We demonstrate an all-fiber Er chirped pulse amplification (CPA) system based on compression in photonic band gap fiber (PBGF) that produces 570 fs pulses with 310 nJ pulse energy. The dispersion of the PBGF is measured precisely and used to design a dispersion-matched nonlinearly-chirped fiber Bragg grating stretcher. We analyze the trade-offs of such all-fiber CPA system design and compare different PBGFs in terms of the derived figure of merit. Such system architecture should be scalable to few micro-Joule level pulse energies close to the compressor nonlinearity limit when PBGFs with improved figure of merit become available.
©2004 Optical Society of America
Fiber-based chirped pulse amplification (CPA) laser systems delivering micro-Joule-level pulses offer high integration level that results in an unprecedented robustness and compactness as suitable for commercial applications . However, because of damage effects due to high peak powers of compressed pulses, until recently the only practical choice for the compressor in a high energy CPA system had been a bulk diffraction grating arrangement.
Recently developed photonic band gap fibers (PBGF) [2–5] exhibit very low nonlinearity, about 1000 times less than that of conventional solid-core fibers . Because of their large group delay dispersion (GDD) and low nonlinearity, PBGFs can be used for high energy pulse compression, as was demonstrated recently [6–8], promising the ultimate integration of micro-Joule-level fiber CPA systems. An all-fiber CPA system based on a large-mode-area (LMA) Yb-doped fiber amplifier and a 2-m-long PBGF compressor delivered 100 fs pulses with 82 nJ pulse energy . All-fiber CPA systems based on single-mode Er-doped fibers and 10-m-long PBGF compressors so far delivered substantially lower energies, 0.1 nJ (Ref. ) and 7 nJ (Ref. ), in about 1 ps compressed pulses.
In this paper we report an all-fiber Er CPA system based on amplification in an LMA fiber delivering 310-nJ, 570-fs linearly-polarized output. The dispersion of the PBGF compressor was measured precisely and used to design a dispersion-matched nonlinearly-chirped fiber Bragg grating (FBG) stretcher. We analyze the trade-offs of such all-fiber CPA system design and compare different PBGFs in terms of the derived figure of merit. The demonstrated system architecture should be scalable to pulse energies close to the compressor nonlinearity limit (estimated as few micro-Joules) when PBGFs with improved figure of merit become available.
2. All-fiber CPA system design considerations
In CPA  substantial stretching of the seed pulses allows for higher pulse energies while keeping the amplifier at below its the peak power limit [10, 11]. Hence in the all-fiber CPA based on compression in the PBGF, the compressor length must be long enough to provide the necessary GDD. However, fundamentally the third-order dispersion (GDD slope) of PBGFs is considerably greater than that of conventional solid-core fibers [3, 7] that are typically used for pulse stretching in fiber CPA systems. This mismatched third-order dispersion leads to the pulse quality deterioration  and effectively limits how much the pulses can be stretched. To overcome this limitation and allow for longer PBGFs, here we use a dispersion-matched nonlinearly-chirped FBG stretcher, the approach recently demonstrated in a fiber CPA with a bulk diffraction grating compressor .
The PBGFs demonstrated so far have substantial propagation losses that appear to be due to the technological but not the fundamental limitations as evidenced by recent progress [4, 13]. While the use of longer stretched pulses allows for extraction of higher pulse energies from fiber amplifiers, the longer length of the PBGF required for compression leads to the increased propagation loss. Specifically, assuming a linear (dispersive) pulse compression in the PBGF (i.e. for peak powers below the nonlinearity limit as discussed further) the pulse energy, U, output from the all-fiber CPA system is
where P peak is the peak power limit of the fiber amplifier, β the excess loss between the amplifier and the PBGF (isolators, splicing/coupling, etc.), D is the GDD of the PBGF, Δλ is
the pulse bandwidth, and α is the propagation loss in dB per unit length. In writing Eq. (1) we assume that the total PBGF dispersion is dominated by the GDD term and that the FBG stretcher matches the total PBGF dispersion, including the higher-order terms. The optimum PBGF length that maximizes the pulse energy is then L opt=10/[ln(10)α]. We note that for the PBGF compressor of optimum length the total PBGF propagation loss is 10/ln(10)≈4.3 dB. For such optimal choice of the compressor length, Eq. (1) reduces to
where FOM=1.60D/α is the figure of merit of the PBGF compressor.
Table 1 compares several published PBGFs in terms of their FOM for pulse compression. The PBGF reported in Ref.  by BlazePhotonics has by far the best FOM because of its record low loss. However, due to the coupling to surface modes, the low-loss region is limited to about 5 nm. The long PBGF length required for an optimum compressor (Table 1) would probably be prohibitively expensive currently as well as would raise concerns about present manufacturing capabilities, which undoubtedly will improve in the future. The second highest FOM belongs to the BlazePhotonics HC-1550-2 fiber at 1650 nm, however this wavelength is far from the main gain band of Er. In the present paper we used the Crystal Fibre AIR-10-1550 PBGF that has a high loss but simultaneously a large dispersion resulting in the third best FOM (Table 1).
As it follows from Eq. (2) the maximum pulse energy obtainable from the all-fiber CPA system based on a PBGF with a given FOM depends on other CPA system parameters. The achievable P peak and Δλ may in turn depend on the choice PBGF, particularly the length of the stretched pulses as dictated by the optimal compressor length. Depending on the chirp of the stretched pulses and the GDD of the amplifier fiber, spectral narrowing or broadening may occur. The peak power limit of the power amplifier is usually due to the self-phase-modulation and is mainly governed by the amplifier core size, length and gain. With the caveat that scaling from the published results may not be trivial we calculate the obtainable pulse energies using Eq. (2) and assume identical system parameters, P peak=15 kW, Δλ=10 nm, and β=2 dB, for optimized compressor designs based on different PBGFs as listed in Table 1.
The ultimate limit on the pulse energy from the PBGF compressor is set by its nonlinearity. To estimate the maximum pulse energy that a PBGF compressor can support, we calculate the B-integral assuming that a strongly-stretched pulse is compressed to the bandwidth limit. Intuitively, we expect the dominant contribution to the B-integral coming from about a dispersion length at the very end of the PBGF compressor, where the pulse peak power is the highest. For this B-integral calculation we assume a Gaussian pulse as it allows for an analytical treatment, resulting in
where γ is the effective nonlinearity, P(z) is the propagation-dependent peak power, P 0 is the peak power of the compressed pulse, L eff the effective length of the PBGF compressor L eff=0.36L D ln(2N), and L D=(2πc/λ2)(Δ/D) is the dispersion length of the PBGF compressor, N=Δτ/Δτ 0 is the pulse compression ratio, where Δτ and Δτ 0 are the stretched and the compressed pulse lengths (FHWM), respectively. We note that ln(2N) is a relatively slowly-varying function of N; for example, for N=10 its value is 3.0 and for N=100 its value is 5.3. Thus we approximate ln(2N)≈4 resulting in
Requiring that the B-integral is B~2, we calculate the energy that the PBGF compressor can support without significant pulse distortions due to nonlinear effects as
It is interesting to note that despite the higher peak power of shorter pulses, U NL is larger because L eff is shorter. We are aware of only one experimental measurement of the PBGF nonlinearity in Ref. , γ~2.1×10-8 1/(W cm). With the caveat that the nonlinearity parameter depends on the PBGF design, we use Eq. (5) to estimate the nonlinearity-limited pulse energy obtainable from a PBGF-based CPA assuming Δλ~10 nm and D~1 ps/(nm m) as U NL~2.5 µJ.
3. Photonic band gap fiber
In our experiments we used the PBGF fabricated by Crystal Fibre (AIR-10-1550). We found that the PBGF showed a large second-order polarization mode-dispersion (PMD) manifesting itself as a wavelength-dependent rotation of the birefringence principal axis. This led to the output pulses showing irregular structure and being not compressible when the PBGF was used in transmission. It appears that similar effects had been observed Refs. [7, 8], where the authors improved the compressed pulse length  and quality  by actually truncating the bandwidth with a 3 nm bandpass filter. To overcome the PMD problem here we used a standard approach of double-passing the PBGF with a Faraday rotator mirror.
The PBGF propagation loss of α=0.16 dB/m was determined with the cut-back method. Thus the optimum length for compression is L opt=10/[ln(10)α]=27 m. We used a shorter effective PBGF length, 18.6 m (i.e. double-passed 9.3 m). With this PBGF length from Eqs. (1) and (2) we expect the output pulse energy be only 6% lower than for a compressor of optimum length, but with the propagation loss (3.0 dB) noticeably lower than that of an optimum compressor (4.3 dB).
To design the dispersion-matched nonlinearly-chirped FBG stretcher , the dispersion of the PBGF was precisely measured with the low-coherence interferometry technique [15, 16], with the setup similar to that of Ref. . We measured the PBGF in the same double-pass configuration with the Faraday rotator mirror that later was used in the CPA experiments. Figure 1 (a) shows the measured group delay per unit length versus wavelength in the range of 1540–1565 nm. We least-squares fitted the data with a third-order polynomial, τ=a 1(λ-λ0)+a 2(λ-λ0)2/2+a 3(λ-λ0)3/6, where λ0=1557 nm, resulting in the fit coefficients a 1=0.940 ps/(nm m) (GDD), a 2=2.9×10-2 ps/(nm2 m) (GDD slope) and a 3=8.4×10-4 ps/(nm3 m). The dispersion, D=dτ/dλ, was extracted by taking the analytical derivative of the fit and is shown in Fig. 1 (b). The accuracy of this measurement is estimated to be 1%. We also measured an adjacent piece from the same fiber spool and observed the dispersion to be larger by 6%.
The nonlinearly-chirped FBG was fabricated using an optimized UV interferometric writing technique. Apodization was achieved by dithering the phase of the interference pattern so that the average refractive index is kept constant along the FBG length. The 11-cm long FBG had a reflectivity bandwidth of 25.5 nm centered at 1557 nm with peak reflectivity of 50%. The FBG had a group delay ripple of better than 2 ps.
4. All-fiber CPA experimental setup and results
We constructed the all-fiber Er CPA system as shown in Fig. 2. The short-pulse seed source was a commercial Femtolite laser  producing 400 fs pulses at 1557 nm at 50 MHz repetition rate with 60 pJ pulse energy. To avoid optical feedback, we used an isolator after the laser as well as between different stages of the system as shown in Fig. 2. The pulses were then coupled through a 50/50 fused fiber splitter to the nonlinearly-chirped FBG and stretched to about 100 ps. After the splitter assembly we placed about 60 m of SMF28 fiber that was used for fine adjustments of the system dispersion to produce the shortest pulses at the output. The stretched pulses were then amplified to about 2 nJ (108 mW average power) in a single-mode Er-doped fiber preamplifier. We used a double-pass configuration with a Faraday rotator mirror and a polarizing beam splitter. The preamplifier fiber was 15 m long and was pumped with 280 mW from a laser diode at 1480 nm. The repetition rate was then reduced to 0.5 MHz with a pigtailed acousto-optic modulator (AOM). A second Er-doped single-mode fiber preamplifier increased the average power to 40 mW. This preamplifier was based on 4.5 m of polarization maintaining Er fiber counter-pumped with 200 mW from a laser diode at 1480 nm. The pulses were further amplified in the power amplifier based on 2.5 meters of LMA Er/Yb-doped fiber with a 30 µm core size. The power amplifier was v-groove counter-pumped with a 4 W diode at 980 nm. Finally, the pulse compressor was based on 9.3 m of the PBGF (double-passed) with a Faraday rotator mirror and a bulk polarizing beam splitter (PBS). The compressor had an overall transmission of 28%, which included 3.0 dB PBGF propagation loss, 0.86 dB coupling loss from the LMA power amplifier to the PBGF, and the rest of the losses due to other components in the beam path.
First we tested the system performance at low gain, at below the threshold for nonlinear effects in the power amplifier. The autocorrelation trace for 73 nJ pulses shown in Fig. 3 has a width of 1.04 ps. We calculated an autocorrelation for a transform-limited pulse based on the 6.2-nm wide pulse spectrum as also shown in Fig. 3. The experimental autocorrelation is about 50% wider than the transform-limited autocorrelation indicating a small amount of uncompensated third-order dispersion in the system, estimated as 0.03 ps3. Using the deconvolution factor of 1.63 as calculated for the transform-limited pulse we estimate the compressed pulse width as 640 fs.
At higher gain we obtained 685 mW average power (1.37 µJ pulse energy) output from the power amplifier, from which we estimate the peak power of about 14 kW. At the output of the PBGF compressor we obtained 310 nJ pulse energy (155 mW average power). To obtain the shortest compressed pulses the length of the SMF28 fiber was reduced slightly from the low gain measurements. From the autocorrelation width of 930 fs (Fig. 3) we estimate the pulse width of 570 fs assuming the deconvolution factor of 1.63. The peak power of the compressed pulses is thus estimated as 550 kW. The compressed pulse spectrum is shown in Fig. 4 and has the bandwidth of about 7.0 nm. The increased temporal pedestal and slight spectral broadening as compared to the low gain measurements are due to the self-phase modulation in the power amplifier. The pulse spectra measured before and after the compressor revealed no indication of nonlinear effects in the PBGF. The system output is linearly-polarized, with the polarization extinction ratio of better than 32 dB.
In conclusion, we reported an all-fiber CPA system architecture based on pulse stretching in a nonlinearly-chirped FBG and compression in a PBGF. In an Er based system with an LMA power amplifier we achieved 570 fs pulses with 310 nJ pulse energy, which is several times higher than pulse energy previously achieved in Er-based systems [7, 8] as well as in Yb based systems . The demonstrated system architecture should be directly scalable to few micro-Joule pulse energy levels when improved PBGFs become available.
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