Full vectorial finite-element analysis of sharp optical waveguidecorners

The transmission efficiency of optical waves through a guided-wave structure, incorporating a sharp corner, is investigated by using rigorous numerical approaches based on the finite-element method. To show the versatility of the proposed numerical approaches, the modal power transmission coefficient of two rib waveguides is calculated, and the results are compared with those obtained by using other approaches     

Full vectorial finite-element-based imaginary distance beampropagation solution of complex modes in optical waveguides

In this paper, we address accurate computation of complex propagation constants and field distributions of different modes, in general, lossless and lossy optical dielectric waveguides. Using the vector finite-element formulation of the beam propagation method combined with the imaginary distance propagation technique, sequence of both the guided and leaky modes can be accurately calculated. To show the versatility and numerical precision of the proposed technique, we compute the modes of three different three-dimensional (3-D) waveguide structures and compare the results against those of other, different, vector formulations. Further, we present the design of a higher order mode filtering device, based on a 3-D leaky mode optical waveguide     

Numerical analysis of nonlinear bistable optical waveguides

Numerical solutions illustrating the onset of bistability and hysteresis are presented for the symmetrical step index, asymmetrical step index, and asymmetrical diffused slab nonlinear optical waveguides. Two different numerical techniques have been used independently-a finite-element method and a variational method. Both methods produce numerically stable solutions, and agreement between them is good for both increasing and decreasing total power from below or above the threshold power. The results are compared with analytical solutions for these structures. The onset and the end of the physically unstable solutions regime coincides with the two power thresholds for the increasing and decreasing powers     

Full-vector finite-element beam propagation method for three-dimensional nonlinear optical waveguides

A full-vector finite-element beam propagation method (VFE-BPM) in terms of all the components of slowly varying electric fields is described for the analysis of three-dimensional (3-D) nonlinear optical waveguides. Electric fields obtained with this approach can be directly utilized for evaluating nonlinear refractive index distributions. To eliminate nonphysical, spurious solutions, hybrid edge/nodal elements are introduced. Furthermore, to avoid spurious reflections from the computational window edges, anisotropic perfectly matched layer boundary conditions are implemented, and to reduce computational effort for the nonlinear optical waveguide analysis, an iterative algorithm is also introduced. The effectiveness of the present approach is verified by way of numerical examples: nonlinear directional couplers, spatial soliton emission phenomena, and soliton couplers.     

Novel vectorial analysis of optical waveguides

A nonlinear iterative (NLI) method, originally developed by Hewson-Browne in geomagnetism, is applied to the vectorial analysis of optical waveguides. The method explicitly shows the interrelations between the scalar, polarized and vectorial operators and can be conveniently implemented using finite difference methods. Excellent accuracy in the normalized propagation constant is claimed along with agreement with earlier work and field distributions. The method presented enables vector results to be obtained simply by using computer programs, often available, for either polarized or scalar modes. This procedure proves more efficient than a standard vectorial finite difference technique     

Vector finite element solution of saturable nonlinear strip-loaded optical waveguides

A numerical solution is given for nonlinear optical waveguides with power confinement in both transverse dimensions. Self-consistent solutions are obtained by using an accurate vector-finite-element formulation along with the penalty technique. Numerical results for the first quasi-transverse-magnetic power-dependent mode are presented for strip-loaded waveguides with saturable self-focusing media. The variations with total power are illustrated for the modal index and for the fraction of the total power carried by different regions, showing interesting abrupt power switching for realistic geometries. It is shown that the switching effect is maintained in the presence of saturation and over a range of two-transverse-dimensions geometries. This switching effect can be controlled with variation of some of the parameters of the guide.<>     

Approximate scalar finite-element analysis of anisotropic optical waveguides

An approximate scalar finite-element program for the analysis of anisotropic optical waveguides with a diagonal permittivity tensor is described. The accuracy of the method has been checked by calculating the eigenmodes of two-dimensional, anisotropic asymmetric slab waveguides. The results obtained for a channel waveguide embedded in LiNbO3 agree well with the results of the earlier vectorial finite-element method.     

Nonlinear finite-element semivectorial propagation method forthree-dimensional optical waveguides

A nonlinear semivectorial beam propagation method based on the finite element method is presented. It applies to three-dimensional optical waveguides and accounts for polarization effects. To show the usefulness of this approach numerical results regarding both E^x (quasi-TE) and E^y (quasi-TM) waves are presented for directional couplers with nonlinear cores. The limits of scalar formulations are highlighted especially when working near and above the coupler threshold power     

Transcendental equation for the vectorial modes of buried optical waveguides

The free-space radiation mode (FSRM) method is extended to allow full vector modal analysis of buried optical waveguides to be computed semi-analytically in a very fast, efficient, yet accurate, manner. Both TE and TM dominated modes are investigated, identifying propagation constants via an explicit transcendental equation, and full field profiles.     

A vectorial boundary element method analysis of integrated optical waveguides

In this paper, a new vectorial boundary element method is introduced and applied to the modal analysis of dielectric waveguides with piecewise homogeneous refractive indexes. The procedure, which is free of spurious modes, determines the full field distribution from the longitudinal fields at the refractive index boundaries. Singular kernels are evaluated through series solutions while the electric field discontinuity at corners is accommodated through either a grid refinement technique or a semianalytic approach. Our formalism generates propagation constants and modal field distributions for several representative refractive index profiles with far higher accuracy than standard finite-difference or finite-element procedures.     

Finite-element solution of integrated optical waveguides

A vectorH-field finite-element method has been used for the solution of optical waveguide problems. The permittivity of the guiding structures can be an arbitrarily tensor, only limited to being lossless. To extend the domain of the field representation, infinite elements have been introduced. To eliminate spurious solutions and to improve eigenvectors, a penalty function method has been introduced. To show the validity and usefulness of this formulation, computed results are illustrated for step channel waveguide, diffused channel waveguide, anisotropic channel waveguide, and channel waveguide directional couplers.     

非线性光波导中的空间双稳态特性

本文讨论了由非线性光波导中的场空间分布引起的双稳态效应，并采用数值方法计算了光功率分布情况，最后讨论了这种无I=P腔双稳态器件的物理机制。     

Comparison of two interactive finite-element programs for analysisof optical and microwave waveguides

This paper presents a comparison of two- finite-element programs developed for accurate cross-sectional analysis of arbitrary optical and microwave waveguiding structures. Both techniques were developed in response to the growing demand from scientists and engineers for application-specific expert systems, and employ advanced interactive pre- and post-processing facilities. They show good agreement, strongly complement one another, and could form the core of a whole library of similar “intelligent” software for computer-assisted analysis and design, with a wide range of possible applications within both supercomputer and workstation environments     

Approximate scalar finite-element beam-propagation method withperfectly matched layers for anisotropic optical waveguides

The perfectly matched layer boundary condition for arbitrary anisotropic media is incorporated into the approximate scalar beam propagation method. The procedure is based on a finite-element method for three-dimensional anisotropic optical waveguides with off-diagonal elements in a permittivity tensor. In order to treat a wide-angle beam propagation, the Pade approximant operator is employed. To show the validity and usefulness of this approach, numerical results are presented for Gaussian beam propagation in free space and Gaussian beam excitation on a three-dimensional anisotropic optical waveguide     

Crystal symmetry effects on nonlinear optical processes in optical waveguides

A general three-wave nonlinear (NL) optical interaction can be phase matched using the dispersion of optical waveguide modes. The phase-match condition can be fine tuned by varying the direction of propagation in a two-dimensional waveguide and using a birefringent NL material with an orientation that preserves TE and TM mode propagation. Two general cases are found where this technique is possible. The effects of crystal symmetry and orientation on the size of the NL interaction are calculated for all birefringent crystal classes and cubic crystal classes.     

Finite-element solution of nonlinear TM waves inmultiple-quantum-well waveguides

Intensity-dependent characteristics for TM-polarized optical waves guided by multiple-quantum-well (MQW) waveguides with arbitrary nonlinear media are numerically analyzed by the finite element method. In this approach, self-consistent solutions are obtained through a simple iterative procedure. The power-dependent dispersion relations and magnetic-field (H_x) as well as two electric-field ( E_y and E_z) profiles for nonlinear TM waves in MQW waveguides with three different nonlinear mechanisms are presented. It is shown that, for the waveguides with molecular orientational mechanism, a distinct power limiting action for nonlinear TM modes exists     

Organic nonlinear optical waveguides formed by solvent-assisted indiffusion

A technique is described for producing robust, low-loss waveguides from a wide range of organic nonlinear optical materials. The linear and nonlinear properties of waveguides produced by this solvent-assisted indiffusion process have been evaluated and intensity-dependent prism coupling demonstrated.     

Numerical solution of silicon-clad diffused planar optical waveguides

Computer modelling studies indicate that silicon-clad diffused planar optical waveguides exhibit a damped periodic oscillation in their attenuation and phase constant curves and that the attenuation is reduced significantly by reducing the maximum index change.     

A SIMPLE SOLUTION FOR MULTILAYER METALLIC OPTICAL WAVEGUIDES

A simple solution for a multilayer metallic optical waveguide by transforming it intoan equivalent three-layer slab waveguide is presented. The dispersion relation of the equivalentthree-layer slab waveguide is solved by using a simple iterative formula. This method itself isexact and can approach any accuracy desired. Moreover, the numerical results for four-layer andfive-layer structures show that the second-order solution is also accurate enough. It is simple andhas the same form of expressions for TE and TM modes and for different layer structures.     

Finite-element solution of planar arbitrarily anisotropic diffused optical waveguides

The finite-element method for propagation in planar anisotropic diffused optical waveguides with arbitrary permittivity tensor is presented. A Galerkin procedure has been introduced to the finite-element formulation, to study both the nonleaky and leaky surface waves. The complex propagation constants are determined as a function of frequency for possible modes of propagation. The accuracy of the method has been checked by calculating the nonleaky and leaky surface waves of Ti-diffused LiNbO3waveguides with Gaussian index profiles. The numerical results of Ti-diffused LiNbO3waveguides with dielectric overlays are also presented and the effects of dielectric overlays on the propagation characteristics for the nonleaky and leaky surface waves are examined.