High-speed tunable photonic crystal fiber-based femtosecond soliton source without dispersion pre-compensation

We present a high-speed wavelength tunable photonic crystal fiber-based source capable of generating tunable femtosecond solitons in the infrared region. Through measurements and numerical simulation, we show that both the pulsewidth and the spectral width of the output pulses remain nearly constant over the entire tuning range from 860 to 1160 nm. This remarkable behavior is observed even when pump pulses are heavily chirped (7400 fs^2), which allows to avoid bulky compensation optics, or the use of another fiber, for dispersion compensation usually required by the tuning device.


I. Introduction
Light sources based on the propagation of solitons in optical fibers have emerged as a compact solution to the need of a benchtop source of ultra-short tunable pulses [1][2][3]. The soliton formation from femtosecond pulses launched into an optical fiber is explained in terms of the interplay between selfphase modulation (SPM) and group-velocity dispersion (GVD) in the anomalous dispersion regime [4]. The wavelength tunability is a consequence of the Raman-induced frequency shift (RIFS) produced on the pulse when traveling through the fiber [5]. The term soliton self-frequency shift (SSFS) [6] was coined to name this effect widely used to produce tunable femtosecond pulses in different wavelength ranges, e.g., from 850 to 1050 nm [7], from 1050 to 1690 nm [8], and from 1566 to 1775 nm [1]. In most cases, photonic crystal fibers (PCF) are used for building these sources since their GVD can be easily tailored to produce solitons in a desired tuning range [9,10]. For a given choice of the PCF, full experimental characterization of the pump and output pulses, complemented with theoretical predictions, is necessary to understand how nonlinear effects modify the output soliton.
The wavelength tunability in a PCF-based light source is provided by the modulation of the pump power injected into the fiber [11][12][13][14]. It is worth noting that the wavelength choice of the output pulse is done without moving any mechanical part, which is clearly attractive for all the proposed and imaginable applications of these soliton sources. Moreover, the wavelength of the output pulse can be chosen as fast as one can modulate the power of the pump pulse, as introduced in Ref. [15,16]. By introducing an acousto-optic modulator (AOM) in the path of the pump pulse, the output wave-length can be changed at a speed which is ultimately limited only by the laser repetition rate. This kind of experimental setup has been presented in some previous reports [14,17], with stunning applications as the one presented in Ref. [18], where a pseudo-CW wideband source for optical coherent tomography is introduced. However, the need to pre-compress the pump pulse to avoid the chirp produced by the AOM contrives against the compact and mechanically robust design of the light source. In this paper, we demonstrate that the PCF-based source presented here is robust against chirped pump pulses. We present a complete set of measurements showing that the temporal and spectral characteristics of the generated solitons in the PCF remain unaltered even when pump pulses are heavily chirped up to ∼ 7400 fs 2 . Results are presented for the whole range of tunability (860 nm to 1160 nm). We also present numerical simulations which remarkably fit the experimental data and help to understand the soliton behavior.
This paper is organized as follows: In section II, we describe the experimental setup. The numerical simulations are described in section III. In section IV, we present experimental and numerical results and in section V we further analyze the results with numerical simulations. Finally, in section VI, we present our conclusions.
The AOM not only allows high speed (up to MHz) and accurate control of the soliton wavelength, as previously discussed, but also prevents feedback into the Ti:Sa, replacing the optical isolator required in similar setups [19]. As the AOM introduces ∼ 56 mm of SF8 glass path, pump pulses gain a positive chirp of about ∼ 7400 fs 2 , which leads to a time spread by a factor of ∼ 3 in them. This can be pre-compensated, for example, by introducing an optical fiber in the anomalous dispersion regime [8,20] or a prism compressor in the well-known configuration presented in [21]. In this work, the chirp was compensated by a pair of SF18 prisms with an apex separation of 78 cm. Additionally, the prism compressor allowed us to up-chirp pump pulses in a controlled fashion from TL to ∼ 1400 fs 2 by introducing an extra glass path at the second prism of the arrangement [22]. This full or partial compensation of the phase distortion introduced by the AOM allowed us to study the role of different chirp figures in the temporal and spectral characteristics of the solitons generated in the PCF.
Pump pulses were coupled into a nonpolarization-maintaining microstructured fiber commercially used for supercontinuum generation (Thorlabs, NL-2.3-790-02). Its main parameters are listed in Table 1 and the dispersion curve and SEM image are shown in Fig. 2. 1 Upon propagation down the fiber, the spectrum is highly broadened so a spatial band-pass filter made of a prism and razor blades, similar to the one presented in [23], allowed to filter the spectral region of the solitonic branch (see Fig. 3) without adding any extra chirp to the solitons.
Once the spectral selection was achieved, a flipper mirror directed the filtered beam for analysis either by the optical spectrum analyzer (OSA) or by the interferometric autocorrelator. A fast-scan system [24] allows to perform fast interferometric auto-correlations. Briefly, a platform with a hollow retroreflector is moved sinusoidally back and forth, with a stepper motor at 11 Hz, to produce and op-  Table 1: PCF parameters relevant to the simulation. Further details can be found in Ref. [14].
tical delay in one of the arms of a Michelson interferometer. The autocorrelation signal is recorded by a PMT and averaged with an oscilloscope.

III. Numerical Simulations
In order to further validate experimental results, we simulated the propagation of femtosecond pulses in the PCF by numerically solving the generalized nonlinear Schrödinger equation (GNLSE) including dispersive, Kerr, instantaneous and delayed Raman response, and self-steepening effects [25], with a conservation quantity error (CQE) adaptive stepsize algorithm [26].
The GNLSE reads is the complex envelope of the electric field, β n are the expansion terms for the propagation constant around the carrier frequency ω 0 and γ is the nonlinear coefficient. f R (t) represents the fractional contribution of the delayed Raman effect h R . Note that Eq. (1) adopts a more accurate description of this effect than the one usually used [4]. In our simulation, we adopted τ 1 = 12.2 fs, τ 2 = 32 fs, τ b = 96 fs, f a = 0.75, f b = 0.21, f c = 0.04, and f R = 0.24 [27]. The dependence of the fiber non-linear parameter γ with the frequency was modeled as a linear function (see Table  1).

i. Transform-limited pump pulses
First, we present the full characterization of the soliton source seeded by TL pump pulses, in an extended wavelength range if compared with the results presented in our previous paper [14].
In order to investigate the dependence of the output spectrum with the coupled power, managed by the AOM, we skipped spectral filtering at first. Fig.  3 shows the measured spectrum at the PCF output as a function of the coupled power. The infrared solitonic branch appears at ∼ 10 mW and undergoes red-shift with increasing power. The maximum wavelength attained is 1130 nm at 55 mW. Spectra in Fig. 3 also shows show that some of the input energy is converted to visible non-solitonic radiation.
The pulsewidth of the filtered soliton as a function of its wavelength, λ s , is shown in Fig. 4. The

ii. Chirped pump pulses
The effect over the soliton produced by the chirp of pump pulses was studied systematically by introducing a known amount of extra glass path on the second prism of the compressor. This scheme allowed to change the GVD of pump pulses from 0 to 1400 fs 2 . Further chirping was achieved by the complete removal of the prism compressor, leading to a total amount of positive chirp ∼ 7400 fs 2 .  The effect of this heavy chirping was evident in the auto-correlation traces of pump pulses, as can be seen by comparing Fig. 6 (a) and (c). However, there is not a clear difference between traces of the output solitons for the TL (b) and the highly chirped (∼ 7400 fs 2 ) case (d).
A color map of the spectra as function of the coupled power, for a highly chirped pump pulse (∼ 7400 fs 2 ), is shown in Fig. 7. As in the TL case, we observe that a solitonic branch is red shifted A comparison of the soliton red-shift between TL and chirped pump pulse cases is presented Fig. 8. The figure shows that more power is always required to attain the same shift when pump pulses are heavily chirped. Figure 9 (a) shows the soliton pulsewidth as a function of its wavelength, λ s , when the pump pulse is heavily chirped (∼ 7400 fs 2 ). We observe an approximately constant output pulsewidth (∼ 45 fs) in the entire tuning range. Furthermore, the ∆t∆ν product, shown in Fig. 9 (b), indicates that the generated pulses can be identified as fundamental solitons (sech 2 -like), as in the case of TL pump pulses [14]. Numerical simulations were also performed for this case (full lines in Fig. 9) showing an excellent agreement with experimental results.

V. DISCUSSION
i. Fiber soliton self-frequency shift effective length In order to further analyze soliton formation, we studied the pulse evolution along the fiber by performing numerical simulations. The spectrum evolution along the fiber, for a given coupled power, in the TL and the chirped cases are shown in Fig. 10 (a) and (b), respectively. These simulations show that in the case of chirped pump pulses (∼ 7400 fs 2 ), the spectrum broadening and the soliton formation take place farther down into the fiber (see Fig. 10), as compared to the TL case. The delay in the formation of the soliton can be explained by an interplay of opposite chirping effects: the positive chirp acquired by traversing the AOM is compensated as the pulse advances into the PCF, in anomalous propagation, leading to pulse compression. The PCF itself provides pulse compression in the first stretch of the fiber previously to the branching of a soliton. Therefore, the SSFS effective length, i.e., the fiber path where nonlinearity broadens the spectrum, is longer in the TL case. If the chirp is overcompensated and a negatively chirped pulse is fed into the fiber, these pulses would also be compressed within the first stretch of the fiber due to SPM [28] leading to the same behavior than in the positively chirped case, resulting in a narrower tunability range. Once the soliton is formed and the peak power is high enough, intrapulse Raman scattering redshifts the soliton as it propagates through the remaining of the fiber. This spectral shift increases with both fiber length and soliton peak power [4]. So the fact that the soliton is formed at different lengths explains the red shifts observed for the same coupled power.
However, as a larger wavelength shift can be achieved with a higher input power, this shortening in the effective length in the chirped case could be compensated by coupling more power into the PCF [1]. Another possibility for compensating this effect on the SSFS is using a longer PCF.  Figure 10: Simulated spectral evolution along the fiber length. Pump pulses with identical peak power produce more soliton shifting with unchirped (a) than with heavily chirped (∼7400 fs 2 ) (b) pump pulses.
ii. Fiber power conversion efficiency Figure 11 shows a simulation where the same shift wavelength obtained for TL pump pulses is achieved by increasing the coupled power in the shorter effective length fiber (7400 fs 2 chirp). Fission of more than one soliton branch is visible in this case, as compared to the case of TL pump pulses, for which only a single soliton branch appears (Fig. 10). Each soliton branch carries a fundamental soliton (N = 1) with a peak power P 0 given by [4] As γ, β 2 and T 0 (see Figs. 4 and 5) are the same in both, the TL and chirped cases, the peak power  Figure 11: Simulation of the spectral evolution along the fiber showing that the same shifting shown in Fig. 10 (a) for unchirped pump pulses is attained with chirped ones (∼ 7400 fs 2 ) with a higher pump power.
of the solitons is also the same. The arising of new soliton branches partially accounts for the increased pump power required in the chirped case (Fig. 11) to attain the same shift. Indeed, the soliton-pump power ratio is 0.2 in the chirped case and 0.44 in the TL case. This result reveals that the use of the PCF as a compressor decreases its power conversion efficiency.
On the other hand, it is possible to achieve the same soliton shift as in the TL case by increasing the fiber length, and keeping the same pump power. In this case, the power conversion efficiency is even lower, 0.17, as predicted by simulations.

VI. Conclusions
We have presented a high-speed tunable soliton infrared source capable of generating ∼ 45 fs transform-limited pulses in the range from 860 to 1160 nm. Both the pulsewidth and the spectral width were shown to remain constant over the entire tuning range, even when pump pulses were heavily chirped up to 7400 fs 2 . Insensitivity to the chirp of pump pulses points out to the feasibility of avoiding bulky compensation optics prior to the PCF, opening up the possibility to build reliable and compact high-speed tunable femtosecond sources in the near infrared region. A minor drawback of this source is that either more power needs to be coupled or a longer PCF needs to be used in order to achieve the same tuning range obtained with transform-limited pump pulses.