PIERS ONLINE, VOL. 5, NO. 5, 29 421 Widely Wavelength-tunable Soliton Generation and Few-cycle Pulse Compression with the Use of Dispersion-decreasing Fiber Alexey Andrianov 1, Sergey Muraviev 1, Arkady Kim 1, and Aleksei Sysoliatin 2 1 Institute of Applied Physics, Russian Academy of Sciences 46 Ulyanov st., Nizhny Novgorod 6395, Russia 2 Fiber Optics Research Center, Russian Academy of Sciences 53 Vavilov st., Moscow 119333, Russia Abstract We have developed an all-fiber source of both, widely wavelength tunable femtosecond solitons and few-cycle optical pulses. It is based on Raman self-frequency shift of soliton pulse in dispersion-decreasing fibers (DDF) and subsequent spectrum broadening due to supercontinuum generation in a short highly nonlinear fiber and its further compression in a fiber compressor. High-quality sech-shaped 5 fs solitons with the wavelength tunable in the range of 1.6 2.1 µm were obtained at the output of dispersion-decreasing fiber. The solitons were used as a pump for the generation of smooth and tunable supercontinuum, which was then compressed down to 24 fs duration corresponding to 4 optical cycles at the central wavelength of 1.8 1.9 µm. 1. INTRODUCTION Creation of laser systems for generating few-cycle optical pulses comprising a small number of field oscillations at different wavelengths has been widely discussed in the recent years. The interest in such few-cycle pulses is explained by both, basic problems of the actively developed extreme nonlinear optics [1, 2] and their practical applications, including high harmonic generation and advance to the attosecond durations [2]. Many research groups use for generation of few-cycle pulses a master oscillator generating femtosecond pulses at a fixed wavelength that are further converted in nonlinear optical media so as to enrich the signal spectrum and then to compress the pulse to few-cycle duration. In this respect, fiber systems are of particular interest for both, nonlinear conversion and construction of femtosecond master oscillator. Initial pulses may be additionally smoothly wavelength-tuned due to Raman self-frequency shift in a special highly nonlinear fibers [3 5] and then spectrally broadened, if necessary, also in the nonlinear waveguides during supercontinuum generation [6, 7]. These ultrabroadband optical pulses may further be compressed in a linear compressor down to few-cycle durations [8 1]. It is worthy of notice that the fiber laser systems have already generated quite short pulses both, using external compressor [9, 1] and in the all-fiber setup with the use of strongly nonlinear fibers [11, 12]. In the present work we propose to use dispersion-decreasing silica fibers for smooth tuning of initial pulses in a broad wavelength interval. One of the advantages of this technique is more efficient frequency tuning of a soliton-type optical pulse due to its location in the frequency domain close to the zero dispersion point [13, 14] and, as a consequence, shorter output pulse duration due to adiabatic compression of the soliton pulse in dispersion-decreasing fiber [15]. Additionally, supercontinuum is actually generated in a section of a similar fiber of smaller diameter, with the zero dispersion point shifted to the longer wavelength region. Thus, this combination is capable of providing an all-fiber source of few-cycle pulses based on dispersion-decreasing fiber. The proposed technique allows one to generate few-cycle pulses in the mid-infrared range that has been poorly developed in terms of extreme nonlinear optics. 2. TUNABLE SOLITON GENERATION IN DDF Here we propose the following scheme of an all-fiber laser system for the generation of tunable fewcycle pulses using dispersion-decreasing fibers. These fibers can provide efficient usage of Raman self-frequency shift of a soliton pulse propagating in DDF, as well as adiabatic compression of such a pulse as it approaches the zero dispersion point [15]. This allows one to implement broadband central wavelength tuning of optical pulse in the range wider than 4 nm using an erbium-doped fiber system and to obtain rather short output femtosecond pulses. Further, making use of spectral broadening by supercontinuum generation in a rather short strongly nonlinear fiber and subsequent compression in the appropriate linear fiber one can obtain few-cycle optical pulses. The schematic
PIERS ONLINE, VOL. 5, NO. 5, 29 422 of the experimental setup is shown in Fig. 1. The source of optical pulses is a femtosecond fiber laser passively modelocked at 21-st harmonic of the ring cavity [16] generating 23 fs pulses with the repetition rate of 6 MHz at the wavelength of 1.57 µm. The signal is amplified up to an average power of 15 mw in erbium-doped amplifier and is fed to a 39 m-long tapered silica DDF. The group velocity dispersion of this single-mode silica fiber is anomalous and increases in magnitude for wavelengths larger than the zero dispersion wavelength that may be shifted towards longer wavelengths by controlling the waveguide contribution to the dispersion when the fiber diameter is changed. In the experiments we used the fiber where the zero dispersion wavelength was shifted from 1.45 µm at the input to 1.7 µm at the output. Erbium fiber laser Amplifier Dispersion-decreasing fiber (DDF), 39 meters 1 meter 2 cm Nonlinear fiber with normal dispersion fiber compressor Spectrum Autocorrelation Figure 1: Schematic of the experimental setup. Such a choice of fiber dispersion properties ensures central wavelength tuning of the signal in the 1.6 2 µm range and high-quality output pulse compressed down to 5 6 fs. As was shown in our previous work [13, 14], the pulse should be launched in DDF in the neighborhood of zero dispersion in its anomalous part, when nonlinear effects lead to formation of a soliton pulse. For sufficient input power, when a considerable part of the pulse power is accumulated in one soliton, during its further propagation in the fiber this pulse experiences strong Raman frequency shifting [4, 17]. Energy losses accompanying soliton propagation leading to a decrease in pulse intensity and slowing down the Raman self-frequency shift may be compensated by adiabatic pulse compression by means of smooth reduction of anomalous dispersion coefficient along the fiber [15]. Thus, by specifying an appropriate law of anomalous dispersion decrease in DDF it is possible to maintain high conversion efficiency throughout the fiber. Besides, by reducing the absolute magnitude of dispersion along the fiber one can compress the pulse, thus providing a smooth sech-shape at the output by virtue of the soliton effects. The central wavelength of the output pulse is determined by fiber length and Raman shift rate which, in turn, depends on soliton energy. Numerical simulation based on the generalized nonlinear Schrödinger equation [18] shows that, in a fiber with the above mentioned dependence of group velocity dispersion on wavelength and coordinate z along the fiber, given sufficient energy, the input pulse evolves to one or several fundamental solitons whose central frequency Ω decreases continuously so that the soliton moves almost along the constant dispersion line β 2 (Ω, z) const nearly at the same distance from the zero dispersion point in frequency domain [13, 14, 19]. The local second-order frequency-dependent dispersion coefficient β 2 (ω, z) = 2 β/ ω 2, where β is propagation constant, fully determines the dispersion properties of the fiber in the corresponding section z, given slow variation of fiber parameters along its length. Results of numerical calculations of changes in the spectra of pulses of different power propagating in DDF are presented in Fig. 2. The picture of spectrum evolution clearly shows the initial stage of pulse compression and spectrum broadening as the pulse approaches the zero dispersion point, as well as subsequent formation of a stable quasi-soliton at a constant distance from the dispersion zero line, that is accompanied only by slight radiation of dispersive waves. The main features of the resulting quasi-soliton pulse may be investigated using a rather simple mathematical model. The rate of Raman self-frequency shift for a soliton in a fiber with nonlinearity γ (in our fibers it was 5 W 1 km 1 ) and characteristic Raman response time T R (typically 5 fs) dω dz = 8 β 2 γt R 15 T 4 (1) strongly depends on soliton duration T = 2 β 2 /(γw ).567T F W HM, which in turn is determined by the local value of second-order dispersion β 2 and soliton energy W [17, 18]. Adiabatic decrease of dispersion as a result of changes in fiber diameter leads to soliton compression, so that the Raman self-frequency shift stabilizes the local value of second-order dispersion, β 2 (Ω, z) = const, due to dispersion growing with decreasing frequency. The latter equality gives us the soliton frequency
PIERS ONLINE, VOL. 5, NO. 5, 29 423 Frequency, THz 2 18 16 14 12 Zero dispersion line Anomalous dispersion Normal dispersion Spectral Intensity, a.u. 1.6 1.2.8.4. 4 nj.6 nj.8 nj. 1nJ.13 nj simulated measured. 2nJ.25 nj 1 1 2 3 Distance, m 16 18 2 22 Wavelength, nm Figure 2: Pulse spectrum evolution during propagation in DDF. Figure 3: Soliton spectra at DDF output for different values of power. dependence Ω(z) along the fiber. Thus, the condition of the equality of Raman shift rate of fundamental soliton to soliton frequency rate following from the stationary propagation model and supported by numerical modeling, provides the following relations for soliton energy W, its central frequency Ω, and duration T : ( TR γ 4 W 4 ) 1/3 ( ) β 2 (Ω, z) =, T = 32/3 TR γw 1/3. (2) 3s 15 s Here, s = dω c /dz (where β 2 (ω c, z) = const) is the rate of constant dispersion points in frequency space. The first relation in Eq. (2) defines implicitly soliton central frequency in the course of propagation along the fiber. Thus, for a given dispersive dependence, there exists a one-parametric family of frequency-tunable quasi-solitons whose duration and constant dispersion line along which the soliton is moving are determined by its energy W only. Smaller energy solitons move along the line of smaller local dispersion and have longer duration, so that the Raman shift rate sharply increasing with decreasing duration [17] allows the pulse to be detuned from the zero dispersion point. It should be noted that the minimum soliton duration is also limited by linear and nonlinear higher-order effects. Limitation of the minimum pulse duration caused by closeness to zero dispersion point (actually, the impact of third-order dispersion β 3 = 3 β/ ω 3 ) that is the first to manifest itself in our experiment may be obtained from the following simple consideration. In order the soliton to be realized, the main part of its spectrum must lie in the region of anomalous dispersion, which imposes a condition on the duration of the transform-limited pulse, T β 3 /β 2, where the dispersion factors are taken at central frequency. Making use of this restriction and the relationship between parameters of the frequency-tunable soliton and local value of second-order dispersion (2) one can find minimum energy W min and the corresponding minimum duration T min at which such a pulse may exist: W min β3/5 3 s 2/5 T 2/5 R γ, T min β 1/5 3 T 1/5 R s 1/5. (3) For the pulse energy approaching a minimum one, energy losses due to linear wave radiation under the action of third-order dispersion increase, which eventually leads to fast soliton breakdown. In our experiments with DDF we investigated spectrum shape and autocorrelation trace at the fiber output for different values of output pulse energy. The soliton spectra at DDF output given in Fig. 3 and corresponding autocorrelation traces demonstrate a well-pronounced sech-shape of a transform limited pulse. About 7% of the input pulse energy is converted into a long-wave soliton; the remainder of energy is in the spectral peak around 1.6 µm and may be filtered, if necessary, by a bandpass filter. Minimum pulse duration of 5 fs is attained at relatively small input pulse energy of about.6 nj, which agrees with the estimates (3); at still smaller energies, the pulse ceases to be transform limited. Therefore, on the one hand, minimum pulse duration in DDF is limited and is attained at relatively small pulse energy; on the other hand, pulse duration grows slowly with
PIERS ONLINE, VOL. 5, NO. 5, 29 424 increasing energy and significant wavelength tuning, which allows using DDF as a tunable source of high-quality pulses for further compression. Thus, DDFs can provide efficient conversion of the input pulse regardless of its shape into widely wavelength tunable high quality solitonic pulses, which can be further compressed down to few-cycle durations by using spectral broadening via self-phase modulation in the highly-nonlinear fiber and subsequent recompression in the standard telecom fiber. 3. SUPERCONTINUUM GENERATION AND PULSE COMPRESSION For further pulse shortening we employed strong spectral broadening of the signal by means of selfphase modulation that may occur in the fiber with small normal dispersion maintaining a rather high pulse quality [2], even for the characteristic values of peak intensity and nonlinearity typical for DDF solitons. We made use of a fiber with low normal dispersion in a wide wavelength range up to 2.2 µm. Such a constant-diameter fiber was made of the preform same as that used for DDF; the only difference was a smaller core diameter, thanks to which the zero dispersion wavelength is shifted to the long wavelength region. A strongly chirped pulse was obtained at the output of the fiber. The spectrum of this chirped pulse for three different values of energy at the DDF input is shown in Fig. 4 together with the spectrum of the soliton used for pumping. It is clear from the figure that, in conformity with the theory [2], a nearly symmetric spectrum broadening occurs in a nonlinear waveguide with normal dispersion, with the supercontinuum central wavelength varying together with the soliton central wavelength. The measured spectra agree qualitatively well with the numerical computations. The pulse chirp and duration at the output of a normal-dispersion fiber assessed by the autocorrelation function for maximum power predicted possible compression down to 2 25 fs during propagation in a section of a standard anomalous-dispersion fiber about 2 cm long. Indeed, after adjusting compressor length we obtained a pulse whose autocorrelation function is presented in Fig. 5 and spectrum coincides with the supercontinuum spectrum taken before pulse compression. We used these data and the appropriate algorithm [21] to reconstruct the pulse phase and intensity. Half-width maximum-intensity pulse duration was 24.5 fs, which corresponds to four optical cycles at the wavelength of 1.9 µm. Intensity (a.u.) 1.6 1.2.8.4.16 nj.8 nj.2 nj 16 18 2 22 Wavelength (nm) AC signal (a.u.) Intensity (a.u.) 8 6 4 2.8.6.4.2 (a) -1 1 Time (fs) (b) 24.5 fs -8-4 4 8 Time (fs) 6 4 2 Phase (rad) Figure 4: Spectra of supercontinuum (solid curves) and of the soliton (dashed curves) used for its generation for different input power of the signal. Figure 5: Autocorrelation function of 24 fs compressed pulse (a); pulse intensity and phase reconstructed from autocorrelation and spectral measurements (b). 4. CONCLUSION We proposed an all-fiber scheme of constructing a laser system for generation of few-optical-cycle pulses, using the Raman self-frequency shift of optical soliton pulse in dispersion-decreasing fibers and supercontinuum generation, with the central wavelength smoothly tunable in a wide (> 4 nm) range. This design, which we believe to be the first of its kind, can produce widely tunable few-cycle
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