A vectorial finite-element method for the analysis of three-dimensional dielectric waveguides is developed in terms of all three components (Hx, Hy, and Hz) of the magnetic field H. In this approach, the divergence relation for H is satisfied and the spurious, nonphysical modes which are included in the solutions of the earlier vectorial finite-element methods do not appear. In order to verify the accuracy of the method, the numerical results for a rectangular waveguide half-filled with dielectric are presented and compared with the exact results. The dielectric rectangular waveguides are also analyzed.

A three-dimensional beam propagation method based on a finite element scheme is described for the analysis of second harmonic generation devices. For the wide-angle beam propagation analysis, the Pade approximation is applied to the differential operator along the propagation direction. In order to avoid spurious reflection from the computational windows edges, the transparent boundary condition is introduced. Numerical results are shown for quasi-phase matched second harmonic generation devices using periodically domain-inverted LiNbO3 and LiTaO3 waveguides. The influences of the shape of domain-inverted regions and the inversion width on the conversion efficiencies are investigated in detail.

Using a full-vector finite element method (FEM) with curvilinear hybrid edge/nodal elements, a single-mode nature of index-guiding photonic crystal fibers, also called holey fibers (HFs), is accurately analyzed as a function of wavelength. The cladding effective index, which is very important design parameter for realizing a single-mode HF and is defined as the effective index of the infinite photonic crystal cladding if the core is absent, is also determined using the FEM. In traditional fiber theory, a normalized frequency, V, is often used to determine the number of guided modes in step-index fibers. In order to adapt the concept of V-parameter to HFs, the effective core radius, aeff, is determined using the actual numerical aperture given by the FEM. Furthermore, the group velocity dispersion of single-mode HFs is calculated as a function of their geometrical parameters, and the modal birefringence of HFs is numerically investigated.

A numerical approach for the solution of the scattering by an inhomogeneous H-plane discontinuity of arbitrary shape in a rectangular waveguide is described. The approach is a combination of the finite-element method and the analytical method. The validity of the method is confirmed by comparing numerical results for a waveguide-type dielectric filter, a right-angle corner bend, an inductive strip-planar circuit mounted in a waveguide, a T-junction and an inhomogeneous waveguide junction with the earlier theoretical and experimental results.

The elliptically-polarized nonlinear beam propagation in a two-dimensional optical guided-wave system containing Kerr media is solved numerically by using the finite-element method. Computed results for a nonlinear substrate exhibit novel transverse effects such as spatially modulational instabilities for solitons emitted from a film. Sensitiveness of the beam propagation on the initial state of polarization suggests a possibility for constructing new photonic devices.

Equivalent network approach has been applied to the guided wave problems in the dielectric thin-film waveguides for optical integrated circuits. The results by this approach for the rib waveguide and the optical strip waveguide agree well with the results by the numerical approaches.

Propagation characteristics of acoustic waves in photonic crystal fibers (PCFs) have been theoretically investigated in details. In order to evaluate acoustic band structures and guided modes for out-of-plane propagation in PCFs, analysis methods based on the finite element method are newly formulated. It is shown through numerical results that complete acoustic band-gaps (ABGs) exist in the cladding region of PCFs and that acoustic guided modes could be localized in the defect region of PCFs by the ABG effect. Furthermore, it is shown that acoustic guided modes could also be localized in the defect region of PCFs by the total internal reflection. These confinement mechanisms of acoustic waves propagating along the fiber length are completely different to those of lightwaves.

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.