Nonlinear coupled-mode equations

Nonlinear coupled-mode equations governing the modal coupling of a two-mode coupled system (such as twin core couplers) are integrable; power swapping in such a system follows a periodical manner and can be expressed analytically. When three or more modes (for systems such as multiple-core couplers) are involved, the nonlinear coupled-mode equations are no longer integrable and chaotic power swapping is expected. A numerical approach is required, in general, to solve such nonlinear coupled systems involving the coupling of three or more modes. We find, however, that for certain structural configurations, such as triple-core couplers with the cores arranged in the shape of an isosceles triangle, the nonlinear coupled-mode equations for multiple-core couplers can be solved analytically under a resonant condition. The analytical solution indicates that power swapping among, for example, the three cores placed in the shape of an isosceles triangle can be aperiodic at high power, although power may flow from core to core periodically at low power.     

Optimal Design of the Nonlinear Phase-Shift via Second-Order Nonlinear Cascading in the Silica Optical Fiber

Based on the second-order nonlinear effect in the periodically thermal/electric-field poling silica optical fiber and starting from the coupled-mode equations, the analytic expressions of nonlinear phase-shift of all-optical switching under the condition of strong pump light are derived in this paper. The nonlinear phase-shift is optimized by selecting the parameters properly.     

Multicomponent gap solitons in superposed grating structures

We demonstrate, numerically, the existence and stability of multicomponent gap solitons in a Kerr nonlinear medium with a superposed grating based on a derived system of coupled-mode equations. Applications to all-optical logic and signal processing are discussed.     

Convective Brillouin amplification in a homogeneous plasma slab

The coupled-mode Brillouin backscatter equations, describing weakly nonlinear decay of a damped pump into two damped daughter waves, are solved analytically in the convective instability regime, yielding the convective instability threshold and backward amplification of a noise source.     

Controlled transmission in the forbidden photonic bandgap via transient nonlinear states

Using three-dimensional time-domain numerical simulations of the nonlinear dispersive Maxwell equations for a defect microcavity in a photonic crystal wire, we show that the transmission through the bandgap can be all-optically modulated via the generation of transient states associated with the nonlinear splitting of the defect mode. Analytical results based on time-domain coupled-mode theory are derived as well.     

Time-domain approach to parametric conversion: A comparative study on the impact of numerical dispersion

Numerical integration schemes of time-domain Maxwell equations in optical dispersive and nonlinear media are considered. In this context, we study quantitatively the impact of numerical dispersion on a typical nonlinear parametric conversion process, comparing the widely used finite difference (FDTD) approach and pseudo-spectral (PSTD) methods. Our results show that, unless using very dense grid, only fourth-order PSTD gives results in good quantitative agreement with standard coupled-mode theory.     

Propagation of ultrashort pulses in a nonlinear two-core photonic crystal fiber

We analyze the propagation of ultrashort pulses in a nonlinear two-core photonic crystal fiber (PCF) by solving a pair of coupled-mode equations that include all the significant linear and nonlinear terms. In particular, we highlight the fact that the coupling coefficient dispersion can cause significant pulse distortion over a short length of a two-core PCF. We also study all-optical switching and multi-frequency generation and obtain a reasonable agreement with recent experimental data.     

Propagation of ultrashort pulses in a nonlinear long-period fiber grating

By solving a pair of normalized nonlinear coupled-mode equations, we analyze in detail the propagation of ultrashort optical pulses in a nonlinear long-period fiber grating and investigate the conditions for the grating to function as an optical limiter or a saturable absorber. We show that the function of the grating depends on whether the nonlinear effect counteracts or enhances the detuning effect, and the nonlinear effect can be weakened significantly by the group-delay difference between the core mode and the coupled cladding mode. We present simulation results to illustrate these effects and discuss the physical conditions required for an effective operation of a nonlinear long-period grating.     

太赫兹金属线波导耦合模理论研究(英文)

基于耦合模假设,研究了描述两太赫兹金属线波导之间耦合特性的耦合模理论.通过采用与光波导耦合模理论等价的近似,研究得到了耦合方程和耦合系数表达式.进而,研究得到了两个相同金属线波导的耦合方程解及耦合特性.所提出的理论对于描述两金属线波导之间的能量传递具有重要的意义.     

统一非对称光波导横向耦合模理论分析

光波导横向耦合模理论包含正交耦合模理论和非正交耦合模理论两大类, 为了追求形式上的完美, 两类理论没有统一的解析解, 并且都没有对非匹配耦合系统中耦合功率的非对称性进行深入研究. 本文一方面由Helmholtz方程出发推导出了一种新型的非正交耦合模方程, 并对两类理论中的耦合模方程进行了统一处理和求解, 得到了一种统一的解析解; 另一方面根据所得到的统一的解析解对非匹配耦合系统中耦合功率的非对称性进行了详细研究, 计算结果表明非匹配耦合系统中的最大互耦合功率和最小自耦合功率均可用统一的解析解进行近似计算. 关键词： 光波导 耦合模理论 耦合器 最大耦合功率     

Coupled Band Gap Solitons in One-Dimensional Alternating Heisenberg Ferromagnetic Chains

The dynamics of coupled band gap solitons in one-dimensional Heisenberg ferromagnetic chains with bond alternation is considered analytically. Using the method of multiple scales the nonlinear coupled-mode equations (i.e. Manakov equations) for the upper cutoff mode of acoustic band and the lower cutoff mode of optical band are derived under the quasi-discreteness approximation. Due to the cross-phase modulation the type of soliton excitations may be changed and the vibrating frequencies of these soliton excitations may locate within or outside the gap of magnon frequency bands.     

Coupled-Mode Analysis of an NRD-Guide Coupler Based on Singular Perturbation Technique

A coupled-mode formulation for an NRD-guide coupler is presented using the singular perturbation technique. The first-order and second-order perturbations are taken into account in the analysis and the coupled-mode equations based on the eigenmodes of each waveguide in isolation are derived. The propagation constants obtained by these equations are compared with those by the exact theory, conventional coupled-mode theory, and improved coupled-mode theory. The numerical results of present formulation are in good agreement with the exact theory and superior to those of the other formulations.     

Coupled Band Gap Solitons in One-Dimensional Alternating Heisenberg Ferromagnetic Chains

The dynamics of coupled band gap solitons in one-dimensional Heisenberg ferromagnetic chains with bond alternation is considered analytically. Using the method of multiple scales the nonlinear coupled-mode equations (i.e.Manakov equations) for the upper cutoff mode of acoustic band and the lower cutoff mode of optical band are derived under the quasi-discreteness approximation. Due to the cross-phase modulation the type of soliton excitations may be changed and the vibrating frequencies of these soliton excitations may locate within or outside the gap of magnon frequency bands.``     

色散缓变光纤耦合器中的调制不稳定性

用奇偶超模对光纤耦合器的耦合模方程重写.讨论了当输入条件使奇偶超模其中之一被单独激发时,色散缓变光纤耦合器中的调制不稳定性,结合调制不稳定性,分析了色散缓变光纤耦合器在准连续波条件下的非线性效应.结果表明：在正常和反常色散区存在新型调制不稳定性.当满足一定条件时,在色散缓变光纤耦合器中传播的准连续波光束可以分解成脉冲序列,并且脉冲几乎不展宽,由此可以分离和提取稳定的超短脉冲;当输入功率一定时,增益谱随着传输距离的改变,形态基本保持不变;当传输距离一定时,增益谱随着输入功率的增强,宽度变宽,强度增强.     

Vectorial coupled—mode solitons in one—dimensional photonic crystals

We study the dynamics of vectorial coupled-mode solitons in one-dimensional photonic crystals with quadratic and cubic nonlinearities. Starting from Maxwell's equations, the vectorial coupled-mode equations for the envelopes of two fundamental-frequency optical mode and one low-frequency mode components due to optical rectification are derived by means of the method of multiple scales. A set of coupled soliton solutions of the vectorial coupled-mode equations is provided. The results show that a modulation of the fundamental-frequency optical modes occurs due to the optical rectification field resulting from the quadratic nonlinearity. The optical rectification field disappears when the frequency of the fundamental-frequency optical fields approaches the edge of the photonic bands.     

Influence of Polarization and Pulse Shape of Femtosecond Initial Laser Pulses on Spectral Broadening in Microstructure Fibers

We theoretically studied the influence of initial parameters of laser pulses, such as polarization, pulse shape and frequency chirp, on the broadening of spectrum during pulse propagation through microstructure fibers (MSFs). We utilized two coupled-mode equations based on the nonlinear Schrödinger equation using an intermediate-broadening model for a Raman response function, and the dispersion coefficients from 2nd to 7th orders for the slow and fast axes, respectively, of highly birefringent MSFs.     

Optical analogue of relativistic Dirac solitons in binary waveguide arrays

We study analytically and numerically an optical analogue of Dirac solitons in binary waveguide arrays in the presence of Kerr nonlinearity. Pseudo-relativistic soliton solutions of the coupled-mode equations describing dynamics in the array are analytically derived. We demonstrate that with the found soliton solutions, the coupled mode equations can be converted into the nonlinear relativistic 1D Dirac equation. This paves the way for using binary waveguide arrays as a classical simulator of quantum nonlinear effects arising from the Dirac equation, something that is thought to be impossible to achieve in conventional (i.e. linear) quantum field theory.     

A 1 × 7 fibre coupler with Kerr nonlinearity

We study for the first time the evolution of the guided field in a 1×7 fibre coupler with a third-order nonlinearity. An analytical solution of the nonlinear coupled-mode equations is presented in terms of the Weierstrass function. In particular, we found that contrary to the equal power distribution in the linear limit, a cross-state appeared if the coupler was initially excited in the central core and a certain input power was chosen. Finally, we analyse the far-field pattern of the coupler output.     

Effect of Material Response Time on Optical Bistability in Nonlinear Distributed Feedback Gratings

The dynamic behaviors of nonlinear periodic waveguides with a finite material response time have been investigated by numerically solving both the coupled-mode equations and Debye relaxation equation. When the response time of the nonlinearity is more than the transit time through the grating, a modulational instability is sufficiently suppressed and one can obtain optical bistability. Unlike a nonlinear Fabry-Perot resonator or ring resonators, overshoot in the transmission never takes place in the case of zero detuning. However, a relaxation (or damped) oscillation always takes place in the presence of detuning. It is also found that the switch-on time depends on the material response time and the switch-off time is almost independent of it.