A simple, stable, and tunable optical pulse source emitting 3.2 ps pulses at a 10 GHz repetition rate is presented. The pulses are obtained through soliton-assisted time-lens compression in a standard single mode fiber, and are fully characterized by wavelength-conversion frequency-resolved optical gating. The use of nonlinear effects relaxes the constraint of the high driving voltage on the phase modulator usually required in this type of source.
©2005 Optical Society of America
Stable sources of picosecond or femtosecond range optical pulses are required for a wide variety of applications including telecommunications, biological imaging, and direct laser inscription. Such pulses are generated routinely by use of different techniques: gain switching, active or passive modelocking, external pulse carving. These techniques respectively suffer from the following drawbacks: residual chirp, instability, and fixed duty ratio. Recently, an extension of the external pulse carving method was demonstrated to be a promising candidate to generate short pulses at high repetition rates, overcoming the duty ratio problem by a time-lens compression stage . A time lens, in analogy to a spatial lens, works by imposing a quadratic phase on an incoming electric field in time instead of space. The concept of time imaging was first demonstrated in bulk optics to generate picosecond pulses [2, 3]. The integrated optics implementation utilizes sinusoidally driven LiNbO3 phase modulators to generate this phase profile. The technique was recently taken a step further to generate alternate multi-wavelength pulses by using several CW lasers and an additional phase modulation step to correct aberrations . In this method, the compression ratio is governed by the amplitude of the phase modulation, which implies the use of high power RF amplifiers to obtain shorter pulses  and/or the special design of low half-wave voltage phase modulators .
In this paper, we demonstrate that the time lens can, in fact, be combined with nonlinear soliton compression to generate 3.2 ps pulses at a 10 GHz repetition rate without using special components or additional phase aberration correction, and at a low driving voltage. The nonlinear regime is simply reached by adding an amplification stage prior to the injection in the standard singlemode fiber (SMF). The appropriate choice of the compression fiber length is optimized using frequency-resolved optical gating (FROG) characterization of the output pulses. The FROG measurement also give access to both intensity and phase profiles of the compressed pulses.
2. Linear compression
The experimental setup is shown in Fig. 1. By imposing a quadratic temporal phase on the signal before launching it in a dispersive element, a phenomenon formally equivalent to the focusing of a beam by a lens in space occurs in the time domain, resulting in the compression of the pulse. Initial pulses are carved in a tunable external cavity laser diode (GN Nettest Tunics Plus) CW signal by a LiNbO3 intensity modulator (Photline MX-LN-10) driven by an electrical signal at 10 GHz in a 50% duty cycle configuration, i. e. biased at half transmission and driven with a V π peak-to-peak signal. The phase modulator (Sumitomo T.PM1.5-40) is driven by the same sinusoidal signal such that the peak-to-peak phase swing is 2.17 π. By modelling the pulse at the output of both modulation stages as a chirped Gaussian pulse and applying the well-known rules of propagation in a dispersive medium, the optimal compression length and compression ratio are found to be z ≈ 2/(β 2Ω2 ϕpp) and T 0/T≈π 2 ϕpp/(8ln2). In these equations, β2 is the group velocity dispersion parameter of the compression fiber, Ω is the electrical modulation angular frequency, and ϕpp is the peak-to-peak phase variation imparted on the optical signal. This result holds for large phase modulation depths. These equations are conveniently used to obtain first estimates of the optimal parameters, and show that the compression ratio is proportional to the phase modulation depth. Therefore, to obtain short pulses, previous implementation of this method have used driving voltages of up to 40V, limited by the damage threshold of the LiNbO3 modulator.
In the experimental setup, a variable delay allows the synchronization of the phase and intensity modulations to select the desired sign of chirp. An erbium-doped fiber amplifier (Keopsys BT-C-30-PB-FA) is located after the modulation stage to tune the power launched in the compression fiber. The compression fiber is standard single mode fiber (Corning SMF-28), with dispersion D=17.5 ps.nm-1.km-1 at 1550 nm, dispersion slope DS=0.09 ps.nm-2.km-1, and nonlinear parameter γ=1.1 W-1 km-1. The length of the compression fiber can be adjusted between 0 and 8 km in 100m increments. At the output of the source, the pulses are characterized using a frequency-resolved optical gating setup similar to the one described in ref. . The main difference is that the dispersion-shifted fiber was replaced by a 1 km-long span of zero dispersion, low dispersion slope highly nonlinear fiber (OFS DK-SMF). The retrieval error was less than 0.005 on a 128×128 grid in all cases, indicating a good accuracy of the method. This allowed the characterization of subpicosecond pulses over the whole C band with a high sensitivity.
Figure 2 shows the intensity profile of pulses compressed linearly for three SMF lengths: 3 km, 5 km, and 7 km. Equations (1) and (2) predict an optimal distance z=3.6 km and T/T 0=12.1. We obtain experimentally z=4.6 km and T/T 0=5. The large difference can be explained by the fact that the phase modulation is not perfectly parabolic. To get better estimates, simulations based on simple models of the modulators and on the numerical resolution of the nonlinear Schrodinger equation that governs the propagation in the compression fiber were performed, giving an optimal distance z=4.3 km and a compression ratio of T/T 0=5.5, in good agreement with the experiment. The shortest pulse full width at half maximum (FWHM) is 10.6 ps, with a FWHM time-bandwidth product of 0.6. Figure 3 shows the pulse phase profiles obtained after the same three lengths. The inversion of the chirp sign is clearly observed. The phase is fairly flat for the shortest pulse, although satellite pulses exhibit a π phase shift, which is also observed in simulations. Reduction of these satellites is possible through aberration correction  or appropriate filtering .
3. Soliton compression
By increasing the power at the input of the anomalous dispersion compression fiber, one expects self-compression phenomena based on Nth order soliton compression. This phenomenon has been extensively studied in the case of unchirped input pulses. Compression of chirped pulses using competing anomalous group-velocity dispersion and self-phase modulationwas proposed  and demonstrated  in an amplfiying medium. In this case, an analytical solution to the propagation problem exists. In an unamplified medium, however, no analytical tool exists, and numerical simulations were carried out to evaluate the optimum compression length and compression ratios. Theoretical studies  suggest that chirped pulse might be optimal to reach high compression ratio and good energy transfer from the initial condition to the final pulse. In our configuration, the simulations suggest that compression into a well identified pulse occurs for average input powers up to 400 mW, and the compression ratio increases with power. Beyond this point, multiple pulses are created simultaneously. The average input power is set to 200 mW in the experiment, and all other parameters are the same as in the linear compression experiment.
For this input power, simulations predict an optimal distance z=3.2 km and compression ratio T/T 0=17.8. The intensity profile of compressed pulses obtained in the experiment for three SMF lengths (3.0 km, 3.4 km, and 3.8 km) are plotted on fig. 4, while the corresponding phase profiles are plotted in fig. 5. The optimum distance and maximum compression ratio are found to be z=3.4 km and T/T 0=15.6, with a FWHM pulse width of 3.2 ps and a FWHM time-bandwidth product of 0.46, indicating a nearly chirp-free pulse. The peak power at this point is estimated to be 4.9 W, a little below the soliton power corresponding to this pulse width Psol=5.6 W. The inversion of the chirp sign as the pulse propagates is observed as in the linear case. We also notice the presence of satellites, and a π phase jump corresponding to the leading satellite. We estimate that the accumulated nonlinear phase shift up to the optimal compression point is 5.1 rad.
To assess the stability of this pulse source, we measured the timing and relative power jitters in the linear and nonlinear compression regimes, using the histogram function of a 40 GHz sampling oscilloscope (Tektronix CSA8000). In the linear case, σP/Pav=2.35.10-2 and σt=1.09 ps. In the nonlinear case, σP/Pav=6.95.10-2 and σt=1.10 ps. In both cases, the timing jitter is dominated by the accuracy of the oscilloscope time base, which places an upper bound on the timing jitter of the pulses. Going from linear to nonlinear compression, we observe an increase in power jitter, which is not surprising since a nonlinear mechanism is used to compress the pulses, enhancing slight power differences. The relative power jitter is nonetheless low enough for most applications.
The proposed setup can be seen as a mixed fiber-grating compressor and soliton compressor. In the first two kilometers, the chirped pulses have low peak power and the compression is essentially linear, making the system similar to a fiber-grating compressor where the phase modulator plays the role of the fiber and the grating is replaced by the dispersive fiber. Nonlinear effects progressively increase as the pulse gets linearly compressed, and are dominant in the final kilometer, making the system more similar to a soliton compressor, even though pulses are chirped througout the compression process.
We have demonstrated a pulse source based on soliton assisted time-lens compression, producing 3.2 ps pulses at a 10 GHz repetition rate with a simple setup. This source is inherently tunable since the pulses are produced fromCW laser radiation. It can be easily modified to produce a carrier-suppressed return-to-zero signal by driving the intensity modulator in the 33% duty ratio configuration. Optimization of the source can be performed by optical filtering or phase shaping. The soliton compression effects can be used in conjunction with the setup presented in ref.  to produce alternate multiwavelength pulses. We anticipate that the femtosecond regime will be attainable by use of a higher drive voltage on the phase modulator.
References and links
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