An exact numerical analysis of coupled planar electron waveguides with asymmetric rectangular potential profiles

An exact numerical analysis is given of electron waves in a pair of coupled semiconductor heterojunction electron waveguides modelled by a rectangular potential distribution. The waveguide lengths required for electron current transfer between the guides agree asymptotically with estimates from Yariv's coupled mode theory and are usefully more accurate. Moreover the electron wave coupling due to an ideal launcher can be worked out, leading to estimates of the off/on current ratio occurring in the waveguides when regarded as an ultrafast switch. For a Poisson probability distribution of the number of electrons N making up a bit-pulse, we have calculated the minimum average N, dependent upon , which would be required to keep the switching bit-error rate below prescribed limits. Pulse rise times and switching delays are derived from the explicit forms for the longitudinal electron wave group velocity. Combining the bit-error and switching-time calculations leads to estimates of the waveguide current densities which would be required in practice. Some normalized sets of curves relating to our analysis are given and used to predict the performance of particular examples of recently proposed AlGaAs/GaAs heterojunction electron waveguide switch/couplers.     

非等效折射近似的多量子阱波导色散关系

本文导出了任意折射分布的多量子阱波导芯子区域的转移矩阵,用非等效折射近似得到了TE和TM两种偏振的色散关系.理论的精确性经数值计算比较证明是完全可靠的.     

Propagation of soliton waves in nonlinear dielectric slab waveguides of parabolic index of refraction

The pulse propagation in a non-linear slab waveguide of parabolic index of refraction is treated by using differential equation techniques. A graded index dielectric slab waveguide free of material dispersion with a cubic order non-linearity is considered. The electromagnetic wave inside the waveguide is described in terms of a non-linear equation. Slowly varying envelope function representation is employed to develop a non-linear partial differential equation for the unknown envelope function of the electric field. An averaging method over the transverse direction is applied to reduce the unknown envelope function non-linear differential equation into a form resembling the well known non-linear Schrödinger differential equation. This equation is solved by applying the Inverse Scattering Method. The N-soliton solution is developed and presented explicitly for the practical case of the single mode dielectric slab waveguide. Numerical results presenting single and double soliton propagation are also given.     

An exact multiple scattering calculation in comparison with the Fresnel approximation

An exact solution to the problem of nucleon scattering from two fixed potentials is compared with its Fresnel approximation. The differential cross sections are found to be in good agreement over the entire range of scattering angles.     

Fresnel zones for modes and analysis of field fluctuations in random multimode waveguides

The notion of Fresnel zones for modes is introduced, which is analogous to the usual Fresnel zones introduced for rays. It is shown that using Fresnel zones for modes one can simplify the analysis of mode scattering at large-scale and random inhomogeneities of a medium in waveguides. Simple formulae to calculate fluctuations of mode amplitudes are obtained. They are similar to well-known formulae of geometrical optics and to those of the Rytov method used to calculate fluctuations of ray complex amplitudes. Relations deduced can be used for calculating field fluctuations both at regular waveguide points and at caustics.     

三平行光子晶体单模波导的耦合特性及其应用

将三光子晶体单模波导的相互耦合看成一个多模干涉系统.本征模的色散曲线相交或近于相交并出现简并模，简并模之间存在强烈耦合并导致模式的分布方式发生转变.多模干涉系统中，不同波长的光波能量在传输过程中由于相干而具有不同的空间输出行为，在近简并点处多模之间的相干解除，能流限制在原输入方向，不发生转移.三光子晶体单模光波导的这种特性可用来制作波分复用或解复用器件. 关键词： 光子晶体波导 简并模 多模干涉 波分复用或解复用     

An analysis of the Lorenz equations: Stable exact solutions

We prove the existence of stable solutions (x(t), y(t), z(t)) to the Lorenz system, t being the time variable. These solutions are valid for b = 2σ and r > 1, b, r and σ being positive parameters, and fall into two classes C_i and C_d depending on whether (x(t), z(t)) are both monotonically increasing or decreasing functions of t. The analytic structure of the solutions is also discussed.     

Specific features of the space-time structure of acoustic signals in multimode waveguides

The effect of the diffraction focusing of an acoustic field on the space-time intensity distribution of narrow-band pulsed signals in multimode oceanic waveguides is analytically and numerically studied. The laws governing this effect and its specific features are illustrated by the results of calculations based on the standard ray approximation and the mode theory for the acoustic field in an isovelocity waveguide.     

Radiative transfer limit of two-frequency Wigner distribution for random parabolic waves: An exact solution

The present Note establishes the self-averaging, radiative transfer limit for the two-frequency Wigner distribution for classical waves in random media. Depending on the ratio of the wavelength to the correlation length the limiting equation is either a Boltzmann-like integral equation or a Fokker–Planck-like differential equation in the phase space. The limiting equation is used to estimate three physical parameters: the spatial spread, the coherence length and the coherence bandwidth. In the longitudinal case, the Fokker–Planck-like equation can be solved exactly. To cite this article: A.C. Fannjiang, C. R. Physique 8 (2007).     

Conditions for the existence of weakly divergent bundles in plane-layered waveguides

We found conditions for the existence of weakly divergent bundles (WDB) of rays of different types in waveguides with a power-law dependence of the square of the refractive index. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika Vol. 42, No. 10, pp. 982–991, October, 1999.     

Investigation of self-imaging based on the field distribution in multimode photonic crystal waveguides

We have investigated the self-imaging phenomena based on the field distribution in two-dimensional multimode photonic crystal waveguides (PCWs) by the finite-difference time-domain (FDTD) method. The new self-imaging conditions are given for the mirrored images and the direct images. The self-imaging distributions in multimode PCWs can be explained by the new self-imaging conditions and the superposition of “sub-images”. The results of numerical simulation show a good agreement with the theoretical predictions.     

On the accuracy of the WKB approximation in optical dielectric waveguides

Eigenvalues and field distributions for optical waveguides obtained from the WKB approximation have been compared with those found from geometrical optics and from more rigorous weakly-guiding LP mode theories in the cases of the step-index and parabolic-index profiles. In all cases it is found that the zero-order WKB approximation yields very accurate eigenvalues provided care is taken in the choice of phase factors in the eigenvalue equation. Expressions are deduced for the required phase factors for guides of arbitrary index profile in both two- and three-dimensions, and physical interpretations are given in terms of ray optics. The first-order WKB field distributions are found to give good agreement with the mode fields everywhere except in the vicinity of the caustics.     

LiNbO_3:Fe晶体中光写入平面光波导的导光特性研究

从光折变效应的单中心模型和载流子的光伏迁移机理出发给出了高斯片光在LiNbO3:Fe晶体中导致的折射率变化分布的解析表达式 .利用片光以“三明治”辐照方式在LiNbO3:Fe晶体中写入了平面光波导结构 .用切片干涉法测量了波导区的折射率分布 ,并对波导进行了简单的导光测试 .根据射线方程以及波导的折射率分布对光写入波导的导光特性进行了模拟计算分析 .研究结果表明 ,在LiNbO3:Fe晶体中光写入光波导是可行的     

LiNbO3:Fe晶体中光写入平面光波导的导光特性研究

从光折变效应的单中心模型和载流子的光伏迁移机理出发给出了高斯片光在LiNbO3:Fe晶 体中导致的折射率变化分布的解析表达式.利用片光以“三明治”辐照方式在LiNbO3:Fe晶 体中写入了平面光波导结构.用切片干涉法测量了波导区的折射率分布，并对波导进行了简 单的导光测试.根据射线方程以及波导的折射率分布对光写入波导的导光特性进行了模拟计 算分析.研究结果表明，在LiNbO3:Fe晶体中光写入光波导是可行的. 关键词： LiNbO3:Fe晶体 光辐照法 平面光波导 导光特性 高斯片光     

The quasicrystalline approximation: Comparison of the spectral density with exact results

The quasicrystalline approximation (QCA) for electronic excitations in a one-dimensional liquid metal is examined by comparing the spectral density A(k, E) to exact numerical results. The numerical method is briefly described and the limitations of teh QCA are indicated.     

Cutoff frequencies in planar optical waveguides with arbitrary index profiles: An efficient numerical method

A numerical method for obtaining mode cutoffs for planar waveguides with arbitrary index profiles is developed. The method is based on the Galerkin method in which the wave equation for modes at cutoff is converted to a matrix eigenvalue equation using a set of orthogonal basis functions. Due to different boundary conditions, we have identified two separate cases; one, in which the cover and the substrate indices are identical leading to same behavior of the field at cutoff in these two regions and, the other, in which the two indices are different and hence, the field behaves differently. We have accordingly chosen different basis functions for the two cases. The method results in a generalized matrix eigenvalue problem which has been converted to a standard symmetric matrix eigenvalue analytically. The method has been used to obtain mode cutoffs for waveguides with a variety of index profiles. Comparisons with available exact results show that very good accuracies can be obtained with moderate matrix sizes.     

Calculation of parameters of plane-transverse inhomogeneities in waveguides with complex cross sections in the multimode regime

We present a method for studying plane-transverse inhomogeneities in waveguides with complex cross sections in the regime of incidence of several propagating and nonpropagating waves on an inhomogeneity. Vector eigenfunctions and critical wave numbers of waveguides with complex cross section have been determined using the method of partial regions allowing for a singularity on the edge. State University, Rostov-on-Don, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 10, pp. 1286–1301, October, 1997.     

A perturbation analysis of modes in diffused optical waveguides with Gaussian index profile

Inclusion of a quartic term with adjustable coefficient in the Taylor expansion approximation to gaussian index profiles of diffused optical waveguides is shown to provide an improved approximation to the true gaussian curve to beyond the e-folding depth. A first-order perturbation to the square-law “harmonic oscillator” solutions is applied to improve the calculations of mode indexes and to illustrate the manner in which the corrected wave functions are extended deeper into the substrate.