基于运动光栅光折变双光束耦合的刚性全息明孤子的动态演化

研究基于运动光栅双光束耦合的耗散光折变系统中的空间光孤子的动态演化问题.数值计算 表明，系统参数同这种孤子的稳定性密切相关.在某组系统参数下，孤子可以在晶体内稳定 传播足够远的距离.双光束耦合的相位与强度耦合系数之比越大，孤子的稳定性越好.讨论了 将这种系统应用于光学开关、中继及分路器件的可能性. 关键词： 空间光孤子 光折变非线性光学 耗散系统 全息光栅     

Stability and instability of nonlinear defect states in the coupled mode equations—Analytical and numerical study

Coupled backward and forward wave amplitudes of an electromagnetic field propagating in a periodic and nonlinear medium at Bragg resonance are governed by the nonlinear coupled mode equations (NLCME). This system of PDEs, similar in structure to the Dirac equations, has gap soliton solutions that travel at any speed between 0 and the speed of light. A recently considered strategy for spatial trapping or capture of gap optical soliton light pulses is based on the appropriate design of localized defects in the periodic structure. Localized defects in the periodic structure give rise to defect modes, which persist as nonlinear defect modes as the amplitude is increased. Soliton trapping is the transfer of incoming soliton energy to nonlinear defect modes. To serve as targets for such energy transfer, nonlinear defect modes must be stable. We therefore investigate the stability of nonlinear defect modes. Resonance among discrete localized modes and radiation modes plays a role in the mechanism for stability and instability, in a manner analogous to the nonlinear Schrödinger/Gross-Pitaevskii (NLS/GP) equation. However, the nature of instabilities and how energy is exchanged among modes is considerably more complicated than for NLS/GP due, in part, to a continuous spectrum of radiation modes which is unbounded above and below. In this paper we (a) establish the instability of branches of nonlinear defect states which, for vanishing amplitude, have a linearization with eigenvalues embedded within the continuous spectrum, (b) numerically compute, using Evans function, the linearized spectrum of nonlinear defect states of an interesting multiparameter family of defects, and (c) perform direct time-dependent numerical simulations in which we observe the exchange of energy among discrete and continuum modes.     

Nonlinear wave interactions in patterned Silica and AlGaAs waveguides

We study nonlinear interactions between discrete optical solitons that propagate in different regimes of diffraction, and the nonlinear scattering of dispersive waves by local optical potentials. It is well known in optics that when linear coherent waves meet, they interfere without interactions. Linear waves also scatter through local optical structures not exchanging any power with the guided modes of these structures. As a focusing Kerr nonlinearity is present, such linearly-inhibited phenomena can exist. Our studies are performed in silica and AlGaAs nonlinear waveguides, excited by ultra-short pulses in the near infrared. Presented at 9-th International Workshop on Nonlinear Optics Applications, NOA 2007, May 17–20, 2007, Świnoujście, Poland     

双光学孤子脉冲的传输特性

本文首先指出了算法分裂步骤(split-step)Fourier法和光束传播(propagating-beam)法的等价性.利用这种算法,数字地模拟了可变等振幅孤子脉冲对在无耗光纤中的传输过程,结果证明:提高振幅可使孤子的相互作用大大减小.     

Microscopic theory of soliton propagation in a mixture of two boson fluid films

A microscopic theory of soliton propagation in a mixture of two boson fluids atT=0°K has been provided.     

Vector NLS solitons interacting with a boundary

We construct multi-soliton solutions of the n-component vector nonlinear Schrödinger equation on the half-line subject to two classes of integrable boundary conditions (BCs): the homogeneous Robin BCs and the mixed Neumann/Dirichlet BCs. The construction is based on the so-called dressing the boundary, which generates soliton solutions by preserving the integrable BCs at each step of the Darboux-dressing process. Under the Robin BCs, examples, including boundary-bound solitons, are explicitly derived; under the mixed Neumann/Dirichlet BCs, the boundary can act as a polarizer that tunes different components of the vector solitons. Connection of our construction to the inverse scattering transform is also provided.     

Deep learning neural networks for the third-order nonlinear Schrödinger equation: bright solitons,breathers, and rogue waves

The dimensionless third-order nonlinear Schrödinger equation (alias the Hirota equation) is investigated via deep leaning neural networks. In this paper, we use the physics-informed neural networks (PINNs) deep learning method to explore the data-driven solutions (e.g. bright soliton, breather, and rogue waves) of the Hirota equation when the two types of the unperturbated and perturbated (a 2% noise) training data are considered. Moreover, we use the PINNs deep learning to study the data-driven discovery of parameters appearing in the Hirota equation with the aid of bright solitons.     

Small amplitude dust-acoustic soliton energy in dusty plasmas with suprathermal polarization force

The effect of suprathermal polarization force on both linear and weakly nonlinear dust-acoustic solitary structures in a three-component dusty plasma is investigated. For this purpose, a new expression of the polarization force acting on dust particles that include the electronic suprathermal effect is derived. The results are applied to two different experimental dusty plasmas. We have found that the polarization force acting on the dust grains decreases as the electron suprathermality becomes more significant. In addition, we have shown that, for a given value of the spectral index κ , the polarization force magnitude fluctuates from one plasma to another. The changes arising in the propagation of small-amplitude dust-acoustic (DA) solitons due to the presence of this suprathermal polarization force are also analysed. Interestingly, an increase in the magnitude of the polarization force leads to an increase in the amplitude and width of DA soliton and provides more energy to the motion of this soliton.     

Oblique interaction of electrostatic nonlinear structures in relativistically degenerate dense magnetoplasmas

We have investigated the interaction of obliquely propagating ion acoustic solitary waves in a magnetoplasma with relativistically degenerate electrons. Using the quantum hydrodynamics model and by employing the extended Poincaré–Lighthill–Kuo technique, we have derived a set of Korteweg de Vries equations for two solitons. We have observed that the system under consideration allows the formation of only compressive solitons and their velocities remain in the sub-acoustic limit. Furthermore, phase shifts of solitons as a result of their interaction have been calculated. The phase shifts have been observed to be dependent on the obliqueness and the physical parameters of plasma. It has also been noticed that phase shifts remain negative for the whole range of parameters generally found in white dwarf stars. We have observed that the phase shifts enhance with the enhancement in number density, however, the converse happens when the magnetic field is enhanced. It has also been observed that the phase shift is slightly greater for the solitons that are less oblique as compared to their more oblique counterparts. Furthermore, we have estimated the spatial scales of interaction of solitons using the parameters found in white dwarf stars.     

Necklace solitons in Bessel photonic lattice: Stability and internal oscillation

Stability, internal modes and internal oscillation of 12-pearled necklace solitons in photorefractive crystal with imprinted Bessel photonic lattices are investigated. It is shown that the imaginary parts of internal modes are negligible comparing with real parts. The stable solitons perform long-distance and quasi-periodic oscillation of intensity and shape under the perturbation of internal modes.