We extend the concept "optical instanton" to arbitrary dielectric media. For these general cases the exact analytical approach is no longer available. We derive an approximate analytical solution that would be valid in the vicinity of the light cone. A comparison is made between the analytical and the numerical solutions.

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.

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.

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 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.

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.

Ultrashort pulsed-beam propagation in a Kerr-type bulk medium is studied theoretically through classical and quantum field solutions of a higher-order nonlinear Schrödinger equation, which is valid for transversely localized femtosecond pulses in an anomalous dispersion regime. Quantum-mechanical stability analysis via a Hartree approximation to interacting bosons shows that within a certain range of a parameter the solitary wave could be stabilized even in the three-dimensional transverse space-time. This feature admits of an exotic route to multidimensional solitons.

A self-induced-transparent (SIT) system that takes advantage of morphology dependent resonances (MDR's) in a Mie-sized microsphere doped with a resonant material is proposed. The present system is doubly resonant: one has microscopic origin (the two-level system), while the other has macroscopic origin (the MDR). In this geometry, owing to the feedback action of MDR's, the pulse area can be much expanded, and thus the electric-field amplitude of the incident pulse can be reduced substantially compared with the conventional one-way SIT propagation. Theoretical results that incorporate dephasing due to structural imperfections are shown.