. 26, 872 (2001) 224 41. P. Glas, M. Naumann, A. Schirrmacher, Th. Pertsch: The multicore fiber – a novel design for a diode pumped fiber laser, Opt. Commun. 151, 187 (1998) 224 42. P. Glas, M. Naumann, A. Schirrmacher: A novel design for a high brightness diode pumped fiber laser source, Opt. Commun. 122, 163 (1996) 224 43. G. P. Lees, D. Taverner, D. J. Richardson, L. Dong, T. P. Newson: Q-switched erbium doped fibre laser utilising a novel large mode area fibre, Electron. Lett. 33, 393 (1997) 224 44. K. Furusawa, A. Malinowski, J. H. V. Price, T. M. Monro, J. K. Sahu, J. Nilsson, D. J. Richardson: Cladding pumped ytterbium-doped fiber laser with holey inner and outer cladding, Opt. Express 9, 714 (2001) 224 45. T. A. Birks, J. C. Knight, P. St. J. Russell: Endlessly single-mode photonic crystal fiber, Opt. Lett. 22, 961–963 (1997) 224 46. D. J. Ripin, L. Goldberg: High efficiency side-coupling of light into optical fibres using imbedded v-grooves, Electron. Lett. 31, 2204 (1995) 225 47. T. Weber, W. L¨ uthy, H. P. Weber, V. Neuman, H. Berthou, G. Kotrotsios: A longitudinal and side-pumped single transverse mode double-clad fiber laser with a special silicone coating, Opt. Commun. 115, 99 (1995) 225 48. C. C. Cook, T. Y. Fan: Spectral beam combining of Yb-doped fiber lasers in and external cavity, in Trends Opt. Photonics Adv. Solid-State Lasers 26, 163–166 (Opt. Soc. Am., Washington, DC 1999) 225 49. W. A. Clarkson, V. Matera, T. M. J. Kendall, D. C. Hanna, J. Nilsson, P. W. Turner: High-power wavelength-combined cladding-pumped Tm-doped silica fibre lasers, in Conference on Lasers and Electro-Optics, OSA Technical Digest, Vol. 56 (Optical Society of America, Washington, DC 2001) pp. 363– 364 225 50. S. J. Augst, A. K. Goyal, R. L. Aggarwal, T. Y. Fan, A. Sanchez: Wavelength beam combining of ytterbium fiber lasers in a MOPA configuration, in CLEO, OSA Tech. Digest (Opt. Soc. Am., Washington, DC 2002) pp. 594–595 225 51. V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bicknese, R. Dohle, E. Wolak, P. S. Yeh, E. Zucker: 110 W fibre laser, Electron. Lett. 35, 1158 (1999) 225 52. J. Limpert, A. Liem, S. H¨ ofer, H. Zellmer, A. T¨ unnermann, S. Unger, S. Jetschke, H.-R. M¨ uller: 150 W Nd/Yb codoped fiber laser at 1.1 µm, in CLEO, OSA Tech. Digest (Opt. Soc. Am., Washington, DC 2002), pp. 590– 591 225 53. M. Pollnau, P. J. Hardman, M. A. Kern, W. A. Clarkson, D. C. Hanna: Upconversion-induced heat generation and thermal lensing in Nd:YLF and Nd:YAG, Phys. Rev. B 58, 16076 (1998) 226


248


54. M. K. Davis, M. J. F. Digonnet, R. H. Pantell: Thermal effects in doped fibers, J. Lightwave Technol. 16, 1013 (1998) 226 55. L. Zenteno: High-power double-clad fiber lasers, J. Lightwave Technol. 11, 1435 (1993) 226 56. N. A. Brilliant, K. Lagonik: Thermal effects in a dual-clad ytterbium fiber laser, Opt. Lett. 26, 1669 (2001) 226 57. B. R. Judd: Optical absorption intensities of rare-earth ions, Phys. Rev. 127, 750 (1962) 228 58. G. S. Ofelt: Intensities of crystal spectra of rare-earth ions, J. Chem. Phys. 37, 511 (1962) 228 59. L. A. Riseberg, H. W. Moos: Multiphonon orbit–lattice relaxation of excited states of rare-earth ions in crystals, Phys. Rev. 174, 429 (1968) 230 60. J. M. F. van Dijk, M. F. H. Schuurmans: On the nonradiative and radiative decay rates and a modified exponential energy gap law for 4f –4f transitions in rare-earth ions, J. Chem. Phys. 78, 5317 (1983) 230 61. D. L. Dexter: A theory of sensitized luminescence in solids, J. Chem. Phys. 21, 836 (1953) 230 62. T. Miyakawa, D. L. Dexter: Phonon sidebands, multiphonon relaxation of excited states, and phonon-assisted energy transfer between ions in solids, Phys. Rev. B 1, 2961 (1970) 230 63. V. P. Gapontsev, N. S. Platonov: Migration-accelerated quenching of luminescence in glasses activated by rare-earth ions, Mater. Sci. Forum 50, 165 (1989) 231 64. W. J. C. Grant: Role of rate equations in the theory of luminescent energy transfer, Phys. Rev. B 4, 648 (1971) 232 65. E. Delevaque, T. Georges, M. Monerie, P. Lamouler, J.-F. Bayon: Modeling of pair-induced quenching in erbium-doped silicate fibers, IEEE Photonics Technol. Lett. 5, 73 (1993) 232 66. J. L. Wagener, P. F. Wysocki, M. J. F. Digonnet, H. J. Shaw, D. J. DiGiovanni: Effects of concentration and clusters in erbium-doped fiber lasers, Opt. Lett. 18, 2014 (1993) 232 67. R. S. Quimby, W. J. Miniscalco, B. Thompson: Clustering in erbium-doped silica glass fibers analyzed using 980 nm excited-state absorption, J. Appl. Phys. 76, 4472 (1994) 232 68. E. Maurice, G. Monnom, B. Dussardier, D. B. Ostrowsky: Clustering-induced nonsaturable absorption phenomenon in heavily erbium-doped silica fibers, Opt. Lett. 20, 2487 (1995) 232 69. M. Pollnau, D. R. Gamelin, S. R. L¨ uthi, H. U. G¨ udel, M. P. Hehlen: Power dependence of upconversion luminescence in lanthanide and transition-metalion systems, Phys. Rev. B 61, 3337 (2000) 232 70. R. A. Hayward, W. A. Clarkson, P. W. Turner, J. Nilsson, A. B. Grudinin, D. C. Hanna: Efficient cladding-pumped Tm-doped silica fibre laser with high power singlemode output at 2 µm, Electron. Lett. 36, 711 (2000) 232, 234, 235 71. S. D. Jackson: 8.8 W diode-cladding-pumped Tm3+ , Ho3+ -doped fluoride fibre laser, Electron. Lett. 37, 821 (2001) 232, 235, 236 72. R. G. Smart, J. N. Carter, A. C. Tropper, D. C. Hanna: Continuous-wave oscillation of Tm3+ -doped fluorozirconate fibre lasers at around 1.47 µm, 1.9 µm and 2.3 µm when pumped at 790 nm, Opt. Commun. 82, 563 (1991) 232, 234



249

73. S. D. Jackson, T. A. King, M. Pollnau: Diode-pumped 1.7-W erbium 3 µm fiber laser, Opt. Lett. 24, 1133 (1999) 232, 240, 241, 242 74. T. Sumiyoshi, H. Sekita, T. Arai, S. Sato, M. Ishihara, M. Kikuchi: Highpower continuous-wave 3- and 2 µm cascade Ho3+ :ZBLAN fiber laser and its medical applications, IEEE J. Sel. Topics Quantum Electron. 5, 936 (1999) 232, 237 75. C. Carbonnier, H. T¨ obben, U. B. Unrau: Room temperature CW fibre laser at 3.22 µm, Electron. Lett. 34, 893 (1998) 232, 243 76. H. T¨ obben: CW-lasing at 3.45 µm in erbium-doped fluorozirconate fibers, Frequenz 45, 250 (1991) 232, 243 77. J. Schneider, C. Carbonnier, U. B. Unrau: Characterization of a Ho3+ -doped fluoride fiber laser with a 3.9 µm emission wavelength, Appl. Opt. 36, 8595 (1997) 232, 243 78. R. M. Percival, S. F. Carter, D. Szebesta, S. T. Davey, W. A. Stallard: Thuliumdoped monomode fluoride fibre laser broadly tunable from 2.25 to 2.5 µm, Electron. Lett. 27, 1912 (1991) 233, 235 79. D. C. Hanna, I. M. Jauncey, R. M. Percival, I. R. Perry, R. G. Smart, P. J. Suni, J. E. Townsend, A. C. Tropper: Continuous-wave oscillation of a monomode thulium-doped fibre laser, Electron. Lett. 24, 1222 (1988) 233 80. W. L. Barnes, J. E. Townsend: Highly tunable and efficient diode pumped operation of Tm3+ doped fibre lasers, Electron. Lett. 26, 746 (1990) 233 81. J. N. Carter, R. G. Smart, D. C. Hanna, A. C. Tropper: CW diode-pumped operation of 1.97 µm thulium-doped fluorozirconate fibre laser, Electron. Lett. 26, 599 (1990) 233 82. T. Y. Fan, G. Huber, R. L. Byer, P. Mitzscherlich: Spectroscopy and diode laser-pumped operation of Tm,Ho:YAG, IEEE J. Quantum Electron. 24, 924 (1988) 233, 235 83. R. C. Stoneman, L. Esterowitz: Efficient, broadly tunable, laser-pumped Tm:YAG and Tm:YSGG CW lasers, Opt. Lett. 15, 486 (1990) 233 84. D. C. Hanna, R. M. Percival, R. G. Smart, A. C. Tropper: Efficient and tunable operation of a Tm-doped fibre laser, Opt. Commun. 75, 283 (1990) 234 85. L. E. Nelson, E. P. Ippen, H. A. Haus: Broadly tunable sub-500 fs pulses from an additive-pulse mode-locked thulium-doped fiber ring laser, Appl. Phys. Lett. 67, 19 (1995) 234 86. R. C. Sharp, D. E. Spock, N. Pan, J. Elliot: 190-fs passively mode-locked thulium fiber laser with a low threshold, Opt. Lett. 21, 881 (1996) 234, 235 87. S. D. Jackson, T. A. King: High-power diode-cladding-pumped Tm-doped silica fiber laser, Opt. Lett. 23, 1462 (1998) 234 88. D. C. Hanna, I. R. Perry, J. R. Lincoln, J. E. Townsend: A 1-Watt thuliumdoped CW fibre laser operating at 2 µm, Opt. Commun. 80, 52 (1990) 234 89. P. S. Golding, S. D. Jackson, P.-K. Tsai, B. C. Dickinson, T. A. King: Efficient high power operation of a Tm-doped silica fiber laser pumped at 1.319 µm, Opt. Commun. 175, 179 (2000) 234 90. T. Yamamoto, Y. Miyajima, T. Komukai: 1.9 µm Tm-doped silica fibre laser pumped at 1.57 µm, Electron. Lett. 30, 220 (1994) 234 91. R. M. Percival, D. Szebesta, C. P. Seltzer, S. D. Perrin, S. T. Davey, M. Louka: 1.6 µm semiconductor diode pumped thulium doped fluoride fibre laser and amplifier of very high efficiency, Electron. Lett. 29, 2110 (1993) 234


250


92. T. Yamamoto, Y. Miyajima, T. Komukai, T. Sugawa: 1.9 µm Tm-doped fluoride fiber amplifier and laser pumped at 1.58 µm, Electron. Lett. 29, 986 (1993) 234 93. S. D. Jackson, T. A. King: Theoretical modeling of Tm-doped silica fiber lasers, J. Lightwave Technol. 17, 948 (1999) 234 94. J. Q. Xu, M. Prabhu, L. Jianren, K. Ueda, D. Xing: Efficient double-clad thulium-doped fiber laser with a ring cavity, Appl. Opt. 40, 1983 (2001) 234 95. K. S. Lai, P. B. Phua, R. F. Wu, Y. L. Lim, E. Lau, S. W. Toh, B. T. Toh, A. Chng: 120-W continuous-wave diode-pumped Tm:YAG laser, Opt. Lett. 25, 1591 (2000) 234 96. R. Allen, L. Esterowitz: CW diode pumped 2.3 µm fiber laser, Appl. Phys. Lett. 55, 721 (1989) 234 97. J. Y. Allain, M. Monerie, H. Poignant: Tunable CW lasing around 0.82, 1.48, 1.88 and 2.35 µm in thulium-doped fluorozirconate fibre, Electron. Lett. 25, 1660 (1989) 234 98. R. M. Percival, D. Szebesta, S. T. Davey: Highly efficient and tunable operation of 2 color Tm-doped fluoride fiber laser, Electron. Lett. 28, 671 (1992) 235 99. K. Tanimura, M. D. Shinn, W. A. Sibley, M. G. Drexhage, R. N. Brown: Optical transitions of Ho3+ ions in fluorozirconate glass, Phys. Rev. B 30, 2429 (1984) 235 100. J. K. Tyminski, D. M. Franich, M. Kokta: Gain dynamics of Tm:Ho:YAG pumped in near infrared, J. Appl. Phys. 65, 3181 (1989) 235 101. V. A. French, R. R. Petrin, R. C. Powell, M. Kokta: Energy-transfer processes in Y3 Al5 O12 :Tm,Ho, Phys. Rev. B 46, 8018 (1992) 235 102. L. B. Shaw, R. S. F. Chang, N. Djeu: Measurement of up-conversion energytransfer probabilities in Ho:Y3 Al5 O12 and Tm:Y3 Al5 O12 , Phys. Rev. B 50, 6609 (1994) 235 103. M. C. Brierley, P. W. France, C. A. Millar: Lasing at 2.08 µm and 1.38 µm in a holmium doped fluorozirconate fiber laser, Electron. Lett. 24, 539 (1988) 236 104. D. C. Hanna, R. M. Percival, R. G. Smart, J. E. Townsend, A. C. Tropper: Continuous-wave oscillation of holmium-doped silica fiber laser, Electron. Lett. 25, 593 (1989) 236 105. A. S. Kurkov, E. M. Dianov, O. I. Medvedkov, G. A. Ivanov, V. A. Aksenov, V. M. Paramonov, S. A. Vasiliev, E. V. Pershina: Efficient silica-based Ho3+ fibre laser for 2 µm spectral region pumped at 1.15 µm, Electron. Lett. 36, 1015 (2000) 236 106. J. Y. Allain, M. Monerie, H. Poignant: High-efficiency CW thulium-sensitized holmium-doped fluoride fiber laser operating at 2.04 µm, Electron. Lett. 27, 1513 (1991) 236 107. R. M. Percival, D. Szebesta, S. T. Davey, N. A. Swain, T. A. King: Thulium sensitized holmium-doped CW fluoride fiber laser of high-efficiency, Electron. Lett. 28, 2231 (1992) 236 108. K. Oh, T. F. Morse, A. Kilian, L. Reinhart, P. M. Weber: Continuous-wave oscillation of thulium-sensitized holmium-doped silica fiber laser, Opt. Lett. 19, 278 (1994) 236 109. Ch. Ghisler, W. L¨ uthy, H. P. Weber, J. Morel, A. Woodtli, R. D¨ andliker, V. Neuman, H. Berthou, G. Kotrotsios: A Tm3+ sensitized Ho3+ silica fibre laser at 2.04 µm pumped at 809 nm, Opt. Commun. 109, 279 (1994) 236



251

110. C. Bollig, R. A. Hayward, W. A. Clarkson, D. C. Hanna: 2-W Ho:YAG laser intracavity pumped by a diode-pumped Tm:YAG laser, Opt. Lett. 23, 1757 (1998) 237 111. P. A. Budni, M. L. Lemons, J. R. Mosto, E. P. Chicklis: High-power/highbrightness diode-pumped 1.9 µm thulium and resonantly pumped 2.1 µm holmium lasers, IEEE J. Select. Topics Quantum Electron. 6, 629 (2000) 237 112. G. Rustad, K. Stenersen: Modeling of laser-pumped Tm and Ho lasers accounting for upconversion and ground-state depletion, IEEE J. Quantum Electron. 32, 1645 (1996) 237 113. L. Wetenkamp: Efficient CW operation of a 2.9 µm Ho3+ -doped fluorozirconate fiber laser pumped at 640 nm, Electron. Lett. 26, 883 (1990) 237 114. T. Sumiyoshi, H. Sekita: Dual-wavelength continuous-wave cascade oscillation at 3 and 2 µm with a holmium-doped fluoride-glass fiber laser, Opt. Lett. 23, 1837 (1998) 237 115. T. Rothacher, W. L¨ uthy, H. P. Weber: Diode pumping and laser properties of Yb,Ho:YAG, Opt. Commun. 155, 68 (1998) 237 116. A. Diening, P. E.-A. M¨ obert, E. Heumann, G. Huber, B. H. T. Chai: Diodepumped CW lasing of Yb,Ho:KYF4 in the 3 µm spectral range in comparison to Er:KYF4 , Laser Phys. 8, 214 (1998) 237 117. B. Peng, T. Izumitani: Ho3+ doped 2.84 µm laser glass for laser knives, sensitised by Yb3+ , Rev. Laser Eng. 22, 9 (1994) 237 118. M. Robinson, P. D. Devor: Thermal switching of laser emission of Er3+ at 2.69µ and Tm3+ at 1.86µ in mixed crystals of CaF2 :ErF3 :TmF∗3 , Appl. Phys. Lett. 10, 167 (1967) 238 119. K. S. Bagdasarov, V. I. Zhekov, V. A. Lobachev, T. M. Murina, A. M. Prokhorov: Steady-state emission from a Y3 Al5 O12 :Er3+ laser (λ = 2.94 µm, T = 300 K), Kvant. Elektr. (Moscow) 10, 452 (1983) [Engl. transl. Sov. J. Quantum Electron. 13, 262 (1983)] 238 120. M. C. Brierley, P. W. France: Continuous wave lasing at 2.71 µm in an erbiumdoped fluorozirconate fibre, Electron. Lett. 24, 935 (1988) 238 121. R. S. Quimby, W. J. Miniscalco: Continuous-wave lasing on a self-terminating transition, Appl. Opt. 28, 14 (1989) 238 122. M. Pollnau, S. D. Jackson: Erbium 3 µm fiber lasers, IEEE J. Select. Topics Quantum Electron. 7, 30 (2001) 238, 241 123. V. Lupei, S. Georgescu, V. Florea: On the dynamics of population inversion for 3 µm Er3+ lasers, IEEE J. Quantum Electron. 29, 426 (1993) 238 124. J. Schneider: Kaskaden-Faserlaser im mittleren Infrarot, Dissertation, Technical University Braunschweig (Cuvillier, G¨ ottingen 1996) 238 125. B. C. Dickinson, P. S. Golding, M. Pollnau, T. A. King, S. D. Jackson: Investigation of a 791-nm pulsed-pumped 2.7 µm Er-doped ZBLAN fibre laser, Opt. Commun. 191, 315 (2001) 238 126. N. J. C. Libatique, J. Tafoja, N. K. Viswanathan, R. K. Jain, A. Cable: ‘Fieldusable’ diode-pumped ≈ 120 nm wavelength-tunable CW mid-IR fibre laser, Electron. Lett. 36, 791 (2000) 238 127. R. C. Stoneman, J. G. Lynn, L. Esterowitz: Direct upper-state pumping of the 2.8 µm Er3+ :YLF laser, IEEE J. Quantum Electron. 28, 1041 (1992) 238 128. R. S. Quimby, W. J. Miniscalco, B. Thompson: Excited state absorption at 980 nm in erbium doped glass, in Fiber Laser Sources and Amplifiers III, Proc. SPIE 1581, 72–79 (1991) 238


252


129. S. Bed¨ o, M. Pollnau, W. L¨ uthy, H. P. Weber: Saturation of the 2.71 µm laser output in erbium doped ZBLAN fibers, Opt. Commun. 116, 81 (1995) 238 130. M. Pollnau, Ch. Ghisler, W. L¨ uthy, H. P. Weber: Cross-sections of excitedstate absorption at 800 nm in erbium-doped ZBLAN fiber, Appl. Phys. B 67, 23 (1998) 238, 239 131. J. Schneider, D. Hauschild, C. Frerichs, L. Wetenkamp: Highly efficient Er3+ :Pr3+ -Co-doped CW fluorozirconate fiber laser operating at 2.7 µm, Int. J. Infrared Millimeter Waves 15, 1907 (1994) 238, 240 132. J. Schneider: Mid-infrared fluoride fiber lasers in multiple cascade operation, IEEE Photonics Technol. Lett. 7, 354 (1995) 238 133. P. S. Golding, S. D. Jackson, T. A. King, M. Pollnau: Energy-transfer processes in Er3+ -doped and Er3+ ,Pr3+ -codoped ZBLAN glasses, Phys. Rev. B 62, 856 (2000) 238, 240, 242 134. M. Pollnau, Ch. Ghisler, G. Bunea, M. Bunea, W. L¨ uthy, H. P. Weber: 150 mW unsaturated output power at 3 µm from a single-mode-fiber erbium cascade laser, Appl. Phys. Lett. 66, 3564 (1995) 239 135. M. Pollnau, Ch. Ghisler, W. L¨ uthy, H. P. Weber, J. Schneider, U. B. Unrau: Three-transition cascade erbium laser at 1.7, 2.7, and 1.6 µm, Opt. Lett. 22, 612 (1997) 239 136. J. Y. Allain, M. Monerie, H. Poignant: Energy transfer in Er3+ /Pr3+ -doped fluoride glass fibres and application to lasing at 2.7 µm, Electron. Lett. 27, 445 (1991) 240 137. L. Wetenkamp, G. F. West, H. T¨ obben: Co-doping effects in erbium3+ - and 3+ holmium -doped ZBLAN glass, J. Non-Crystal. Solids 140, 25 (1992) 240 138. M. Pollnau: The route toward a diode-pumped 1-W erbium 3 µm fiber laser, IEEE J. Quantum Electron. 33, 1982 (1997) 240 139. S. D. Jackson, T. A. King, M. Pollnau: Modelling of high-power diode-pumped erbium 3 µm fibre lasers, J. Mod. Opt. 47, 1987 (2000) 240 140. B. Srinivasan, J. Tafoya, R. K. Jain: High-power ‘watt-level’ CW operation of diode-pumped 2.7 µm fiber lasers using efficient cross-relaxation and energy transfer mechanisms, Opt. Express 4, 490 (1999) 240 141. S. D. Jackson, T. A. King, M. Pollnau: Efficient high power operation of erbium 3 µm fibre laser diode-pumped at 975 nm, Electron. Lett. 36, 223 (2000) 240, 242 142. M. Pollnau, R. Spring, Ch. Ghisler, S. Wittwer, W. L¨ uthy, H. P. Weber: Efficiency of erbium 3 µm crystal and fiber lasers, IEEE J. Quantum Electron. 32, 657 (1996) 241 143. Ch. Wyss, W. L¨ uthy, H. P. Weber, P. Rogin, J. Hulliger: Emission properties of an optimised 2.8 µm Er3+ :YLF laser, Opt. Commun. 139, 215 (1997) 241 144. M. Pollnau, R. Spring, S. Wittwer, W. L¨ uthy, H. P. Weber: Investigations on the slope efficiency of a pulsed 2.8 µm Er3+ :LiYF4 laser, J. Opt. Soc. Am. B 14, 974 (1997) 242 145. T. Jensen: Upconversion-Prozesse und Wirkungsquerschnitte in Er3+ -dotierten 3 µm Fluorid- und Granat-Lasern, gepumpt mit CW und quasi-CW Dioden-Arrays, Dissertation, University of Hamburg, Germany (1996) 242 146. M. Pollnau, S. D. Jackson: Energy recycling versus lifetime quenching in erbium-doped 3 µm fiber lasers, IEEE J. Quantum Electron. 38, 162 (2002) 242



253

147. B. Srinivasan, E. Poppe, J. Tafoya, R. K. Jain: High-power (400 mW) diodepumped 2.7 µm Er:ZBLAN fibre lasers using enhanced Er-Er cross-relaxation processes, Electron. Lett. 35, 1338 (1999) 242 148. T. Sandrock, D. Fischer, P. Glas, M. Leitner, M. Wrage, A. Diening: Diodepumped 1-W Er-doped fluoride glass M-profile fiber laser emitting at 2.8 µm, Opt. Lett. 24, 1284 (1999) 242 149. R. Reisfeld: Chalcogenide glasses doped by rare earths: structure and optical properties, Ann. Chim. Fr. 7, 147 (1982) 243 150. S. R. Bowman, L. B. Shaw, B. J. Feldman, J. Ganem: A 7 µm praseodymiumbased solid-state laser, IEEE J. Quantum Electron. 32, 646 (1996) 243 151. J. Schneider: Fluoride fibre laser operating at 3.9 µm, Electron. Lett. 31, 1250 (1995) 243 152. W. H. Dumbaugh, J. C. Lapp: Heavy-metal oxide glasses, J. Am. Ceram. Soc. 75, 2315 (1992) 243 153. T. Schweizer, B. N. Samson, J. R. Hector, W. S. Brocklesby, D. W. Hewak, D. N. Payne: Infrared emission from holmium doped gallium lanthanum sulphide glass, Infrared Phys. Technol. 40, 329 (1999) 243, 244 154. T. Schweizer, B. N. Samson, J. R. Hector, W. S. Brocklesby, D. W. Hewak, D. N. Payne: Infrared emission and ion–ion interactions in thulium- and terbium-doped gallium lanthanum sulfide glass, J. Opt. Soc. Am. B 16, 308 (1999) 243, 244 155. T. Schweizer, D. W. Hewak, B. N. Samson, D. N. Payne: Spectroscopic data of the 1.8-, 2.9-, and 4.3 µm transitions in dysprosium-doped gallium lanthanum sulfide glass, Opt. Lett. 21, 1594 (1996) 243, 244 156. D. W. Hewak, J. A. Medeiros Neto, B. N. Samson, R. S. Brown, K. P. Jedrzejewski, J. Wang, E. Taylor, R. I. Laming, G. Wylangowski, D. N. Payne: Quantum-efficiency of praseodymium doped Ga:La:S glass for 1.3 µm optical fibre amplifiers, IEEE Photonics Technol. Lett. 6, 609 (1994) 243 157. C. C. Ye, D. W. Hewak, M. Hempstead, B. N. Samson, D. N. Payne: Spectral properties of Er3+ -doped gallium lanthanum sulphide glass, J. Non-Cryst. Solids 208, 56 (1996) 243 158. T. Schweizer, D. J. Brady, D. W. Hewak: Fabrication and spectroscopy of erbium doped gallium lanthanum sulphide glass fibres for mid-infrared laser applications, Opt. Express 1, 102 (1997) 243 159. T. Schweizer, B. N. Samson, R. C. Moore, D. W. Hewak, D. N. Payne: Rareearth doped chalcogenide glass fibre laser, Electron. Lett. 33, 414 (1997) 243 160. M. Asobe, T. Ohara, I. Yokohama, T. Kaino: Fabrication of Bragg grating in chalcogenide glass fibre using the transverse holographic method, Electron. Lett. 32, 1611 (1996) 243 161. R. Mossadegh, J. S. Sanghera, D. Schaafsma, B. J. Cole, V. Q. Nguyen, R. E. Miklos, I. D. Aggarwal: Fabrication of single-mode chalcogenide optical fiber, J. Lightwave Technol. 16, 214 (1998) 243 162. T. M. Monro, Y. D. West, D. W. Hewak, N. G. R. Broderick, D. J. Richardson: Chalcogenide holey fibres, Electron. Lett. 36, 1998 (2000) 243


Index

absorption, 222–224, 228 – coefficient, 224, 228 bleaching, 231 branching ratio, 228 broadening (lifetime), 227 cascade lasing, 237, 239 ceramics, 222, 223 chalcogenide, 222, 243 – glass, 232, 243, 244 cladding – pumped, 223 co-dopant, 240 co-doped, 231, 236, 240 core pumped, 223, 226, 228 cross-relaxation, 231, 233, 235–237, 240 cross-section, 228, 238 double-clad – fiber, 224, 226, 240 – geometry, 239 – pump, 224 Dy3+ , 243, 244 electric-dipole – transition, 228 emission cross-section, 222, 223, 228, 230 emission spectra, 228 energy migration, 231, 232 energy recycling, 241, 242 energy transfer, 230–232, 235, 237, 240 – upconversion (ETU), 231, 240–242 energy-level scheme, 227, 233, 235, 237, 239, 240 Er3+ , 223, 227, 232, 243 excited-state absorption (ESA), 228, 230, 238, 239

fluoride, 230 fluoride fiber , 222 fluoride glass, 222 – fluoride, 222 four-level – CW laser, 234 – fiber laser, 237 – laser, 240 – – transition, 238 GaLaS (GLS), 221, 222, 243 ground-state, 231 – bleaching, 228, 240 – transition, 233, 236 ground-state absorption (GSA), 228, 231, 235, 238 heat, 226 Ho3+ , 232, 243, 244 lanthanide, 227 laser, 234 – self-terminating, 231 – three-level, 234, 238 – transition-metal-ion-doped, 226 lifetime, 228, 230, 231 – quenching, 226 loss, 221, 223, 224, 243, 244 multiphonon – relaxation, 220, 222, 226, 228, 230 multiplet, 227, 228 Nd3+ , 223, 225, 243, 244 nonradiative decay, 228, 230 numerical aperture, 224 oxides, 230, 243


Index parity, 228 phonon energy, 220–222, 230, 232, 243 Pr3+ , 240, 243, 244 Pr3+ -co-doped, 240 pump, 224 pump absorption, 224, 226, 228 pump cladding, 223, 224 quantum efficiency, 220, 222, 226, 230, 234, 240 quenching, 231, 233, 240, 244 radiative decay, 228, 230 radiative transition, 228 rare-earth ion, 222, 226–228, 231, 243, 244 rare-earth solubility, 222 rare-earth-doped – chalcogenides, 222 – fiber laser, 232 – heavy-metal oxide, 243 – solid-state laser, 230, 231 rate constant, 228, 230 reabsorption, 226, 230, 234 recycling, 239, 240 refractive index, 222, 224 – fluctuation, 224 resonator, 225, 230 self-terminating laser, 231

255

self-terminating transition, 237 sensitizing, 231, 235–237, 244 silica, 221 – glass, 232 silicate, 222 slope efficiency, 232, 236, 238–242 solubility, 220, 222 spectral-line broadening, 222, 227, 228 Stark, 227, 233, 238 – component, 238 – level, 234 stimulated emission, 228, 230 Stokes efficiency, 234, 238–240 sulfide fiber, 244 sulfide glass, 222 Tb3+ , 243 thermal conductivity, 221–223 three-level laser, 234, 238 threshold, 228, 230, 234–236, 240, 243 Tm3+ , 232, 235–237, 243 transition-metal ion, 223, 226 transition-metal-ion-doped laser, 226 transparency, 220–222, 232 tunability, 234, 235, 238 – of lasers, 228 Yb3+ , 223, 225, 237 ZBLAN, 221–223, 228, 230, 232, 243
