1. Introduction

Fiber-based amplification is becoming a desirable platform for generating high energy pulses [1]. Advantages over bulk solid-state systems include compactness and reduction of complex components. However, owing to the small effective area of the fiber core as well as the long interaction length (typically a few meters), Kerr nonlinearity, i.e. self-phase modulation (SPM), poses limitations on pulse energy and quality. To avoid nonlinear effects, chirped-pulse amplification (CPA) is typically employed where pulses are stretched before amplification to reduce peak power and compressed afterward. However, because pulses can only be practically stretched to ~ 1 ns, nonlinearites may still degrade pulse energy and quality. We note that it only takes approximately one radian of accumulated SPM before pulses exhibit noticeable broadening and distortion [2]. Compensation of SPM therefore may prove to be a highly valuable tool in extending fiber-based CPA systems to a higher performance. Compensation has been demonstrated in the past through various techniques such as the use of the negative nonlinear index n₂ of semiconductor materials [3], spatial light modulators (SLM) in a pulse-shaping configuration [4,5], and residual third-order dispersion (TOD) [6,7].

An alternative route for compensating SPM in a fiber-based CPA system is to use a temporal pulse shaping technique based on electro-optic (EO) phase modulators. We recently used this technique to compensate 1.0 π of SPM in a fiber-based CPA system [8]. The advantages of the technique are its simple construction, compatibility with existing fiber CPA system, and nearly complete removal of SPM. In this paper, we demonstrate that by employing the RF waveform synthesizing technique [9] to generate the driving signal of the EO phase modulator, SPM compensation up to 2.0 π can be achieved. The use of RF waveform synthesis allows the compensation of higher values of SPM due to the availability of narrow band, high power RF amplifiers. Furthermore, because narrow band, high power RF amplifiers are relatively inexpensive, waveform synthesis technique also reduces the cost of SPM compensation.

2. Experiment and result

 

Fig. 1. Experimental setup. C: circulator, G: grating, L: lens, M: mirror, D: RF delayline, A: variable-gain RF amplifier, PD: photo-detector, BP: band-pass filter at 10 GHz, FD: frequency doubler, DCF: dispersion compensating fiber, PM: phase modulator. The inset in the lower left corner shows the measured optical pulse after stretching and the synthesized electrical signal.

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The experimental setup is shown in Fig. 1. The pulsed source is a mode-locked fiber laser (IMRA; femtolite) producing 0.08 nJ, 370 fs pulses at a center wavelength of 1556 nm and a repetition rate of 50 MHz. Pulses were stretched to ~ 33 ps by a grating stretcher and pre-amplified by an erbium doped fiber amplifier (EDFA) to account for some of the loss in the stretcher and following SPM compensation device. To compensate the dispersion of the fibers in the system, five meters of dispersion compensating fiber was placed after the pre-amp. The SPM compensator consisted of a phase modulator driven by a RF waveform synthesizer (outlined by the dashed box in Fig. 1). The synthesized RF signal was obtained by first deriving a 10 GHz RF tone from the optical pulse train using a combination of a 10 GHz photo-detector (Discovery; DSC-R402) and a narrow band RF band-pass filter with a center frequency near 10 GHz. This technique is similar to conventional clock recovery in optical communications and provides an RF tone that is an integer multiple of the laser repetition rate. We then generate a 20 GHz tone (second harmonic of the recovered 10 GHz tone) using a frequency doubler, and combine it with the original 10 GHz tone [9]. By adjusting the amplitudes and phases of the 10 and 20 GHz tones, we can generate a 10 GHz repetition rate RF pulse train with a pulse shape closely matching that of the stretched optical pulse (inset in Fig. 1). Two independent sets of variable-gain RF amplifiers and RF delaylines were used in the synthesizer setup in order to facilitate the waveform adjusting process. When the sign, phase, and amplitude of the synthesized RF signal are correctly tuned, the phase modulator pre-compensates each pulse with the desired amount of “negative SPM”. After SPM pre-compensation, pulses were amplified from 0.02 nJ to 13 nJ by a commercial EDFA (IPG; EAU-1-C) where they simultaneously acquire ~ 2.0 π of SPM. The optical signal was then compressed by the grating compressor and measured by a second order autocorrelator.

 

Fig. 2. Second order interferometric autocorrelation traces at high power (pulse energy: 13 nJ) (a) without SPM compensation, (b) with 1.0 π rad compensation, (c) with 2.0 π rad compensation, and (d) at low power (pulse energy: 0.4 nJ) with negligible nonlinearity. The deconvolved pulse widths (FWHM) are indicated in the plots. The deconvolution factor for a Gaussian pulse was used because the measured optical spectrum before the high power amplifier was approximately Gaussian.

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Second order interferometric autocorrelation traces with and without SPM compensation are measured in order to demonstrate the concept of the device. For all cases, the grating stretcher and compressor were fixed in a matched configuration in which the compressor grating separation was determined by maximizing the two-photon photocurrent of a silicon diode (Thorlabs; SM05PD1A) at low output pulse energy (0.4 nJ), and therefore with negligible nonlinearity. At high output optical power after amplification (13 nJ pulses), we measured that the best pre-compensation RF drive has a peak-to-peak voltage of 9.1 V, corresponding to approximately 2V_π of the EO phase modulator at 10 GHz. Figure 2(a) shows the second order autocorrelation trace at 13 nJ pulse energy without SPM compensation (RF amplifiers off), 2(b) shows the trace for 1.0 π SPM compensation, 2(c) shows the trace for 2.0 π SPM compensation, and 2(d) shows the trace at low power (0.4 nJ pulses) with negligible nonlinearity. Significant pulse distortion and broadening were present without the SPM pre-compensation (Fig. 2(a)). However, by applying the correct amount of SPM compensation, nearly distortion free amplification can be achieved (Fig. 2(c)). The significant reduction in pulse broadening and distortion clearly demonstrates the effectiveness of our SPM compensation technique. We have also performed numerical modeling of our experimental setup using the standard split-step Fourier transform method with the measured optical spectrum before the high power amplifier as the simulation input (using the spectral phase calculated from the dispersion of the stretcher). The simulated results are shown here on the right side of Fig. 2. A good agreement between experiments and simulations was obtained.

 

Fig. 3. Optical spectrum of CW light modulated by (a) experimentally, and (b) numerically synthesized RF signal with 2.0 π amplitude.

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To further verify that the SPM that has been compensated is indeed 2.0 π, we experimentally measured the optical spectrum of a CW DFB laser modulated by the synthesized RF signal, Fig. 3(a), and compared that with the numerical simulation result, Fig. 3(b). The excellent match between the experimentally measured and numerically simulated optical spectrum gives an extra confirmation that 2.0 π of nonlinear phase shift from SPM has been compensated in our experimental demonstration.

 

Fig. 4. (a) Measured and (b) simulated autocorrelation trace for a nonlinear phase shift of 2.0 π rad and an optimally mismatched grating compressor. The deconvolved pulse widths (FWHM) are indicated in the plots.

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Partial SPM mitigation can be obtained by deliberately mismatching the grating compressor with the stretcher. However, the resulting pulse quality is significantly worse than that obtained using the SPM compensation technique demonstrated here. Figure 4(a) shows the measured autocorrelation trace for the system with 2.0 π radians of SPM and an optimally mismatched grating compressor by adjusting the grating separation distance of the compressor to maximize the two-photon photocurrent. Calculated result from the simulation is shown in Fig. 4(b). Figure 4 shows that the pulse width for this configuration is 25% broader than that with the SPM compensation and a matched stretcher-compressor system. In addition, a significant amount of pulse energy resides in the incompressible side-lobes. Note that as the nonlinear phase shift increases, the technique of using residual dispersion from a mismatched compressor will become even less effective, as we have verified numerically.

Waveform synthesis with two RF frequencies was used in our experimental demonstration to remove the SPM because the close match between the electrical and optical pulses ensures nearly distortion free pulse amplification. The improvement in pulse quality using the waveform synthesis is evident when compared to that of a SPM compensator with a single RF frequency (i.e. without waveform synthesis). Figure 5 shows the numerical simulation results of the pulse intensity profile with and without waveform synthesis, using the measured optical spectrum as the simulation input. Although the pulse width is only 2% broader in the case of SPM compensation with a single RF tone (10 GHz), the side-lobe increases by nearly a factor of 10, and there is a corresponding increase in the pulse energy that resides in the incompressible wings. We note, however, the effectiveness of the single-tone compensator depends on the shape of the optical spectrum. For example, our simulation indicated that a single-tone compensator will be more effective if the optical pulse has a Gaussian rather than a Sech spectrum. Thus, SPM compensators with a single RF frequency drive can be effective if the optical spectrum of the pulse happens to match well with a sinusoidal waveform, further reducing the complexity of the compensation scheme. On the other hand, waveform synthesis with more than two RF frequencies can also be employed to improve the matching of the electrical and optical waveforms, leading to even higher quality output pulses. In practice, numerical calculations can provide effective guidance for such a compromise between simplicity and performance so that an optimized SPM compensation scheme can be designed to meet the system requirement.

 

Fig. 5. Simulated pulse intensity profile with 2.0 π of SPM compensated by (a) waveform synthesized signal, and (b) single-tone 10 GHz signal. The pulse widths (FWHM) are indicated in the plots.

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3. Conclusion

In summary, we have demonstrated the removal of 2.0 π radians of nonlinear phase shift in a fiber-based CPA system by using an electro-optic phase modulator to emulate negative n₂ and an RF waveform synthesis technique. Our SPM compensator is all-fiber, and can readily be integrated into existing fiber CPA systems. Our technique uses cost-effective narrow band, high power RF amplifiers, and can thus compensate higher values of SPM than previously demonstrated [8]. Finally, we note that RF waveform synthesis is particularly suited for small pulse stretching (~ 33 ps in this work), allowing a more compact CPA system as well as an increased tolerance to effects from higher order dispersion. Although the experimental demonstration compensates SPM at wavelength of 1550 nm, our technique can be extended to other wavelengths such as 1.3 um and 1.06 um, where fiber amplifiers and efficient electro-optic phase modulators are both available.

The authors gratefully acknowledge IMRA America for loaning the fiber laser, and valuable discussions with James van Howe and Prof. Frank W. Wise.