Simultaneous direct amplification and compression ... - OSA Publishing

Simultaneous direct amplification and compression of picosecond pulses to 65-kW peak power without pulse break-up in erbium fiber ∗

J. C. Jasapara1 , M. J. Andrejco1 , J. W. Nicholson1 , A. D. Yablon1 , and Z. Várallyay2 1. OFS Laboratories, 19 Schoolhouse Rd., Somerset, NJ 08873. 2. FETI Ltd., Késmárk utca 24-28, H-1158 Budapest, Hungary. jasapara@ofsoptics.com

Abstract: Picosecond pulses at 1.56 µmm wavelength are directly amplified with a diffraction limited beam quality in a core-pumped Er fiber with an 875 µm2 effective area. The interplay between nonlinear spectral broadening and anomalous fiber dispersion compresses the input pulse duration during amplification so that 42 nJ energy pulses with ∼ 65 kW peak power are achieved without pulse break-up. © 2007 Optical Society of America OCIS codes: (060.2320) Fiber optics amplifiers and oscillators; (060.2410) Erbium fiber.

References and links 1. M. E. Fermann, A. Galvanauskas, and G. Sucha, Ultrafast Lasers – Technology and Applications (Marcel Dekker, New York, 2003). 2. J. W. Nicholson, A. Yablon, P. Westbrook, K. Feder, and M. Yan, “High Power, Single Mode, All-Fiber Source of Femtosecond Pulses at 1550 nm and its Use in Supercontinuum Generation,” Opt. Express 12, 3025–3034 (2004). 3. G. Lin, Y. Lin, and C. Lee, “Simultaneous Pulse Amplification and Compression in All-Fiber-Integrated PreChirped Large-Mode-Area Er-Doped Fiber Amplifier,” Opt. Express 15, 2993–2999 (2007). 4. J. Limpert, A. Liem, M. Reich, T. Schreiber, S. Nolte, H. Zellmer, A. Tünnermann, J. Broeng, A. Petersson, and C. Jakobsen, “Low-Nonlinearity Single -Transverse-Mode Ytterbium-Doped Photonic Crystal Fiber Amplifier,” Opt. Express 12, 1313–1319 (2004). 5. L. Dong, J. Li, and X. Peng, “Bend-Resistant Fundamental Mode Operation in Ytterbium-Doped Leakage Channel Fibers with Effective Areas Upto 3160 µm2 ,” Opt. Express 14, 11512–11519 (2006). 6. S. Ramachandran, J. W. Nicholson, S. Ghalmi, M. F. Yan, P. Wisk, E. Monberg, and F. V. Dimarcello, “Light Propagation with Ultralarge Modal Areas in Optical Fibers,” Optics Letters 31, 1797–1799 (2006). 7. G. P. Agrawal, in Nonlinear Fiber Optics (Academic Press, 1995), Chap. (5) Optical Solitons, (11) Fiber Amplifiers. 8. K. J. Blow, N. J. Doran, and D. Wood, “Generation and Stabilization of Short Soliton Pulses in the Amplified Nonlinear Schrödinger Equation,” J . O p t . S o c . A m . B 5, 381–390 (1988). 9. A. Shirakawa, J. Ota, M. Musha, K. Nakagawa, K. Ueda, J. R. Folkenberg, and J. Broeng, “Large-Mode-Area Erbium-Ytterbium-Doped Photonic-Crystal Fiber Amplifier for High-Energy Femtosecond Pulses at 1.55 µm,” Opt. Express 13, 1221–1227 (2005). 10. J. W. Nicholson, R. S. Windeler, and D. J. DiGiovanni, “Optically Driven Deposition of Single-Walled CarbonNanotube Saturable Absorbers on Optical Fiber End-Faces,” Opt. Express 15, 9176–9183 (2007). 11. J. Jasapara, M. J. Andrejco, A. D. Yablon, J. W. Nicholson, C. Headley, and D. DiGiovanni, “Picosecond Pulse Amplification in a Core Pumped Large-Mode-Area Erbium Fiber,” Optics Letters 32, 2429–2431 (2007). 12. M. E. Fermann, “Single-Mode Excitation of Multimode Fibers with Ultrashort Pulses,” Optics Letters 23, 52–54 (1998).

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Received 29 Aug 2007; revised 22 Oct 2007; accepted 28 Oct 2007; published 11 Dec 2007

24 December 2007 / Vol. 15, No. 26 / OPTICS EXPRESS 17494

13. J. M. Fini, “Bend-Resistant Design of Conventional and Microstructure Fibers with Very Large Mode Area,” Optics Express 14, 69–81 (2006). 14. P. V. Mamyshev and S. V. Chernikov, “Ultrashort-pulse propagation in optical fibers,” Opt. Lett. 15, 1076-1078 (1990). 15. G. P. Agrawal, “Optical pulse propagation in doped fiber amplifiers,” Phys. Rev. A 44, 7493-7501 (1991). 16. C. R. Giles and E. Desurvire, “Modeling Erbium-Doped Fiber Amplifiers,” Journal of Lightwave Technology 9, 271–283 (1991).

1.

Introduction

Modelocked fiber lasers are a compact alternative to bulk-optic laser systems. However the high nonlinearity experienced by short pulses due to the tight mode confinement limits the pulse peak powers of typical modelocked fiber oscillators to ∼ 1 kW [1]. Higher pulse energies and peak powers are required for most applications and therefore the pulses must be amplified. Chirped pulse, and parabolic pulse amplification have been effectively used to overcome the nonlinear limit to generate sub-picosecond pulses with micro-joule level pulse energies [1]. Both these techniques require pulse compression in bulk media after amplification, which is undesirable for applications requiring an alignment-free compact footprint. Many nonlinear microscopy and spectroscopy applications require ∼ 10 kW level peak powers, with smaller pulse energies of a few tens of nanojoule. This can be achieved with simpler laser systems employing direct amplification of pulses (i.e. without the use of additional pulse stretcher or compressor elements) from an oscillator. Fiber laser-amplifier systems using small core fibers for pulse compression have generated subpicosecond pulses with peak powers in excess of 100 kW, albeit with severe nonlinear pulse distortion where a large fraction of energy lies in the pedestals of the pulse [2]. Lin et.al. [3] have generated pedestal-free 56-fs pulses with 46-kW peak power but with low pulse energy of 2.6 nJ. For direct amplification to high pulse energies the fiber must be designed to, (i) have a large mode area to mitigate nonlinear distortions, and (ii) support single mode operation. The fiber designs demonstrated recently include “rod-like” photonic crystal fibers [4], “leaky channel” microstructured fiber [5], and higher-order-mode fiber [6], all of which enable large effective areas > 2000 µm2 while maintaining single mode operation. A 1000 µm2 area Yb doped photonic crystal fiber amplified 10-ps pulses at 1 µm wavelength to 65-kW peak power with low nonlinear pulse distortion [4]. In the 1.5 µm wavelength region, since material dispersion dominates over waveguide dispersion in large mode area fibers, the amplification occurs in the anomalous dispersion regime. Effects such as modulation instability, and nonlinear soliton-effect pulse compression due to the interplay between self-phase-modulation and anomalous dispersion, cause pulse break-up and limit the achievable peak power. Simultaneous amplification and nonlinear pulse compression has been exploited to achieve high peak powers [7, 8]. For example 700 fs pulses were compressed to 100 fs during amplification in a 26 µm mode field diameter Er-Yb doped crystal fiber to achieve 7.4-nJ energy, and 54-kW peak power, although with significant pulsepedestals that extended several picoseconds beyond the main 100-fs width central peak [9]. Whereas pedestals may be acceptable for certain applications such as continuum generation, other applications such as time resolved pump-probe spectroscopy, and ranging require pulses with high temporal integrity. In this paper we examine the generation of high energy and peak power pulses at 1.56 µm through direct amplification in the soliton compression regime. One picosecond duration pulses are amplified to a diffraction limited output using a single-clad large-mode-area (LMA) Er fiber with 875 µm2 effective area. The large area raises the peak power threshold for pulse break up. Record 42-nJ pulse energy and 65-kW peak powers are achieved in pedestal-free subpicosecond pulses at the tip of the fiber. Different amplifier lengths are analyzed to explore the #87025 - $15.00 USD

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balance between nonlinearity and dispersion. Our observations are verified through nonlinear Schrödinger equation simulations [7] which include gain. 2.

Experimental setup

Our all-fiber laser-amplifier system is shown in Fig. 1. Picosecond pulses were generated in a modelocked Erbium fiber laser that used a carbon nanotube layer sandwiched between fiber connectors to provide saturable absorption [10]. It was followed by a single mode Er fiber amplifier which delivered pulses of 1.06-ps duration with 0.136-nJ energy at a repetition rate of 22 MHz. The spectrum was centered at 1562 nm and had a 2.4 nm full width at half maximum (FWHM). Er–doped fiber

mode matched splice

70/30 splitter

Mode locked ps fiber laser FC/ APC

980 nm

PC isolator

carbon nanotube layer

SM Er amp

Er 45/125

1480/1550 WDM

1480 nm Raman fiber laser

915 nm

Booster amplifier

Fig. 1. Schematic of picosecond modelocked laser and amplifier system. Laser is followed by a single mode (SM) Er amplifier and the booster amplifier comprising the LMA Er fiber. PC: Polarization controller; FC/APC: fiber connector.

An LMA Er fiber with a 45/125 µm core/clad diameter was used in the final amplifier stage [11]. It had a step index profile with a numerical aperture of 0.17, effective area Aeff ∼ 875 µm2 , and an absorption of ∼ 12 dB/m at 1480 nm. Its dispersion, calculated from the measured index profile, was D = 22 ps/nm-km. A 8-W, 1480 nm Raman fiber laser, pumped by 915 nm multimode diodes, was used to pump the LMA fiber. A 1480/1550 nm fused fiber coupler coupled the pump and signal into the LMA Er fiber through a fiber based mode transformer that matched the fundamental modes between the two fibers at both pump and signal wavelengths. The fundamental mode propagation of both pump and signal minimizes the number of amplified spontaneous emission (ASE) modes supported and maximizes gain for the fundamental mode. As shown in [11] the amplifier had a near Gaussian beam quality with a measured M 2 = 1.05 ± 0.05 demonstrating single mode operation. The susceptibility for mode coupling decreases with increase in the difference in mode propagation constants, which in turn is proportional to λ /d 2 , where λ is the wavelength of light, and d is the diameter of the core [12] – therefore operation with a stable output mode at λ = 1.55 µm is possible in these large core diameters compared to amplifiation in Yb doped fibers operating at λ = 1.0 µm. The Er fiber was loosely coiled in a diameter > 30 cm to minimize bend induced reduction in effective area [13]. 3.

Amplifier performance results

Amplification in three LMA Er fiber lengths of L1 = 2.3 m, L2 = 2.8 m, and L3 = 3.9 m are presented. The pulse intensity autocorrelation, average power, and spectrum were monitored as the pump power was increased either to the maximum pump level or to the level where pulse breakup was evident in the autocorrelation. To avoid nonlinear distortions, the pulses were freespace coupled into an optical spectrum analyzer. The fraction of power in the signal (versus the #87025 - $15.00 USD

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unused pump) was calculated from the spectrum. Figure 2 shows the increase in average power Pav , and pulse energy E p (E p = Pav /Rr , where Rr is the pulse repetition rate), as a function of the 1480-nm pump power, and the accompanying decrease in the FWHM of the autocorrelation, for Er lengths L1 , L2 , and L3 . 45 36

600

27

400

18 L1=2.3 m L2=2.8 m L3=3.9 m

200

(a)

0 0

1

2

3

4

5

6

7

pump power (W)

9 0 8

autocorrelation FWHM (fs)

800

from oscillator

1600

pulse energy (nJ)

average power (mW)

1000

1400 1200

L1=2.3 m L2=2.8 m L3=3.9 m simulation

1000 800 600 400 200 0

(b) 0

5 10 15 20 25 30 35 40 45 pulse energy (nJ)

Fig. 2. (a) Average power and pulse energy versus 1480 nm pump power, and (b) decrease in autocorrelation FWHM with pulse energy, for various LMA Er lengths.

3.1.

Amplifier gain length L3 = 3.9 m

With an LMA Er fiber length of L3 = 3.9 m, the energy extraction was efficient, but limited by the onset of pulse breakup. Figure 3(a) shows the spectra recorded at various pulse energies. Self phase modulation broadened the spectrum with increase in pulse energy. Simultaneously the anomalous dispersion of the fiber compressed the new spectral components resulting in temporal shortening, as shown by the measured autocorrelations at various pulse energies in Fig. 3(b). With an increase in pulse energy the correlation narrowed to a triangular form consistent with higher order soliton pulse compression [7]. At an energy of E p = 27 nJ (average power 590 mW), the pulse reached its shortest duration before break-up. The FWHM of the correlation peak was 260 fs which translates to a duration of 168 fs if a Sech pulse shape is assumed (the transform limited pulse duration calculated from the spectrum is 121 fs). At a higher pulse energy of 38.5 nJ, the modulation in the autocorrelation indicates pulse breakup. A clear pedestal formed around a central peak of width 109 fs which corresponds to a 71 fs duration if a Sech pulse shape is assumed. The nonlinear Schrödinger equation, detailed in section 4, was used to simulate the experimental conditions. The calculated evolution of the pulse shape with increase in pulse energy is shown in Fig. 4(a). A nonlinear parameter γ = (2πn2 )/(λc Aeff ) = 2.4×10−4 W−1 m−1 , gave the best agreement with experimental observations. The value of γ used is higher than the expected value γ = 1.38 × 10−4 W−1 m−1 for Aeff = 875 µm2 , and n2 = 3 × 10−20 m2 W−1 – the discrepancy is probably due to uncertainties in n2 , the exact gain length, reduction in mode area due to fiber coiling [13], and higher order effects not included in our model. The crosses in Fig. 2 (b) show the FWHM of the autocorrelation obtained by multiplying the simulated pulse FWHM with the correlation factor 1.543 relevant for Sech shaped pulses. From our simulations we calculated the root-mean-square pulse width at 27 nJ pulse energy to be ∼ 540 fs which implies that ∼ 50 kW peak power (defined as the ratio of pulse energy to the FWHM pulse duration) was obtained before the onset of pulse break-up. Figure 4(b) shows the calculated evolution of pulse energy and duration as a function of position along the amplifier length, when the final output pulse energy is ∼ 39 nJ (circles) and 27 nJ (squares). The graph demonstrates that substantial pulse compression sets in for positions greater than 3 m into the fiber. #87025 - $15.00 USD

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(a)

Ep = 38.5 nJ

1.0

amplitude (arb. units)

normalized amplitude

1.0 0.5 0.0 1.0 0.5 0.0 1.0 0.5 0.0 1.0 0.5 0.0 1.0 0.5 0.0

Ep = 26.9 nJ

Ep = 20.5 nJ Ep = 8.6 nJ

(b)

oscillator Ep=8.6 nJ Ep=20.5 nJ Ep=26.9 nJ Ep=38.5 nJ

0.8 0.6 0.4 0.2

Ep = 0.6 nJ

1520

1540

1560

1580

0.0 -4

1600

wavelength (nm)

-3

-2

-1

0

1

2

3

4

1.0 0.5 0.0 1.0 0.5 0.0 1.0 0.5 0.0 1.0 0.5 0.0 1520

(c)

Ep = 42.2 nJ



delay (ps)

Ep = 27.7 nJ

Ep = 17.3 nJ

1560

1580

0.6 0.4

-3

-2 -1

0

1

2

3

4

5

2

3

4

5

delay (ps)

Ep = 1 nJ Ep = 24.7 nJ

1.0

(e)



0.8

0.0 -5 -4

1600

wavelength (nm)

1.0

(d)

0.2

Ep = 0.6 nJ 1540

1.0

0.5

(f)

0.8 0.6 0.4 0.2

0.0 1520

1540

1560

1580

wavelength (nm)

1600

0.0 -5 -4 -3 -2 -1

0

1

delay (ps)

Fig. 3. (a)&(b), (c)&(d), and (e)&(f): Spectra, and intensity autocorrelation pairs, recorded for LMA Er lengths of L3 = 3.9 m, L2 = 2.8 m, and L1 = 2.3 m respectively. For L3 the dramatic change in autocorrelations with pulse energies are shown in (b). For lengths L2 and L1 the autocorrelations recorded (solid line) at the highest pulse energies and the simulated (crosses) autocorrelation assuming a Sech shaped pulse of duration 648 fs and 683 fs respectively are shown in (d) and (f).

3.2.


The Er fiber was cut to length L2 = 2.8 m to maximize the pulse energy and reduce the solitoneffect compression which leads to the formation of pedestals and eventual break-up. Figure 3(c) shows the spectral broadening with pulse energy. At this length, consistent with expectations from our simulations, the pulse energy could be increased without significant compression over the entire pump power range. A maximum pulse energy (average power) of ∼ 42 nJ (928 mW) was achieved. The pulse compression saturated to a minimum correlation FWHM of 980 fs (solid line in Fig. 3(d)). The correlation is narrower near the center and broader in the wings #87025 - $15.00 USD

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1.2

40

1.0

35

pulse FWHM Tp (ps)

0.8 0.6 0.4 0.2 0 −4 −3 −2 −1 0

1

2

duration (ps)

3

4 0

5

40 30 35 20 25 10 15 pulse energy (nJ)

(a)

30 0.8

25

0.6

20 15

0.4

10 0.2

5

pulse energy Ep (nJ)

normalized power (arb. units)

1

0

0.0 0

1

2

3

4

amplifier position (m)

(b)

Fig. 4. Simulation results for amplifier length L3 = 3.9 m. (a) Calculated pulse shape evolution as a function of output pulse energy. (b) Evolution of pulse energy and duration along the amplifier length when the output pulse energy is 26.9 nJ (squares) and 38.5 nJ (circles).

when compared to a Sech pulse of the same duration (crosses in Fig. 3(d)). A deconvolution factor of 1.51 for estimating the pulse duration from the measured correlation was calculated from the correlation of a bandwidth limited pulse calculated from the measured spectrum. The shortest pulse duration achieved with L2 was 648 fs, which is three times longer than the transform limited duration of 202 fs calculated from the recorded spectrum. The pulse peak power was therefore ∼ 65 kW which is a record for pedestal-free sub-picosecond pulses at 1.5 µm wavelength. Since the exact pulse shape is not known, the peak power is approximated as the pulse energy divided by the FWHM pulse duration. The chirped pulses could potentially be further compressed in an external compressor to achieve higher peak intensities. 3.3.


With an Er length of L1 ∼ 2.3 m, both nonlinear, and dispersion effects were relatively small. The spectrum broadened only slightly with increase in pulse energy as shown in Fig. 3(e) while the pulse compression saturated to a minimum duration of 683 fs (Fig. 3(f)). A maximum pulse energy (average power) of ∼ 25 nJ (543 mW) was obtained, and the corresponding peak power was ∼ 37 kW. This near linear regime of amplification is attractive when low spectral and temporal distortions are desirable. 4.

NLSE simulation

We used the split-step Fourier (SSF) method to numerically solve a simplified form of the well known generalized nonlinear Schrödinger equation (GNSE) (see Ref. [14]) valid for pulse durations >> 10-fs and given by [7],     gain disp. z }| {  ∂ E(z,t) g(z, ω) i i ∂ ∂ |E|2   ∂ 2E   = E − β2 + ig(z, ω0 )T22  2 + iγ |E|2 E + |E|2 E − TR E , | {z } ∂z 2 2 ∂t ω ∂t ∂t   0 | {z } | {z } | {z } SPM gain SRS | {z } self−steepening | {z } GDD nonlinearity

(1) where t is the retarded time, and E(z,t) is the complex field envelope. See Table 1 for definitions and values of the various variables used in the simulation. #87025 - $15.00 USD

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Table 1. Parameter list used for modeling pulse amplification in the LMA Er fiber.

Parameter Center wavelength FWHM Average power Repetition rate Overlap factor Wavelength Power Overlap factor Length Background loss (@λc ) Background loss (@λ p ) Dispersion (@λc ) Nonlinear refractive index Nonlinear parameter Raman adjustable param. No.1 Raman adjustable param. No.2 Fractional Raman contribution Fluorescence lifetime Dipole relaxation time Er concentration Radius of the doped region Number of polarization states

Symbol Pulse parameters λc TFWHM Pav Rr Γsk Pump parameters λp Pp Γ pk Fiber parameters L αs αp D = − 2πc β λc2 2 n2 γ τ1 τ2 fR τ T2 CEr3+ Reff m

Magnitude

Unit

1562 1.1 3 22 0.8

nm ps mW MHz

1480 variable: 0.9-2.2 0.8

nm W

3.9 0.25 4 22 3.8 × 10−20 2.4 × 10−4 12.2 32 0.18 10 60 1.6 × 1025 22.5 2

m dB/km dB/km ps/(nm·km) m2 /W W−1 m−1 fs fs ms fs m−3 µm

The effects of gain g(z, f ), group delay dispersion (GDD), gain dispersion (treated as in Ref. [15]), Kerr nonlinearities, and stimulated Raman scattering (SRS) were included in the model. The first moment of the nonlinear response function associated with stimulated Raman scattering (SRS) effect was calculated as, Z ∞ 2 τ1 + τ22 t t TR ≈ fR t sin exp − dt. (2) τ1 τ22 τ1 τ2 0 To determine gain accurately as a function of frequency at position z in the doped fiber, we subdivide every SSF segment in the numerical algorithm and solve the power evolution equation together with a two-level rate equation [16] over the SSF segment. The analytical expression for the metastable population (N2 ) in the steady-state approximation is, !, ! Γk σak τ Γk (σak + σek )τ Pk 1+∑ Pk , (3) N2 = CEr3+ ∑ 2 h fk R2eff π k h f k Reff π k where CEr3+ is the concentration of the erbium-ions, Γk is the overlap integral between the optical modes and the erbium ions where k denotes the kth frequency component ( fk ), σak and σek are the absorption and emission cross section for the erbium respectively. τ is the #87025 - $15.00 USD

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fluorescence lifetime for the metastable level, h is the Planck constant, Reff is the effective core radius and Pk is the optical power at the kth frequency component. The corresponding power evolution equations are given by, dPk = Γk (σak + σek )N2 Pk − (Γk σakCEr3+ + αk )Pk dz

(4)

for the signal and pump, and dPk = Γk (σak + σek )N2 Pk + Γk σek N2 mh fk ∆ fk − (Γk σakCEr3+ + αk )Pk dz

(5)

for the amplified spontaneous emission (ASE), where m is the number of the polarization states, ∆ f is the bandwidth used for ASE calculation, and αk is the background loss of the fiber without the doping ions. These equations are solved by a fourth order Runge-Kutta (RK) algorithm in each SSF segment. Finally the gain parameter in each SSF segment was calculated as Pk (z + ∆z) ∆z , (6) g(z, fk ) = ln Pk (z) where ∆z is the size of the SSF segment. 5.

Summary

In summary, we have demonstrated simultaneous amplification and compression of picosecond pulses in a large-mode-area Erbium fiber amplifier. Using an amplifier fiber with approximately three times the Aeff used previously [9], we have achieved 42 nJ energy and 65 kW peak power in pedestal-free pulses which is a record for directly amplified sub-picosecond pulses in a fiber in the 1.5 µm wavelength range. Our amplifier system provides a simple all-fiber approach to boosting ultrashort fiber oscillator pulse energies and peak powers.

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