Nonlinear propagation effects in an AlGaAs Bragg grating filter

We present experimental observations of nonlinear propagation effects in an integrated AlGaAs waveguide filter. We demonstrate pulse shaping, pulse compression, and the production of gap solitons within the stop band of the grating for switching powers of ~130 W . This nonlinear behavior is associated with the counterbalancing effects of self-phase modulation and the large dispersion effects introduced by the grating itself.     

Observation of resonance soliton trapping due to a photoinduced gap in wave number

We investigate the nonlinear propagation of two forward propagating modes coupled by a resonant traveling-wave grating, which is photoinduced by illuminating an optical fiber with a beat signal. This interaction, representative of systems whose dispersion relation K=K(Omega) exhibits a gap in momentum K, shows evidence of localization mediated by resonance solitons. The signature of a still (in the grating frame) soliton is grating-induced cancellation of modal group-velocity mismatch.     

Conservative and dissipative fiber Bragg solitons (a review)

We present a comparative review of two classes of optical solitons—conservative and dissipative solitons—propagating in single-mode optical fibers in which refractive-index gratings are induced such that their period is comparable with the radiation wavelength. Fibers that have the Kerr nonlinearity and negligibly small losses and that do not gain radiation (conservative system) are described by traditional equations of the approximation of slowly varying amplitudes, and effects caused by the nonlinearity of the medium, such as nonlinear switching, optical bistability, and formation of conservative Bragg solitons are considered. It is shown that the passage beyond the scope of the approximation of slowly varying amplitudes makes it possible to describe new important effects, including localization of soliton centers near maxima of the refractive-index grating. Bright and dark conservative solitons are demonstrated, which are formed when the Kerr nonlinearity is replaced by the nonlinearity of two-level atomic systems. The properties of conservative solitons in resonance semiconductor Bragg structures with quantum wells are considered. Results of experimental studies of nonlinear effects in fibers with Bragg gratings are presented. For an active single-mode fiber with a Bragg refractive-index grating and nonlinear gain and absorption, dissipative solitons are described using the approximation of slowly varying amplitudes and inertialess nonlinearity. It is shown that the dissipative factors qualitatively change the properties of solitons compared to the conservative case. Using the Maxwell-Bloch equations, it is demonstrated that the ratio between the gain and absorption relaxation times significantly affects the stability of localized structures. The interaction of dissipative optical Bragg solitons is described. It is shown that, beyond the scope of the approximation of slowly varying amplitudes, the average velocity of propagating dissipative Bragg solitons acquires only discrete values, and formation of pairs of solitons with two values of the phase difference becomes possible. For a birefringent fiber, dissipative vector optical Bragg solitons are demonstrated.     

Optoacoustic solitons in Bragg gratings

Optical gap solitons, which exist due to a balance of nonlinearity and dispersion due to a Bragg grating, can couple to acoustic waves through electrostriction. This gives rise to a new species of "gap-acoustic" solitons (GASs), for which we find exact analytic solutions. The GAS consists of an optical pulse similar to the optical gap soliton, dressed by an accompanying phonon pulse. Close to the speed of sound, the phonon component is large. In subsonic (supersonic) solitons, the phonon pulse is a positive (negative) density variation. Coupling to the acoustic field damps the solitons' oscillatory instability, and gives rise to a distinct instability for supersonic solitons, which may make the GAS decelerate and change direction, ultimately making the soliton subsonic.     

光纤布拉格光栅中隙孤子的EPP方法分析

提出了利用EPP方法分析光纤布拉格光栅中隙孤子的解。基于非线性耦合模式方程(NLCME)定性地分析了无微扰条件下的隙孤子参数与孤子的其它特性的关系。利用EPP方法分析了隙孤子的能量特性。证明了隙孤子的速度影响形态特性和能量分布。从理论上解释了已观察到的一系列隙孤子的试验现象,对光纤布拉格光栅中产生隙孤子的应用具有理论意义。     

光纤布拉格光栅中的隙孤子存在条件

提出光纤布拉格光栅中产生隙孤子的条件和参量制约关系。利用非线性耦合模式方程建立光纤布拉格光栅中孤子的传播方程,通过扰动方法建立了参量的微分方程,计算得到参量近似解。以周期非线性光学介质中隙孤子存在的条件为依据,数学计算分析得到两组参量关系不等式。最终通过数值计算说明了这些参量之间存在制约关系和物理意义。从而理论上说明了在光纤布拉格光栅中隙孤子存在需要选择适当参量。为光纤布拉格光栅中产生隙孤子的实验和进一步的工程应用提供了理论基础。     

Excitation of self-transparency Bragg solitons in quadratic media

We show that self-transparent or gap solitons with leading-order components at fundamental frequency can be generated in a singly resonant Bragg grating by second-harmonic generation. We discuss the conditions required for exciting these localized waves.     

Observation of surface gap solitons in semi-infinite waveguide arrays

We report on the observation of surface gap solitons found to exist at the interface between uniform and periodic dielectric media with defocusing nonlinearity. We demonstrate strong self-trapping at the edge of a LiNbO3 waveguide array and the formation of staggered surface solitons with propagation constant inside the first photonic band gap. We study the crossover between linear repulsion and nonlinear attraction at the surface, revealing the mechanism of nonlinearity-mediated stabilization of the surface gap modes.     

Nonreciprocal effects in active nonlinear optical fibers with nonlinearity dispersion

The nonreciprocity of the dynamics of Gaussian optical pulses propagating in inhomogeneous nonlinear active optical fibers with nonlinearity dispersion is considered. A substantial nonreciprocity of the time of pulse propagation along the optical fiber in the forward and backward directions is revealed. The possibility of realizing the regime of superluminal propagation of a pulse in one of the directions of the optical fiber is indicated.     

Nonlinear wave interaction in photonic band gap materials

We present detailed analytical and numerical studies of nonlinear wave interaction processes in one-dimensional (1D) photonic band gap (PBG) materials with a Kerr nonlinearity. We demonstrate that some of these processes provide efficient mechanisms for dynamically controlling so-called gap-solitons. We derive analytical expressions that accurately determine the phase shifts experienced by nonlinear waves for a large class of non-resonant interaction processes. We also present comprehensive numerical studies of inelastic interactions, and show that rather distinct regimes of interaction exist. The predicted effects should be experimentally observable, and can be utilized for probing the existence and parameters of gap solitons. Our results are directly applicable to other nonlinear periodic structures such as Bose–Einstein condensates in optical lattices.     

Subpicosecond pulse compression in nonlinear photonic crystal waveguides based on the formation of high-order optical solitons

We investigate by numerical simulation the compression of subpicosecond pulses in two-dimensional nonlinear photonic crystal (PC) waveguides. The compression originates from the generation of high-order optical solitons through the interplay of the huge group-velocity dispersion and the enhanced self-phase modulation in nonlinear PC waveguides.Both the formation of Bragg grating solitons and gap solitons can lead to efficient pulse compression. The compression factors under different excitation power densities and the optimum length for subpicosecond pulse compression have been determined. As a compressor, the total length of the nonlinear PC waveguide is only ten micrometres and therefore can be easily incorporated into PC integrated circuits.     

Observation of nonlinear self-trapping of broad beams in defocusing waveguide arrays

We demonstrate experimentally the localization of broad optical beams in periodic arrays of optical waveguides with defocusing nonlinearity. This observation in optics is linked to nonlinear self-trapping of Bose-Einstein-condensed atoms in stationary periodic potentials being associated with the generation of truncated nonlinear Bloch states, existing in the gaps of the linear transmission spectrum. We reveal that unlike gap solitons, these novel localized states can have an arbitrary width defined solely by the size of the input beam while independent of nonlinearity.     

Temporal Soliton Propagation in Nonlinear Fiber Gratings

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Periodic solitons in nonlocal nonlinear media

We identify periodic solitons in nonlocal nonlinear media: multi-hump soliton solutions propagating in a fully periodic fashion. We also demonstrate recurrences and breathers whose evolution is statistically periodic and discuss why some systems support periodic solitons while others do not.     

Raman gap solitons

We show that an intense pump pulse, detuned far from the Bragg resonance of a nonlinear periodic structure, can excite a gap soliton at a wavelength within the band gap that corresponds to the Raman shift of the medium. This Raman gap soliton is a stable, long-lived, quasistationary excitation that exists within the grating even after the pump pulse has passed. We find both stationary solitons as well as slow Raman gap solitons with velocities as low as 1% of the speed of light. The predicted phenomena should be observable in fiber Bragg gratings and other nonlinear photonic band gap structures.     

高非线性光子晶体光纤中飞秒脉冲的传输特性和超连续谱产生机制的实验研究及模拟分析

用实验和数值模拟两种方法研究了高非线性光子晶体光纤中飞秒激光脉冲的传输特性和超连续谱的产生机理，给出了抽运脉冲在三种不同中心波长情况下输出光谱展宽并形成超连续谱的实际测量及理论模拟结果.研究表明：在零色散波长抽运时，光谱展宽以自相位调制为主，同时三阶色散的影响明显，传输脉冲在时域内出现振荡次峰.而在反常色散区抽运时，光谱展宽的初期以自相位调制为主，随后根据抽运功率的不同孤子自频移、高阶光孤子的裂变和四波混频效应会逐渐增强，进而成为光谱展宽的主要原因.与此相应，在时域中能明显看到孤子的形成和红移，飞秒传输脉 关键词： 光子晶体光纤 高非线性光子晶体光纤 飞秒脉冲激光 超连续谱     

Spatial solitons in an optical lattice with varying diffraction and spatially inhomogeneous nonlinearity

In this paper, we present the (1+1)-dimensional inhomogeneous nonlinear Schrödinger (NLS) equation that describes the propagation of optical waves in nonlinear optical systems exhibiting optical lattice, inhomogeneous nonlinearity and varying diffraction at the same time. A series of interesting properties of spatial solitons are found from the numerical calculations, such as the stable propagation in the a nonperiodic optical lattice induced by periodic diffraction variations and periodic nonlinearity variations. Finally, the interaction of neighboring spatial solitons in a nonperiodic optical lattice is discussed, and the results reveal that two spatial solitons can propagate periodically and separately in the optical lattice without interaction.     

Nonautonomous Solitons in the(3+1)-Dimensional Inhomogeneous Cubic-Quintic Nonlinear Medium

We have constructed explicit nonautonomous soliton solutions of the generalized nonlinear Schrdinger equation in the(3+1)-dimensional inhomogeneous cubic-quintic nonlinear medium.The gain parameter has no effects on the motion of the soliton's phase or their velocities,and it affects just the evolution of their peaks.As two examples,we discuss the propagation of nonautonomous solitons in the periodic distributed amplification system and the exponential dispersion decreasing system.Results show that the presence of the chirp not only makes the intensity of solitons weaken more promptly,but also broadens their width.     

Controlled generation and steering of spatial gap solitons

We demonstrate the first fully controlled generation of immobile and slow spatial gap solitons in nonlinear periodic systems with band-gap spectra, and observe the key features of gap solitons that distinguish them from discrete solitons, including a dynamical transformation of gap solitons due to nonlinear interband coupling. We also describe theoretically and confirm experimentally the effect of the anomalous steering of gap solitons in optically induced photonic lattices.