Papers in Physics, vol. 4, art. 040001 (2012) Received: 7 July 2011, Accepted: 1 February 2012 Edited by: A. Goñi Reviewed by: J. Chavez Boggio, Leibniz Institut für Astrophysik Potsdam, Germany. Licence: Creative Commons Attribution 3.0 DOI: http://dx.doi.org/10.4279/PIP.040001 www.papersinphysics.org ISSN 1852-4249 High-speed tunable photonic crystal fiber-based femtosecond soliton source without dispersion pre-compensation Mart́ın Caldarola,1∗ Vı́ctor A. Bettachini,2 Andrés A. Rieznik,2 Pablo G. König,2 Mart́ın E. Masip,1 Diego F. Grosz,2, 3 Andrea V. Bragas1, 4 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 fs2), 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 solu- tion to the need of a benchtop source of ultra-short tunable pulses [1–3]. The soliton formation from femtosecond pulses launched into an optical fiber is explained in terms of the interplay between self- phase modulation (SPM) and group-velocity dis- persion (GVD) in the anomalous dispersion regime [4]. The wavelength tunability is a consequence of the Raman-induced frequency shift (RIFS) pro- duced on the pulse when traveling through the fiber ∗E-mail: caldarola@df.uba.ar 1 Laboratorio de Electrónica Cuántica, Departamento de F́ısica, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria, (C1428EHA) Buenos Aires, Argentina. 2 Instituto Tecnológico de Buenos Aires, Eduardo Madero 399, (C1106ACD) Buenos Aires, Argentina. 3 Consejo Nacional de Investigaciones Cient́ıficas y Técnicas, Argentina. 4 IFIBA, Consejo Nacional de Investigaciones Cient́ıficas y Técnicas, Argentina. [5]. The term soliton self-frequency shift (SSFS) [6] was coined to name this effect widely used to pro- duce tunable femtosecond pulses in different wave- length 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 de- sired tuning range [9, 10]. For a given choice of the PCF, full experimental characterization of the pump and output pulses, complemented with theo- retical 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 [11–14]. 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- 040001-1 Papers in Physics, vol. 4, art. 040001 (2012) / M Caldarola et al. length can be changed at a speed which is ulti- mately limited only by the laser repetition rate. This kind of experimental setup has been presented in some previous reports [14, 17], with stunning ap- plications as the one presented in Ref. [18], where a pseudo-CW wideband source for optical coher- ent tomography is introduced. However, the need to pre-compress the pump pulse to avoid the chirp produced by the AOM contrives against the com- pact 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 spec- tral characteristics of the generated solitons in the PCF remain unaltered even when pump pulses are heavily chirped up to ∼ 7400 fs2. Results are pre- sented for the whole range of tunability (860 nm to 1160 nm). We also present numerical simula- tions 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. II. Experimental Setup A scheme of the experimental setup is shown in Fig. 1. A Ti:Sa laser (KMLabs) generates ultra- short transform-limited (TL) pulses of ∆t = 31 fs (FWHM-sech2), λpump = 830 nm, with a spec- tral width ∆λ = 23 nm, and a repetition rate of 94 MHz. The AOM not only allows high speed (up to MHz) and accurate control of the soliton wave- length, as previously discussed, but also prevents feedback into the Ti:Sa, replacing the optical isola- tor required in similar setups [19]. As the AOM in- troduces ∼ 56 mm of SF8 glass path, pump pulses gain a positive chirp of about ∼ 7400 fs2, which leads to a time spread by a factor of ∼ 3 in them. This can be pre-compensated, for example, by in- troducing an optical fiber in the anomalous disper- sion regime [8, 20] or a prism compressor in the well-known configuration presented in [21]. In this Figure 1: Experimental setup. (a) Titanium- Sapphire (Ti:Sa) laser, (b) Prism compressor, (c) Acousto-optic modulator (AOM), (d) Coupling lens, (e) Photonic crystal fiber (PCF), (f) Collima- tor objective, (g) Spatial filter, (h) Flipper mirror, (i) Fast-scan interferometric autocorrelator, (j) Op- tical spectrum analyzer (OSA). work, the chirp was compensated by a pair of SF18 prisms with an apex separation of 78 cm. Addition- ally, the prism compressor allowed us to up-chirp pump pulses in a controlled fashion from TL to ∼ 1400 fs2 by introducing an extra glass path at the second prism of the arrangement [22]. This full or partial compensation of the phase distortion in- troduced by the AOM allowed us to study the role of different chirp figures in the temporal and spec- tral characteristics of the solitons generated in the PCF. Pump pulses were coupled into a non- polarization-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 flip- per 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- 1Datasheet available in http://www.thorlabs.com. 040001-2 Papers in Physics, vol. 4, art. 040001 (2012) / M Caldarola et al. Figure 2: Dispersion curve of the PCF, showing the zero dispersion wavelength (ZDW) at 790 nm. The inset is the scanning electron microscope image of the PCF core. The curve and image were provided by the manufacturer. L 75 cm ZDW 790 nm β2 −12.4 ps2km−1 β3 0.07 ps 3km−1 γ(ω) γ0(ω0) + (ω −ω0)γ1 γ0(ω0) 78 W −1km−1 γ1 γ0/ω0 ω0 2271 THz Table 1: PCF parameters relevant to the simula- tion. Further details can be found in Ref. [14]. tical delay in one of the arms of a Michelson inter- ferometer. 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 step- size algorithm [26]. The GNLSE reads ∂A ∂z + β1 ∂A ∂t + i β2 ∂2A ∂t2 (1) −β3 ∂3A ∂t3 + ... = i γ(ω) ( 1 + i ω0 ∂ ∂t ) × ( A(z,t) ∫ ∞ −∞ R(t′)|A(z,t− t′)|2dt′ ) , R(t) = (1 −fR) δ(t) + fRhR(t), hR(t) = (fa + fc) ha(t) + fbhb(t), ha(t) = τ1 ( τ−21 + τ −2 2 ) e−t/τ2 sin (t/τ1), hb(t) = [ (2τb − t) /τ2b ] e−t/τb, where A(z,t) is the complex envelope of the electric field, βn are the expansion terms for the propaga- tion constant around the carrier frequency ω0 and γ is the nonlinear coefficient. fR(t) represents the fractional contribution of the delayed Raman effect hR. Note that Eq. (1) adopts a more accurate de- scription of this effect than the one usually used [4]. In our simulation, we adopted τ1 = 12.2 fs, τ2 = 32 fs, τb = 96 fs, fa = 0.75, fb = 0.21, fc = 0.04, and fR = 0.24 [27]. The dependence of the fiber non-linear parameter γ with the fre- quency was modeled as a linear function (see Table 1). IV. RESULTS 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 out- put 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 under- goes red-shift with increasing power. The maxi- mum 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 func- tion of its wavelength, λs, is shown in Fig. 4. The 040001-3 Papers in Physics, vol. 4, art. 040001 (2012) / M Caldarola et al. λ [nm] C o u p le d p o w e r [m W ] 500 600 700 800 900 1000 1100 1200 10 20 30 40 50 Figure 3: Experimental spectra vs coupled power to the PCF with transform limited (TL) pump pulses. The color map shows spectral intensity. The max- imum achieved soliton shift, λs ' 1130 nm, was reached at 55 W. pulsewidth remains constant at ∼ 45 fs, for the entire tunability range. Numerical simulations are also plotted in the same figure, showing an excellent agreement with experimental measurements. 850 900 950 1000 1050 1100 1150 λ s [nm] 35 40 45 50 55 ∆ t [f s ] Figure 4: Experimental pulsewidth of the soliton as a function of its wavelength, pumping the PCF with TL pulses. The results for the three lower wavelengths were already present in Ref. [14]. Full line: numerical simulations. ii. Chirped pump pulses The effect over the soliton produced by the chirp of pump pulses was studied systematically by in- troducing 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 fs2. Further chirping was achieved by the complete removal of the prism compressor, leading to a total amount of positive chirp ∼ 7400 fs2. 0 400 800 1200 1600 Chirp [fs 2 ] 35 40 45 50 55 ∆ t [ fs ] 7400 0 400 800 1200 1600 Chirp [fs 2 ] 15 20 25 30 ∆ λ [ n m ] 7400 Figure 5: Soliton temporal (a) and spectral width (b) vs. chirp of input pump pulses . Full line: numerical results. The soliton wavelength is λs = 1075 nm. Figure 5 (a) shows the pulsewidth of solitons with wavelength λs = 1075 nm upon variation of pump pulses chirp. Even for a ∼ 7400 fs2 chirp, the soli- ton output pulsewidth remained around 45 fs. Nu- merical simulations show very good agreement with these observations, as they predict nearly constant pulsewidth regardless of the input chirp (full line in Fig. 5). Measurements and numerical simulations in the spectral domain also indicate that the band- width of the output solitons is almost unaffected by the pump pulses chirp [see Fig. 5 (b)]. The product ∆t∆ν was found to be near 0.315, as it is expected for transform-limited sech2 pulses. 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). How- ever, there is not a clear difference between traces of the output solitons for the TL (b) and the highly chirped (∼ 7400 fs2) case (d). A color map of the spectra as function of the coupled power, for a highly chirped pump pulse (∼ 7400 fs2), is shown in Fig. 7. As in the TL case, we observe that a solitonic branch is red shifted 040001-4 Papers in Physics, vol. 4, art. 040001 (2012) / M Caldarola et al. Figure 6: Interferometric auto-correlation traces of TL (a) and heavily chirped, ∼ 7400 fs2, Ti:Sa pump pulses (c). Interferometric auto-correlation traces of the output solitons are similar in both cases, unchirped (b) and heavily chirped (d). Soli- ton wavelength is λs ' 1075 nm. by increasing the coupled power. However, in this case, 80 mW of coupled power is required to pro- duce a 1160 nm soliton which represents an incre- ment of about ∼ 45% in comparison to the TL case. λ [nm] C o u p le d p o w e r [m W ] 500 600 700 800 900 1000 1100 1200 0 10 20 30 40 50 60 70 80 Figure 7: Spectra vs coupled power to the PCF with highly chirped (∼ 7400 fs2) input pulses. 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 re- quired to attain the same shift when pump pulses are heavily chirped. 0 20 40 60 80 P [mW] 0 100 200 300 400 ∆ λ s [ n m ] 0 fs 2 7400 fs 2 Figure 8: Soliton wavelength shift for chirped (full squares) and TL pump pulses (empty squares) vs pump pulse power. Dashed and full lines cor- respond to numerical results for TL and highly chirped pump pulses, respectively. Figure 9 (a) shows the soliton pulsewidth as a function of its wavelength, λs, when the pump pulse is heavily chirped (∼ 7400 fs2). We observe an ap- proximately 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 (sech2-like), as in the case of TL pump pulses [14]. Numerical simulations were also per- formed 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 per- forming numerical simulations. The spectrum evo- lution 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 simula- tions show that in the case of chirped pump pulses (∼ 7400 fs2), the spectrum broadening and the soli- ton 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 ef- fects: the positive chirp acquired by traversing the AOM is compensated as the pulse advances into the 040001-5 Papers in Physics, vol. 4, art. 040001 (2012) / M Caldarola et al. 1000 1050 1100 1150 λ s [nm] 35 40 45 50 55 ∆ t [f s ] 1000 1050 1100 1150 λ s [nm] 0,1 0,2 0,3 0,4 0,5 ∆ t ∆ ν Figure 9: (a) Soliton pulsewidth and (b) the prod- uct ∆t∆ν vs wavelength in the case of highly chirped pump pulses (∼7400 fs2). PCF, in anomalous propagation, leading to pulse compression. The PCF itself provides pulse com- pression 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 nonlin- earity broadens the spectrum, is longer in the TL case. If the chirp is overcompensated and a nega- tively 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 be- havior 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 red- shifts the soliton as it propagates through the re- maining 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 shorten- ing 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. λ [nm] L e n g th [ c m ] 500 600 700 800 900 1000 1100 1200 0 10 20 30 40 50 60 70 λ [nm] L e n g th [ c m ] 500 600 700 800 900 1000 1100 1200 0 10 20 30 40 50 60 70 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 fs2) (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 fs2 chirp). Fis- sion 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 ap- pears (Fig. 10). Each soliton branch carries a fun- damental soliton (N = 1) with a peak power P0 given by [4] N2 = 1 = γP0T 2 0 |β2| , (2) As γ, β2 and T0 (see Figs. 4 and 5) are the same in both, the TL and chirped cases, the peak power 040001-6 Papers in Physics, vol. 4, art. 040001 (2012) / M Caldarola et al. λ [nm] L e n g th [ c m ] 500 600 700 800 900 1000 1100 1200 0 10 20 30 40 50 60 70 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 fs2) with a higher pump power. of the solitons is also the same. The arising of new soliton branches partially ac- counts 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 en- tire tuning range, even when pump pulses were heavily chirped up to 7400 fs2. Insensitivity to the chirp of pump pulses points out to the feasi- bility of avoiding bulky compensation optics prior to the PCF, opening up the possibility to build reli- able and compact high-speed tunable femtosecond sources in the near infrared region. 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