Numerical Techniques in Electromagnetics is designed to show the reader how to pose, numerically analyze, and solve electromagnetic (EM) problems. It gives them the ability to expand their problem-solving skills using a variety of available numerical methods. Topics covered include fundamental concepts in EM; numerical methods; finite difference methods; variational methods, including moment methods and finite element methods; transmission-line matrix or modeling (TLM); and Monte Carlo methods. The simplicity of presentation of topics throughout the book makes this an ideal text for teaching or self-study by senior undergraduates, graduate students, and practicing engineers.

Numerical Techniques in Electromagnetics, Second Edition

Using a simple approach based on the scalar finite element method, propagation characteristics of multilayer chan- nel waveguides are calculated. The effective index, modal field, confinement factor, far-field intensity pattern, and radiation angle of the far-field pattern (full width at half maximum intensity) for multilayer channel waveguides formed with multiple quantum well (MQW) materials and with the MQW materials replaced by a single homogeneous material with the root mean square value of the refractive indexes are compared. Numerical results confirm that the root-mean-square-value approximation, which has been widely used for planar MQW (two-dimensional) waveguides, is useful also for MQW channel (three-dimensional) waveguides with a large number of layers.

http://ieeexplore.ieee.org/iel1/50/7266/00293974.pdf

A Comprehensive Analysis of

Discrete scale invariance and complex dimensions

Cascading is the process by which the exchange of energy between optical beams interacting via second order nonlinearities (χ(2)) leads to various effects such as nonlinear phase shifts, the generation of new beams, all-optical transistor action, the formation of soliton-like (solitary) waves, etc. Here we review the fundamentals of the processes and discuss experimental verification of the effects and various related applications.

χ(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons

The investigation of nonlinear wave phenomena has been one of the main direc tions of research in optics for the last few decades. Soliton concepts applied to the description of intense electromagnetic beams and ultrashort pulse propagation in various media have contributed much to this field. The notion of solitons has proved to be very useful in describing wave processes in hydrodynamics, plasma physics and condensed matter physics. Moreover, it is also of great importance in optics for ultrafast information transmission and storage, radiation propagation in resonant media, etc. In 1973, Hasegawa and Tappert made a significant contribution to optical soliton physics when they predicted the existence of an envelope soliton in the regime of short pulses in optical fibres. In 1980, Mollenauer et al. conducted ex periments to elucidate this phenomenon. Since then the theory of optical solitons as well as their experimental investigation has progressed rapidly. The effects of inhomogeneities of the medium and energy pumping on optical solitons, the interaction between optical solitons and their generation in fibres, etc. have all been investigated and reported. Logical devices using optical solitons have been developed; new types of optical solitons in media with Kerr-type nonlinearity and in resonant media have been described.

Optical Solitons

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.

Approximate scalar finite-element analysis of anisotropic optical waveguides

A unified computer-aided numerical approach, based on the finite-element method, is developed for analyzing optical waves guided by dielectric slab waveguiding structures with arbitrary nonlinear media. In the formulations, both TE and TM polarizations are considered. For the TM case, the biaxial nature of nonlinear refractive index is considered without any approximation. Numerical results are presented for nonlinear TE and TM waves propagating in symmetric slab waveguides. The dependence of dispersion relations on the refractive-index profile of the film is examined. >

Finite-element formalism for nonlinear slab-guided waves

A new vectorial finite-element method for the analysis of dielectric waveguide problems is formulated in terms of all three components of the magnetic field H. In this approach, the relation div H = 0 is satisfied and the spurious non-physical solutions do not appear.

Vectorial finite-element method without spurious solutions for dielectric waveguide problems

An approximate scalar finite-element program for the analysis of anisotropic optical waveguides having a permittivity tensor with nonzero off-diagonal elements is described. In this approach, the nonphysical spurious solutions which are included in the solutions of the earlier vectorial finite-element method in an axial-components formulation do not appear. Numericaf examples On an anisotropic dielectric rectangular wave-guide composed of a uniaxial medium are given. Our results for the waveguide whose optic axis lies in the plane ( xy-plane) normal to the direction (z-axis) of propagation agree well with the results of the vectorial wave analysis using the variational method. We also demonstrate the application of this approach by analyzing the anisotropic dielectric rectangular waveguide whose optic axis lies in the xz - or yz -plane.

https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/6043/1/ITMTT32_6.pdf

Approximate Scalar Finite-Element Analysis of Anisotropic Optical Waveguides with Off-Diagonal Elements in a Permittivity Tensor

A useful numerical simulation technique is presented to solve nonlinear guided-wave problems in a planar or coaxial optical waveguide This technique is a combination of the finite-element method and the finite-difference method The former is applied to the waveguide cross section (xy or rθ plane), whereas the latter is applied to the propagation direction (z axis) With the split-step procedure a significant enhancement of computational efficiency is achievable The usefulness of the present approach is demonstrated through a number of numerical examples, some of which are displayed here

Kazuya Hayata

Papers

Approximate scalar finite-element analysis of anisotropic optical waveguides

Finite-element formalism for nonlinear slab-guided waves

Vectorial finite-element method without spurious solutions for dielectric waveguide problems

Approximate Scalar Finite-Element Analysis of Anisotropic Optical Waveguides with Off-Diagonal Elements in a Permittivity Tensor

Split-step finite-element method applied to nonlinear integrated optics