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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 27 — Dec. 17, 2012
  • pp: 28672–28682
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Optimization of femtosecond Yb-doped fiber amplifiers for high-quality pulse compression

Hung-Wen Chen, JinKang Lim, Shu-Wei Huang, Damian N. Schimpf, Franz X. Kärtner, and Guoqing Chang  »View Author Affiliations


Optics Express, Vol. 20, Issue 27, pp. 28672-28682 (2012)
http://dx.doi.org/10.1364/OE.20.028672


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Abstract

We both theoretically and experimentally investigate the optimization of femtosecond Yb-doped fiber amplifiers (YDFAs) to achieve high-quality, high-power, compressed pulses. Ultrashort pulses amplified inside YDFAs are modeled by the generalized nonlinear Schrödinger equation coupled to the steady-state propagation-rate equations. We use this model to study the dependence of compressed-pulse quality on the YDFA parameters, such as the gain fiber’s doping concentration and length, and input pulse pre-chirp, duration, and power. The modeling results confirmed by experiments show that an optimum negative pre-chirp for the input pulse exists to achieve the best compression.

© 2012 OSA

1. Introduction

Yb-doped fiber amplifiers (YDFAs) feature superior power scalability, high electrical-to-optical conversion efficiency, large single-pass gain (~30 dB), excellent beam quality, as well as compactness and robustness. To avoid detrimental effects from fiber nonlinearities (e.g., self-phase modulation (SPM), stimulated Raman scattering etc.) when amplifying ultrashort pulses, YDFAs normally operate in a low-nonlinearity regime using chirped pulse amplification (CPA) [1

1. D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 55(6), 447–449 (1985). [CrossRef]

, 2

2. A. Galvanauskas, “Mode-scalable fiber-based chirped pulse amplification systems,” IEEE J. Sel. Top. Quantum Electron. 7(4), 504–517 (2001). [CrossRef]

], in which the spectral bandwidth of the amplified pulse only changes slightly during the amplification.

2. Modeling nonlinear amplification of femtosecond pulses in YDFAs

Amplification of femtosecond pulses in an YDFA involves nonlinear interaction among the pump, signal (i.e., the input pulses to be amplified), and Yb-fiber. The process can be accurately modeled by coupling two sets of eqs [4

4. R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Sel. Top. Quantum Electron. 33(7), 1049–1056 (1997). [CrossRef]

6

6. J. Limpert, T. Gabler, A. Liem, H. Zellmer, and A. Tünnermann, “SPM-induced spectral compression of picosecond pulses in a single-mode Yb-doped fiber amplifier,” Appl. Phys. B 74(2), 191–195 (2002). [CrossRef]

]: (1) the steady-state propagation rate eqs. that treat the Yb-fiber as a two-level system and (2) the generalized nonlinear Schrödinger equation (GNLSE) that describes the evolution of the amplified pulses. Such a model, with all the modeling parameters experimentally determined, enables us to study and therefore optimize a femtosecond MOPA system.

YDFA can be pumped in the co-propagating scheme (i.e., pump and signal propagate in the same direction.), counter-propagating scheme (i.e., pump and seed propagate in the opposite direction.), or both. In this paper, we focus on co-propagating pumping scheme which is normally adopted in monolithic femtosecond nonlinear fiber amplifiers. Under this scenario and with amplified spontaneous emission (ASE) neglected, the model includes the following steady-state propagation-rate eqs [7

7. C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol. 9(2), 271–283 (1991). [CrossRef]

9

9. F. He, J. H. Price, K. T. Vu, A. Malinowski, J. K. Sahu, and D. J. Richardson, “Optimisation of cascaded Yb fiber amplifier chains using numerical-modelling,” Opt. Express 14(26), 12846–12858 (2006). [CrossRef] [PubMed]

]. and the GNLSE:

N2(t,z)t=[R12(λ,z)+W12(λ,z)]N1(t,z)[R21(λ,z)+W21(λ,z)+1/τ21]N2(t,z)N1(t,z)t=[R21(λ,z)+W21(λ,z)+1/τ21]N2(t,z)[R12(λ,z)+W12(λ,z)]N1(t,z)Pp(λ,z)z=Γp(λ)[σe(λ)N2(z)σa(λ)N1(z)]ρPp(λ,z)Ps(λ,z)z=Γs(λ)[σe(λ)N2(z)σa(λ)N1(z)]ρPs(λ,z).
(1)
Az=0g(ω)A˜(ω)eiωTdωβ22i2AT2+β363AT3+iγ(1+iω0T)(A(z,T)0R(t')|A(z,Tt')|2dt').
(2)

The nonlinear propagation of the signal pulse is governed by the standard GNLSE (i.e., Eq. (2)), taking into account the gain, dispersion, self-phase modulation, self-steepening, and stimulated Raman scattering. A(z,t), βn, γ, and ω0 are the amplitude of the slowly varying envelope of the pulse, n-th order fiber dispersion, fiber nonlinearity, and central frequency of the pulse, respectively. R(t) denotes both the instantaneous electronic and delayed molecular responses of silica molecules, and is defined as R(t) = (1-fR)δ(t) + fR12 + τ22)/(τ1τ22)exp(-t/τ2)sin(t/τ1) where fR, τ1, and τ2 are 0.18, 12.2 fs, and 32 fs, respectively [11

11. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2006).

]. The GNLSE is solved by the split-step Fourier method implemented using the fourth-order Runge-Kutta method in the interaction picture [12

12. J. Hult, “A fourth-order Runge–Kutta in the interaction picture method for simulating supercontinuum generation in optical fibers,” J. Lightwave Technol. 25(12), 3770–3775 (2007). [CrossRef]

] with adaptive step-size control [13

13. A. Heidt, “Efficient adaptive step size method for the simulation of supercontinuum generation in optical fibers,” J. Lightwave Technol. 27(18), 3984–3991 (2009). [CrossRef]

].

Table 1

Table 1. Amplifier Parameters Used in the Simulation

table-icon
View This Table
lists the key simulation parameters. For a single-mode step-index fiber with its fundamental mode approximated by a Gaussian, the overlap of the optical mode and ion distribution becomes Γ = 1-exp(−2a2/w2). a is the ion dopant radius or core radius and w the mode field radius at 1/e2 power intensity approximated by the Whitely model: w = a(0.616 + 1.66/V1.5 + 0.987/V6) [10

10. T. J. Whitley and R. Wyatt, “Alternative Gaussian spot size polynomial for use with doped fiber amplifiers,” IEEE Photon. Technol. Lett. 5(11), 1325–1327 (1993). [CrossRef]

], where V is the normalized frequency. The wavelength dependent emission cross-section σe and absorption cross-sections σa are adapted from Fig. 2
Fig. 2 (a) Pump and signal power as a function of Yb-fiber length. (b) RMS duration of the optimum compressed- pulse and the transform-limited pulse as a function of Yb-fiber length.
in Ref. 4

4. R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Sel. Top. Quantum Electron. 33(7), 1049–1056 (1997). [CrossRef]

.

3. Optimization of different amplifier parameters

3.1 Optimization of the pre-chirp

Figure 4
Fig. 4 (a) Optimum RMS duration of the compressed-pulse and the corresponding transform-limited RMS duration as a function of pre-chirping GDD for the input pulse. Insets: compressed pulses and transform-limited pulses for three different pre-chirp. (b) bandwith evolution inside the Yb-fiber amplifier. (c) output sepctra for three different pre-chirp.
summarizes the simulation results with the total GDD varying from −7 × 104 to 4 × 104 fs2 for pre-chirping the input signal pulse prior to amplification; hereafter, we refer to such GDD as pre-chirping GDD. While the transform-limited RMS duration (green, dashed line in Fig. 4(a)) slightly varies, the optimum RMS duration for the compressed pulse strongly depends on the pre-chirping GDD. Insets of Fig. 4(a) show the compressed pulse (blue, solid line) and transform-limited pulse (green, dashed line) for three different GDD: (I) −5 × 104 fs2, (II) 0, and (III) 1.9 × 104 fs2. Figure 4(b) illustrates the evolution of RMS bandwidth along the Yb-fiber for these three pre-chirping cases. For a negatively pre-chirped input-pulse (e.g., case I), its spectrum (blue line) experiences an initial spectral compression [5

5. M. Oberthaler and R. A. Höpfel, “Special narrowing of ultrashort laser pulses by self‐phase modulation in optical fibers,” Appl. Phys. Lett. 63(8), 1017–1019 (1993). [CrossRef]

,6

6. J. Limpert, T. Gabler, A. Liem, H. Zellmer, and A. Tünnermann, “SPM-induced spectral compression of picosecond pulses in a single-mode Yb-doped fiber amplifier,” Appl. Phys. B 74(2), 191–195 (2002). [CrossRef]

] and then subsequent spectral broadening. While the case II (i.e., zero pre-chirp) generates the broadest spectrum in terms of RMS bandwidth, both its transform-limited pulse and the optimum compressed-pulse are longer than the other two cases due to the existence of strong pedestals. This simulations suggests that varying the input pulse pre-chirp leads to different spectra, some of which exhibit considerable temporal pedestals that severely limit the quality of the compressed pulse. This can be clearly seen in Fig. 4(c), in which the output spectrum corresponding to negative pre-chirp (shown as blue curve) exhibits less steep wings than the other two cases; the resulting transform-limited pulse has minimal pedestals in general. In this case, there exists an optimum negative pre-chirping GDD that leads to a compressed pulse with the shortest duration close to its transform-limited duration (see case I inside Fig. 4(a)).

In fact, this phenomenon appears in mode-locked Yb-fiber oscillators as well. Depending on the amount of net cavity GDD, an Yb-fiber oscillator may operate in different mode-locking regimes (i.e., stretched-pulse, similariton, and dissipative soliton) [14

14. B. Ortaç, J. Limpert, and A. Tünnermann, “High-energy femtosecond Yb-doped fiber laser operating in the anomalous dispersion regime,” Opt. Lett. 32(15), 2149–2151 (2007). [CrossRef] [PubMed]

]. For a stretched-pulse Yb-fiber oscillator that features a net cavity GDD close to zero, the intra-cavity pulse prior to entering the gain fiber acquires negative chirp from dispersion over-compensation by optical elements with negative GDD (e.g., diffraction-grating pair, chirped fiber Bragg grating, and hollow-core photonic-crystal fiber). On the contrary, the intra-cavity pulse in similariton or dissipative soliton Yb-fiber oscillators exhibits positive chirp before entering the gain fiber. Our simulation results presented in Fig. 4, despite modeling a single-pass Yb-fiber amplifier, explains why stretched-pulse mode-locking produces better pulse quality than the other two regimes of mode-locking.

3.2 Optimization of the input power and optical bandwidth

Figure 5
Fig. 5 Calculated RMS duration for optimum compressed-pulse as a function of input signal power for five different spectral bandwidth corresponding to transform-limited pulse FWHM duration of 200 fs, 300 fs, 400 fs, 500 fs, and 600fs.
illustrates the optimum compressed duration versus input power for an input pulse with different transform-limited duration. The optimum compressed RMS duration occurs at ~20-mW input power, corresponding to a pulse energy of ~0.25 nJ. For an input power less than 20mW, the optimum compressed duration starts to increase significantly because the accumulated nonlinearity is too small to broaden the spectrum enough for achieving substantial pulse compression. Even for an input pulse duration of 500 fs, it can be compressed to 63 fs, a factor of 6.7 in RMS duration shortening. That is, as long as we apply a suitable pre-chirp, the RMS duration of the compressed pulse varies slightly as the transform-limited input pulse duration changes from 200 fs to 500 fs. These results indicate that, while the amplified output power is nearly the same (slight difference due to wavelength dependent emission/absorption cross-section) for all cases (~560 mW), the best compressed pulse is achieved by optimizing both the pre-chirp and the input power.

3.3 Optimization of the Yb-ion doping concentration

Furthermore, at 20-mW input seed power and 600-mW pump power, we study the effect of three different Yb-ion doping concentrations: 1025/3 m−3, 1025 m−3, and 3 × 1025 m−3. Varying the doping concentration allows us to better understand the interplay between nonlinearity and the amplifier gain. To get the same amplified power for these three cases, the fiber lengths are chosen to be 6 m, 2 m, 2/3 m, respectively since the amplified power is determined by the product of the Yb-fiber length and its doping concentration. Figure 6
Fig. 6 Calculated RMS duration of the optimum compressed pulse as a function of the FWHM pulse duration of the transform-limited Gaussian input pulse for three doping levels: blue-triangle curve for high doping at 1025/3 m−3; red-circle curve for medium doping at 1025 m−3; and black-square curve for low doping at 3 × 1025 m−3. The purple-diamond curve shows the compressed-pulse RMS duration obtained with a low-doping Yb-fiber amplifer seeded with transform-limited pulses.
shows that, for different transform-limited input-pulse duration, the optimized compressed pulse duration depends on Yb-fiber doping concentration. For a higher doping concentration with shorter fiber-length, the accumulated nonlinearity is reduced. This is a consequence of the reduced effective length of the amplifier. In general, Yb-fiber with higher doping concentration is preferred for the input signal pulse with shorter transform-limited duration.

For a long Yb-fiber (here 6 meters) with low doping concentration, the resulting nonlinear fiber amplifier works in a well-studied regime known as parabolic similariton amplification; that is, any input pulse to an amplifier constructed from sufficiently long Yb-fiber will asymptotically evolve into a positively chirped pulse with a parabolic temporal profile and propagates inside the fiber amplifier self-similarly [15

15. M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84(26), 6010–6013 (2000). [CrossRef] [PubMed]

, 16

16. V. I. Kruglov, A. C. Peacock, J. D. Harvey, and J. M. Dudley, “Self-similar propagation of parabolic pulses in normal-dispersion fiber amplifiers,” J. Opt. Soc. Am. B 19(3), 461–469 (2002). [CrossRef]

]. Most existing investigations employed a transform-limited pulse at the input, corresponding to the purple-diamond curve in Fig. 6. The curve shows that achieving shorter compressed pulses prefers longer transform-limited pulses at the fiber input for low-doped Yb-fibers. The compressed pulse duration can be further reduced if the input pulses are optimally pre-chirped; see the black-square curve in Fig. 6. Note that parabolic similariton amplification suffers from limited gain bandwidth and stimulated Raman scattering [17

17. G. Chang, A. Galvanauskas, H. G. Winful, and T. B. Norris, “Dependence of parabolic pulse amplification on stimulated Raman scattering and gain bandwidth,” Opt. Lett. 29(22), 2647–2649 (2004). [CrossRef] [PubMed]

]. These limitations have been numerically studied assuming a finite Lorentzian gain bandwidth [18

18. D. B. Soh, J. Nilsson, and A. B. Grudinin, “Efficient femtosecond pulse generation using a parabolic amplifier combined with a pulse compressor. II. Finite gain-bandwidth effect,” J. Opt. Soc. Am. B 23(1), 10–19 (2006). [CrossRef]

]. With the gain derived from the rate eq. in our model, we can perform a more accurate optimization of parabolic similariton amplification.

4. Experimental results on pre-chirp management for optimizing compressed pulse quality

In this section, we experimentally investigate the effect of input pulse pre-chirp on the compressed pulse quality after amplification. Figure 7
Fig. 7 Experimental set-up, OSC: oscillator, HP: half waveplate. M: mirror, G: Grating, LS: lens, FBS: fiber beam splitter, LD: laser diode, PBC: polarization beam combiner, WDM: wavelength division multiplexer, YDF: Yb doped fiber, QP: quarter waveplate, OSA: optical spectrum analyzer, AC: autocorrelator, P.M.: power meter.
schematically illustrates the experimental setup consisting of an Yb-fiber oscillator serving as a seed source, a diffraction-grating pair to adjust the pre-chirp of the input pulse launched into the Yb-doped fiber amplifier, and finally another diffraction-grating pair to compress the amplified pulse to the shortest pulse duration. The oscillator of 280-MHz repetition rate is passively mode-locked with a saturable Bragg reflector and cavity dispersion is managed by highly dispersive mirrors [19

19. H.-W. Chen, T. Sosnowski, C.-H. Liu, L.-J. Chen, J. R. Birge, A. Galvanauskas, F. X. Kärtner, and G. Chang, “Chirally-coupled-core Yb-fiber laser delivering 80-fs pulses with diffraction-limited beam quality warranted by a high-dispersion mirror based compressor,” Opt. Express 18(24), 24699–24705 (2010). [CrossRef] [PubMed]

]. The output pulse has a duration of 2.1 ps with ~6 nm FWHM bandwidth centered at 1030 nm. Since the pulse is positively chirped, use of a grating pair (600 grooves/mm) providing negative chirp allows to continuously tune the input-pulse pre-chirp from positive to negative by changing the separation of the grating pair. The pre-chirped pulses are coupled into the YDFA with >60% efficiency. The 10% tap from the splitter monitors the seed power into the YDFA including a 2-m Yb-fiber (Nufern, SM-YSF-LO) pumped by two laser diodes combined with a polarization beam combiner. The amplified pulses are compressed by the second grating pair to the shortest pulse duration.

With the fixed 20-mW input power, we achieved amplified pulses of 600-mW average power at 1-W pump power. We varied the pre-chirp by changing the separation of the first grating pair and then adjusted the second grating pair to compress the amplified pulses to its shortest FWHM duration measured by an autocorrelator. We recorded the compressed-pulse spectra as we varied pre-chirp and then calculated from these spectra the RMS duration of the transform-limited pulses. Such a RMS duration was plotted in Fig. 8(a)
Fig. 8 (a) Calculated RMS pulse duration of optimum compressed pulses from the measured spectrum (black scattered) and simulated curve (green line). The shortest autocorrelation (AC) trace is achieved at the lowest RMS pulse duration. τAC (FWHM) = 134 fs for a pre-chirping GDD of −6.3 × 104 fs2, τAC (FWHM) = 149 fs for −1.8 × 104 fs2, and τAC (FWHM) = 169 fs for 1 × 104 fs2 respectively. (b) The spectra corresponding to three AC traces in (a). The pulse has the largest spectral bandwidth and smoothest edge for the pre-chirping GDD of −6.3 × 104 fs2.
as a function of pre-chirping GDD. Figure 8(b) plots the input pulse spectrum (black dashed curve) and three compressed-pulse spectra corresponding to different pre-chirping GDD: −6.3 × 104 fs2 (black curve), −1.8 × 104 fs2 (blue curve), and 1.0 × 104 fs2 (red curve).

For all three cases, the input spectrum is broadened from ~6 nm to >20 nm. However, the shape of the amplified pulse spectra varies substantially with different pre-chirp, which in turn supports different transform-limited pulse duration. The black scattered curve shows that the minimum duration is achieved at a negative pre-chirping GDD of −6.3 × 104 fs2. Also plotted in Fig. 8(a) are the autocorrelation traces for the three compressed pulses corresponding to these three pre-chirping GDDs. The FWHM of these autocorrelation traces are 134 fs, 149 fs, and169 fs, respectively. Apparently, the best compression quality occurs at the pre-chirping GDD of −6.3 × 104 fs2 with a measured autocorrelation trace of 134-fs, suggesting a de-convolved pulse of ~100-fs. Deviation from this optimum pre-chirp degrades the compressed-pulse quality featuring an increased temporal pedestal. The spectra in Fig. 8(b), similar to the results shown in Fig. 4(c), show that, as we vary the pre-chirping GDD from the optimum value of −6.3 × 104 fs2 to −1.8 × 104 fs2 and then to 104 fs2, the corresponding spectra start to develop sharper edges, which leads to larger pedestal for the compressed pulses. Note that there are two sections of HI1060 single mode fiber before (2.45m) and after (0.33 m) the YDFA. These two fibers would introduce excessive nonlinearity and hence further optimization of other parameters other than pre-chirp is needed to achieve even shorter pulse duration.

5. Conclusion and discussion

In this paper, we use a model —which couples the steady-state propagation-rate eqs. and the GNLSE—to study nonlinear amplification of femtosecond pulses in Yb-fiber amplifiers configured in the co-pumping scheme. We investigated these femtosecond Yb-fiber amplifiers to achieve better compressed pulse quality by optimizing the parameters, such as the input pulse pre-chirp and power, input pulse bandwidth, and Yb-fiber doping concentration. The results show that, in general, a negative pre-chirp exists to achieve the best compression which is verified experimentally.

The presented study has practical applications. For example, we recently demonstrated a fundamentally mode-locked Yb-fiber oscillator emitting ~206 fs pulses with 15-pJ pulse energy and 3-GHz repetition rate [20

20. H.-W. Chen, G. Chang, S. Xu, Z. Yang, and F. X. Kärtner, “3 GHz, fundamentally mode-locked, femtosecond Yb-fiber laser,” Opt. Lett. 37(17), 3522–3524 (2012). [CrossRef] [PubMed]

]. Stabilization of the oscillator’s repetition rate and the carrier-envelope phase offset will result in a femtosecond frequency comb with 3-GHz line spacing. Such a large line spacing is desired in many spectral-domain applications, e.g., frequency combs optimized for precision calibration of astronomical spectrographs [21

21. C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1.,” Nature 452(7187), 610–612 (2008). [CrossRef] [PubMed]

26

26. G. G. Ycas, F. Quinlan, S. A. Diddams, S. Osterman, S. Mahadevan, S. Redman, R. Terrien, L. Ramsey, C. F. Bender, B. Botzer, and S. Sigurdsson, “Demonstration of on-sky calibration of astronomical spectra using a 25 GHz near-IR laser frequency comb,” Opt. Express 20(6), 6631–6643 (2012). [CrossRef] [PubMed]

]. Stabilization of the carrier-envelope phase offset using the well-known 1f-2f heterodyne detection technique involves generation of low-noise supercontinuum using ~100-fs (or even shorter) pulses with ~1-nJ pulse energy. Both our theoretical and experimental results enable us to construct an optimized Yb-fiber amplifier followed by a proper compressor to achieve these pulse requirements from the initially long (~206 fs) and weak (15 pJ) oscillator pulses.

Acknowledgment

This work was supported by the National Aeronautics and Space Administration (NASA) through grants NNX10AE68G, NNX09AC92G and by the National Science Foundation (NSF) through grants AST-0905592 and AST-1006507 and the Center for Free-Electron Laser Science.

References and links

1.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 55(6), 447–449 (1985). [CrossRef]

2.

A. Galvanauskas, “Mode-scalable fiber-based chirped pulse amplification systems,” IEEE J. Sel. Top. Quantum Electron. 7(4), 504–517 (2001). [CrossRef]

3.

S. A. Diddams, “The evolving optical frequency comb,” J. Opt. Soc. Am. B 27(11), B51–B62 (2010). [CrossRef]

4.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, “Ytterbium-doped fiber amplifiers,” IEEE J. Sel. Top. Quantum Electron. 33(7), 1049–1056 (1997). [CrossRef]

5.

M. Oberthaler and R. A. Höpfel, “Special narrowing of ultrashort laser pulses by self‐phase modulation in optical fibers,” Appl. Phys. Lett. 63(8), 1017–1019 (1993). [CrossRef]

6.

J. Limpert, T. Gabler, A. Liem, H. Zellmer, and A. Tünnermann, “SPM-induced spectral compression of picosecond pulses in a single-mode Yb-doped fiber amplifier,” Appl. Phys. B 74(2), 191–195 (2002). [CrossRef]

7.

C. R. Giles and E. Desurvire, “Modeling erbium-doped fiber amplifiers,” J. Lightwave Technol. 9(2), 271–283 (1991). [CrossRef]

8.

C. R. Giles and E. Desurvire, “Propagation of signal and noise in concatenated erbium-doped fiber optical amplifiers,” J. Lightwave Technol. 9(2), 147–154 (1991). [CrossRef]

9.

F. He, J. H. Price, K. T. Vu, A. Malinowski, J. K. Sahu, and D. J. Richardson, “Optimisation of cascaded Yb fiber amplifier chains using numerical-modelling,” Opt. Express 14(26), 12846–12858 (2006). [CrossRef] [PubMed]

10.

T. J. Whitley and R. Wyatt, “Alternative Gaussian spot size polynomial for use with doped fiber amplifiers,” IEEE Photon. Technol. Lett. 5(11), 1325–1327 (1993). [CrossRef]

11.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2006).

12.

J. Hult, “A fourth-order Runge–Kutta in the interaction picture method for simulating supercontinuum generation in optical fibers,” J. Lightwave Technol. 25(12), 3770–3775 (2007). [CrossRef]

13.

A. Heidt, “Efficient adaptive step size method for the simulation of supercontinuum generation in optical fibers,” J. Lightwave Technol. 27(18), 3984–3991 (2009). [CrossRef]

14.

B. Ortaç, J. Limpert, and A. Tünnermann, “High-energy femtosecond Yb-doped fiber laser operating in the anomalous dispersion regime,” Opt. Lett. 32(15), 2149–2151 (2007). [CrossRef] [PubMed]

15.

M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, “Self-similar propagation and amplification of parabolic pulses in optical fibers,” Phys. Rev. Lett. 84(26), 6010–6013 (2000). [CrossRef] [PubMed]

16.

V. I. Kruglov, A. C. Peacock, J. D. Harvey, and J. M. Dudley, “Self-similar propagation of parabolic pulses in normal-dispersion fiber amplifiers,” J. Opt. Soc. Am. B 19(3), 461–469 (2002). [CrossRef]

17.

G. Chang, A. Galvanauskas, H. G. Winful, and T. B. Norris, “Dependence of parabolic pulse amplification on stimulated Raman scattering and gain bandwidth,” Opt. Lett. 29(22), 2647–2649 (2004). [CrossRef] [PubMed]

18.

D. B. Soh, J. Nilsson, and A. B. Grudinin, “Efficient femtosecond pulse generation using a parabolic amplifier combined with a pulse compressor. II. Finite gain-bandwidth effect,” J. Opt. Soc. Am. B 23(1), 10–19 (2006). [CrossRef]

19.

H.-W. Chen, T. Sosnowski, C.-H. Liu, L.-J. Chen, J. R. Birge, A. Galvanauskas, F. X. Kärtner, and G. Chang, “Chirally-coupled-core Yb-fiber laser delivering 80-fs pulses with diffraction-limited beam quality warranted by a high-dispersion mirror based compressor,” Opt. Express 18(24), 24699–24705 (2010). [CrossRef] [PubMed]

20.

H.-W. Chen, G. Chang, S. Xu, Z. Yang, and F. X. Kärtner, “3 GHz, fundamentally mode-locked, femtosecond Yb-fiber laser,” Opt. Lett. 37(17), 3522–3524 (2012). [CrossRef] [PubMed]

21.

C.-H. Li, A. J. Benedick, P. Fendel, A. G. Glenday, F. X. Kärtner, D. F. Phillips, D. Sasselov, A. Szentgyorgyi, and R. L. Walsworth, “A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s-1.,” Nature 452(7187), 610–612 (2008). [CrossRef] [PubMed]

22.

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23.

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25.

T. Wilken, G. L. Curto, R. A. Probst, T. Steinmetz, A. Manescau, L. Pasquini, J. I. González Hernández, R. Rebolo, T. W. Hänsch, T. Udem, and R. Holzwarth, “A spectrograph for exoplanet observations calibrated at the centimetre-per-second level,” Nature 485(7400), 611–614 (2012). [CrossRef] [PubMed]

26.

G. G. Ycas, F. Quinlan, S. A. Diddams, S. Osterman, S. Mahadevan, S. Redman, R. Terrien, L. Ramsey, C. F. Bender, B. Botzer, and S. Sigurdsson, “Demonstration of on-sky calibration of astronomical spectra using a 25 GHz near-IR laser frequency comb,” Opt. Express 20(6), 6631–6643 (2012). [CrossRef] [PubMed]

OCIS Codes
(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(140.3280) Lasers and laser optics : Laser amplifiers

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: October 12, 2012
Revised Manuscript: November 28, 2012
Manuscript Accepted: November 28, 2012
Published: December 10, 2012

Citation
Hung-Wen Chen, JinKang Lim, Shu-Wei Huang, Damian N. Schimpf, Franz X. Kärtner, and Guoqing Chang, "Optimization of femtosecond Yb-doped fiber amplifiers for high-quality pulse compression," Opt. Express 20, 28672-28682 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-27-28672


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