Numerical simulations for the (3+1)-dimensional optical-field dynamics of nonstationary pulsed beams that propagate down Kerr-like nonlinear channel waveguides are carried out for what is to our knowledge the first time. Time-resolved intrapulse switching due to spontaneous symmetry breaking of optical fields from a quasilinear symmetric field to a nonlinear asymmetric field is analyzed. A novel instability phenomenon triggered by the symmetry breakdown is found.

A method for the solution of the discontinuity problem of SH-type modes in a piezoelectric plate waveguide of crystal symmetry 6 mm is described. The approach is a combination of the finite-element and the analytical method. This method can also be applied to the discontinuity problem of SH-type piezoelectric surface modes by increasing the plate-thickness. The numerical examples on the reflection, transmission and bulk wave scattering of Bleustein-Gulyaev waves by a groove, a rib and an overlay in an oversize piezoelectric plate waveguide are given.

A novel physical concept "optical instanton" is presented, which exhibits a particular quasi-particle form of spatiotemporally localized light field in an intensity-dependent nonlinear medium. The physical relevance of the ultimate localization to an ultrafast nonlinear coherent process is discusseed.

We predict that chemical waves can propagate as a guided mode in a reaction-diffusion system that consists of two regions with different wave speeds. In comparison with electromagnetic waveguides, unique features of the guided chemical waves can be seen in their dispersion characteristics. Conditions for supporting lowest-loss guided waves are discussed.

An efficient finite-element program utilizing approximate analytical solutions is described for the analysis of topographic waveguides for acoustic surface waves. In this method, the only ridge region is divided into triangular elements, and therefore it is possible to use computer memory more economically. Calculations have been made for the rectangular ridge waveguide, the dovetail ridge waveguide, the truncated knife edge waveguide and the wedge waveguide. The results obtained agree well with the earlier theoretical and experimental results.

A simple and efficient adaptive mesh generation for the approximate scalar analysis of optical waveguides is proposed. Two types of local weight estimates which can take into account both a field amplitude and its variation on a problem domain are introduced. One is a difference between linear and quadratic element solutions and the other is a residual for the partial differential equation to be solved. To show the validity and usefulness of the present scheme, the guided-mode analysis of a rib waveguide and the beam propagation analysis of a tilted slab waveguide and a Y-branching rib waveguide are performed.

A finite-element analysis is presented for predicting dispersion characteristics of layered waveguides with semi-infinite media for piezoelectric surface waves. This approach utilizes the finite-element method and the analytical solutions. The former is used for the layered interior region except the semi-infinite media, while the latter is used for the semi-infinite media, namely the exterior region. Numerical examples on the dispersion characteristics for the piezoelectric surface waves in a waveguide composed of a metal layer of finite thickness on the (001)-plane of the semi-infinite cubic crystal are given.

A 3-dimensional beam propagation method is described for the analysis of nonlinear optical fibers, where the finite element and finite difference methods are, respectively, utilized for discretizing the fiber cross section and the propagation direction. For efficient evaluation of wide-angle beam propagation, Pade approximation is applied to the differential operator along the propagation direction. In order to improve accuracy of solutions, isoparametric elements and numerical integration formulae derived by Hammer et al. are introduced. The propagation characteristics of nonlinear optical fibers with linear core and nonlinear cladding are analyzed, and unique features of nonlinear guided-wave propagation, such as spatial soliton emission, are investigated.

The finite-element method is adapted to handle scattering from periodic structures. The formalism developed by us treats both TE and TM waves in a unified form. The validity of the method is confirmed by comparing numerical results with the earlier theoretical results.

The length dependence of the crosstalk in multi-core fibers has been investigated by introducing random fluctuation along longitudinal direction. The power coupling coefficients in the coupled-power theory in heterogeneous multi-core fiber with seven cores were estimated based on consideration of the power coupling coefficients of the homogeneous multi-core fiber. The crosstalk can be quantitatively evaluated by employing coupled-power theory instead of coupled-mode theory.

The accuracy of an approximate scalar finite-element formulation for the analysis of dielectric optical waveguides is examined numerically. It is confirmed that this approach can give more accurate results for the waveguide with smaller index variation in the lateral direction of the region in which most of the energy is concentrated or the waveguide with wider guide-width.

This paper presents a useful numerical approach based on a self-consistent finite-element method for solving stationary properties of third-order nonlinear guidedwave phenomena in a planar optical waveguide which supports nonlinearly coupled transverse-electric and transverse-magnetic modes. This method can be useful for the stability analysis as well by tracing intermediate solutions generated through iterative processes. Depending on the transitional behavior of the intermediate solutions we can identify the nonlinear excitation under consideration to be absolutely stable, quasi-stable, or unstable.

The microwave network approach has been applied to the guided wave problems in the dielectric waveguides for millimeter waves made of a dielectric strip and a planar dielectric layer. This approach utilizes transmission-lines and equivalent networks which furnish physical insight, and application of the so-called transverse resonance technique yields, in very simple fashion, approximate but fairly accurate analytical expressions for the dispersion relations of these dielectric waveguides. The results computed from these relations for the strip dielectric guide, the insulated image guide, the single material guide and the inverted strip dielectric guide which have recently received considerable attention agree well with the experimental results by McLevige et al. and Azarmanèche et al. and the results obtained numerically by Ogusu.

The finite-element solutions of the discontinuity problems in a dielectric slab waveguide bounded by perfect electric or magnetic conductors are examined numerically and it is confirmed that the finite-element formulation for the bounded configuration facilitates solving the discontinuity problems in an open surface waveguide by placing the bounds appropriately away from the guiding surface.

Recent progress in research on the finite element method (FEM) for optical waveguide design and analysis is reviewed, focusing on the author's works. After briefly reviewing fundamentals of FEM such as a theoretical framework, a conventional nodal element, a newly developed edge element to eliminate nonphysical, spurious solutions, and a perfectly matched layer to avoid undesirable reflections from computational window edges, various FEM techniques for a guided-mode analysis, a beam propagation analysis, and a waveguide discontinuity analysis are described. Some design examples are introduced, including current research activities on multi-core fibers.

A numerical approach for the solution of the scattering by the discontinuities in an elastic plate waveguide for SH waves is described. The approach is a combination of the boundary element method and the analytical method. The results by this approach for the step discontinuity in a plate waveguide agree well with earlier theoretical results.