光子晶体光纤超连续谱产生过程中色散波的孤子俘获研究

基于光子晶体光纤中脉冲演化遵循的非线性薛定谔方程, 用数值模拟的方法分别研究了飞秒脉冲在单零色散点和双零色散点光子晶体光纤中超连续谱的产生和色散波的孤子俘获现象. 结果表明: 与单零色散点光子晶体光纤相比, 双零色散点光子晶体光纤产生的超连续谱既包含了蓝移色散波, 又包含了红移色散波, 且当满足群速度匹配时, 孤子通过四波混频不仅能俘获蓝移色散波, 而且能俘获红移色散波, 从而产生新的俘获波频谱成分. 为了清楚地观察脉冲传输的时频特性, 通过模拟交叉相关频率分辨光学开关技术, 得到了孤子俘获色散波的演化过程. 关键词： 超连续谱 色散波 孤子俘获 光子晶体光纤     

双折射光子晶体光纤中超连续谱产生的实验研究

研究了30 fs激光在双折射光子晶体光纤中传输时,泵浦光功率和偏振态对超连续谱产生的影响。实验结果表明:随着泵浦光功率增加,光谱宽度显著增加,出现红移的光孤子和蓝移的色散波;当泵浦光的偏振态分别平行于光子晶体光纤长轴和短轴时,二者都有红移的光孤子和蓝移的色散波,但前者色散波波长更短;当泵浦光偏振态介于长轴与短轴之间,可能在色散波之外出现了交叉相位波,产生的超连续谱最强,且其近场光斑最大且最亮。     

Spectral incoherent solitons: a localized soliton behavior in the frequency domain

We show both theoretically and experimentally in an optical fiber system that a noninstantaneous nonlinear environment supports the existence of spectral incoherent solitons. Contrary to conventional solitons, spectral incoherent solitons do not exhibit a confinement in the spatiotemporal domain, but exclusively in the frequency domain. The theory reveals that the causality condition inherent to the nonlinear response function is the key property underlying the existence of spectral incoherent solitons. These solitons constitute nonequilibrium stable states of the incoherent field and are shown to be robust with respect to binary collisions.     

Taylor collocation method for the numerical solution of the nonlinear Schrödinger equation using quintic B-spline basis

In this study, we construct a Taylor collocation method for the numerical solution of the nonlinear Schrödinger (NLS) equation. We use suitable initial and boundary conditions. Taylor series expansion is used for time discretization. The cubic B-spline collocation method is applied to spatial discretization. Test problems concerning the single soliton motion, interaction of two colliding solitons, and the formation and bound states of solitons of the NLS equation are studied to evaluate the method. The L ₂ and L _∞ error norms are calculated to improve the accuracy of the numerical results.     

Velocity locking of incoherent nonlinear wave packets

We show both theoretically and experimentally in an optical fiber system that a set of incoherent nonlinear waves irreversibly evolves to a specific equilibrium state, in which the individual wave packets propagate with identical group velocities. This intriguing process of velocity locking can be explained in detail by simple thermodynamic arguments based on the kinetic wave theory. Accordingly, the selection of the velocity-locked state is shown to result from the natural tendency of the isolated wave system to approach the state that maximizes the nonequilibrium entropy.     

Localization of optical pulses in guided wave structures with only fourth order dispersion

Inspired by the recent realization of pure-quartic solitons (Blanco-Redondo et al. (2016) [1]), in the present work we study the localization of optical pulses in a similar system, i.e., a silicon photonic crystal air-suspended structure with a hexagonal lattice. The propagation of ultrashort pulses in such a system is well described by a generalized nonlinear Schrödinger (NLS) equation, which in certain conditions works with near-zero group-velocity dispersion and third order dispersion. In this case, the NLS equation has only the fourth order dispersion term. In the present model, we introduce a quasiperiodic linear coefficient that is responsible to induce the localization. The existence of Anderson localization has been confirmed by numerical simulations even when the system presents a small defocusing nonlinearity.     

Optical soliton perturbation for time fractional resonant nonlinear Schrödinger equation with competing weakly nonlocal and full nonlinearity

In this article, we retrieve optical soliton solutions of the perturbed time fractional resonant nonlinear Schrödinger equation having competing weakly nonlocal and full nonlinearity. We study the equation for two different forms of nonlinearity, namely Kerr law and anti-cubic law. The F-expansion method along with fractional complex transformation is used to obtain the optical solitons. Moreover, the existence of these solitons are guaranteed with the constraint relations between the model coefficients and the traveling wave frequency coefficient.     

在色散渐减光子晶体光纤中产生超连续谱的实验研究

本文利用非线性偏振锁模激光器产生的重复频率50 MHz, 脉宽为1.8 ps的脉冲分别抽运外径均匀和色散渐减两种高非线性光子晶体光纤, 在三阶非线性效应 (自相位调制、交叉相位调制、四波混频和受激拉曼散效应等) 和色散共同作用下得到扩展至蓝光部分的超连续谱. 模拟了光谱在色散渐减光纤和均匀光纤中的展宽过程, 通过对比均匀光纤发现色散渐减光纤在调控色散, 加强拉曼孤子和色散波的群速度匹配条件, 产生超带宽光谱方面具有很大优势. 实验利用20 m长的色散渐减光纤, 得到了406.1至671.8 nm的可见光波段增强的较为平坦的超连续谱. 关键词： 超连续谱 色散渐减光子晶体光纤 群速度匹配 非线性效应     

Breakdown of weak-turbulence and nonlinear wave condensation

The formation of a large-scale coherent structure (a condensate) as a result of the long time evolution of the initial value problem of a classical partial differential nonlinear wave equation is considered. We consider the nonintegrable and unforced defocusing NonLinear Schrödinger (NLS) equation as a representative model. In spite of the formal reversibility of the NLS equation, the nonlinear wave exhibits an irreversible evolution towards a thermodynamic equilibrium state. The equilibrium state is characterized by a homogeneous solution (condensate), with small-scale fluctuations superposed (uncondensed particles), which store the information necessary for “time reversal”. We analyze the evolution of the cumulants of the random wave as originally formulated by D.J. Benney and P.G. Saffman [D.J. Benney, P.G. Saffman, Proc. Roy. Soc. London A 289 (1966) 301] and A.C. Newell [A.C. Newell, Rev. Geophys. 6 (1968) 1]. This allows us to provide a self-consistent weak-turbulence theory of the condensation process, in which the nonequilibrium formation of the condensate is a natural consequence of the spontaneous regeneration of a non-vanishing first-order cumulant in the hierarchy of the cumulants’ equations. More precisely, we show that in the presence of a small condensate amplitude, all relevant statistical information is contained in the off-diagonal second order cumulant, as described by the usual weak-turbulence theory. Conversely, in the presence of a high-amplitude condensate, the diagonal second-order cumulants no longer vanish in the long time limit, which signals a breakdown of the weak-turbulence theory. However, we show that an asymptotic closure of the hierarchy of the cumulants’ equations is still possible provided one considers the Bogoliubov’s basis rather than the standard Fourier’s (free particle) basis. The nonequilibrium dynamics turns out to be governed by the Bogoliubov’s off-diagonal second order cumulant, while the corresponding diagonal cumulants, as well as the higher order cumulants, are shown to vanish asymptotically. The numerical discretization of the NLS equation implicitly introduces an ultraviolet frequency cut-off. The simulations are in quantitative agreement with the weak turbulence theory without adjustable parameters, despite the fact that the theory is expected to breakdown nearby the transition to condensation. The fraction of condensed particles vs energy is characterized by two distinct regimes: For small energies (H?H_c) the Bogoliubov’s regime is established, whereas for H?H_c the small-amplitude condensate regime is described by the weak-turbulence theory. In both regimes we derive coupled kinetic equations that describe the coupled evolution of the condensate amplitude and the incoherent field component. The influence of finite size effects and of the dimensionality of the system are also considered. It is shown that, beyond the thermodynamic limit, wave condensation is reestablished in two spatial dimensions, in complete analogy with uniform and ideal 2D Bose gases.     

Stationary wave packets in the Kerr nonlinear media with imaginary harmonic potential and linear gain

The existence of stationary wave packets in the nonlinear Kerr media with an imaginary harmonic potential and a linear gain is investigated. By employing a variational approach the existence of stable bright solitons is shown for the case of a defocusing nonlinearity. In focusing nonlinear media, the bright solitons have been shown to be unstable. The predictions of variational approach are confirmed by numerical simulations of the full modified NLS equation. The predicted stationary localized wave packets can be observed in a quasi-one-dimensional BEC with an imaginary optical potential and atoms feeding.     

Multi-peak solitons in PT-symmetric Bessel optical lattices with defects

This paper presents a theoretical analysis of the existence and stability of multi-peak solitons in parity–time-symmetric Bessel optical lattices with defects in nonlinear media. The results demonstrate that there always exists a critical propagation constant μ _c for the existence of multi-peak solitons regardless of whether the nonlinearity is self-focusing or self-defocusing. In self-focusing media, multi-peak solitons exist when the propagation constant μ > μ _c . In the self-defocusing case, solitons exist only when μ < μ _c . Only low-power solitons can propagate stably when random noise perturbations are present. Positive defects help stabilize the propagation of multi-peak solitons when the nonlinearity is self-focusing. When the nonlinearity is self-defocusing, however, multi-peak solitons in negative defects have wider stable regions than those in positive defects.     

Single- and multi-peak solitons in two-component models of metamaterials and photonic crystals

We report results of the study of solitons in a system of two nonlinear-Schrödinger (NLS) equations coupled by the XPM interaction, which models the co-propagation of two waves in metamaterials (MMs). The same model applies to photonic crystals (PCs), as well as to ordinary optical fibers, close to the zero-dispersion point. A peculiarity of the system is a small positive or negative value of the relative group-velocity dispersion (GVD) coefficient in one equation, assuming that the dispersion is anomalous in the other. In contrast to earlier studied systems of nonlinearly coupled NLS equations with equal GVD coefficients, which generate only simple single-peak solitons, the present model gives rise to families of solitons with complex shapes, which feature extended oscillatory tails and/or a double-peak structure at the center. Regions of existence are identified for single- and double-peak bimodal solitons, demonstrating a broad bistability in the system. Behind the existence border, they degenerate into single-component solutions. Direct simulations demonstrate stability of the solitons in the entire existence regions. Effects of the group-velocity mismatch (GVM) and optical loss are considered too. It is demonstrated that the solitons can be stabilized against the GVM by means of the respective “management” scheme. Under the action of the loss, complex shapes of the solitons degenerate into simple ones, but periodic compensation of the loss supports the complexity.     

Blue light and infrared continuum generation by soliton fission in a microstructured fiber

The nonlinear propagation of ultrashort pulses in a microstructured fiber is experimentally investigated. By working around 800 nm, in the anomalous dispersion region, clear evidence of pulse break-up and soliton propagation is obtained. This is consistent with the recently suggested mechanism of spectral broadening based upon the fission of higher order solitons into red-shifted fundamental solitons and blue-shifted dispersion waves. When 190-fs pulses at high input intensities are used, the output spectrum is made of a broad infrared supercontinuum coexisting with a sharp and very intense blue peak that takes up to 24% of the input power. We tentatively propose an explanation of this effect by invoking pulse-trapping phenomena controlled by the group-velocity matching of infrared and visible pulses. PACS 42.65.Tg; 42.81.Dp     

Solitonen in Wellenleitern mit nichtlinearer optischer Beschichtung

Solitons in a Waveguide with a Thin Nonlinear Optical Slab Starting from Maxwell's equations the influence of a thin nonlinear optical slab embed in a waveguide on the propagation of a monomode (TE) pulse is investigated. The amplitude of the pulse is described by a nonlinear Schrödinger equation (NLS) containing parameters of the waveguide with the nonlinear slab and leading to solitons in the nonlinear modified waveguide.     

Solitons in a linearly coupled system with separated dispersion and nonlinearity

We introduce a model of dual-core waveguide with the cubic nonlinearity and group-velocity dispersion (GVD) confined to different cores, with the linear coupling between them. The model can be realized in terms of photonic-crystal fibers. It opens a way to understand how solitons are sustained by the interplay between the nonlinearity and GVD which are not "mixed" in a single nonlinear Schrodinger (NLS) equation, but are instead separated and mix indirectly, through the linear coupling between the two cores. The spectrum of the system contains two gaps, semi-infinite and finite ones. In the case of anomalous GVD in the dispersive core, the solitons fill the semi-infinite gap, leaving the finite one empty. This soliton family is entirely stable, and is qualitatively similar to the ordinary NLS solitons, although shapes of the soliton's components in the nonlinear and dispersive cores are very different, the latter one being much weaker and broader. In the case of the normal GVD, the situation is completely different: the semi-infinite gap is empty, but the finite one is filled with a family of stable gap solitons featuring a two-tier shape, with a sharp peak on top of a broad "pedestal." This case has no counterpart in the usual NLS model. An extended system, including weak GVD in the nonlinear core, is analyzed too. In either case, when the solitons reside in the semi-infinite or finite gap, they persist if the extra GVD is anomalous, and completely disappear if it is normal.     

Low Reynolds number hydrodynamics of asymmetric,oscillating dumbbell pairs

Numerical simulations are used to discuss various aspects of “optical rogue wave” statistics observed in noise-driven fiber supercontinuum generation associated with highly incoherent spectra. In particular, we consider how long wavelength spectral filtering influences the characteristics of the statistical distribution of peak power, and we contrast the statistics of the spectrally filtered SC with the statistics of both the peak power of the most red-shifted soliton in the SC and the maximum peak power across the full temporal field with no spectral selection. For the latter case, we show that the unfiltered statistical distribution can still exhibit a long-tail, but the extreme-events in this case correspond to collisions between solitons of different frequencies. These results confirm the importance of collision dynamics in supercontinuum generation. We also show that the collision-induced events satisfy an extended hydrodynamic definition of “rogue wave” characteristics.     

Femtosecond Er<Superscript>3+</Superscript> fiber laser for application in an optical clock

The main elements needed for the realization of a compact femtosecond methane optical clock are developed and studied. A femtosecond laser system on an Er³⁺ fiber (λ = 1.55 μm) contains an oscillator, an amplifier, and a fiber with a relatively high nonlinearity in which the supercontinuum radiation is generated in the range 1–2 μm. In the supercontinuum spectrum, the fragments separated by an interval that is close to the methane-optical reference frequency (λ = 3.39 μm) exhibit an increase in intensity. The supercontinuum radiation is converted into the difference frequency in a nonlinear crystal to the range of the methane-reference frequency (λ = 3.3–3.5 μm), so that the frequency components of the transformed spectrum have sufficient intensities for the subsequent frequency-phase stabilization with respect to the methane reference. A system that stabilizes the pulse repetition rate of the femtosecond Er³⁺ laser is also employed. Thus, the repetition rate of the ultrashort pulses of the femtosecond fiber laser is locked to the methane reference. The pulse repetition rate is compared with the standard second. Thus, the scheme of an optical clock is realized.     

Optical <Emphasis Type="Italic">Gaussons</Emphasis> and dark solitons in directional couplers with spatiotemporal dispersion

This paper study the dynamics of optical solitons for nonlinear directional couplers. This coupler system is considered with the group velocity dispersion and the cross-phase modulation of two components along with the spatiotemporal dispersion coefficients. The constraint conditions for the existence of optical Gaussons and dark solitons are listed under the log law and Kerr law nonlinearities, repectively. Additionally, a couple of other solutions known as singular periodic and combined dark-singular solitons, fall out as a by-product of this scheme. This scheme however fails to retrieve bright soliton solution.