Convergence of the galerkin method for numerical calculation of the guided modes of an integrated optical guide

The Galerkin method for numerical calculation of the natural modes of an integrated optical guide is proposed and the convergence of the Galerkin method is proved

Green's function expansions in dyadic root functions for shielded layered waveguides - Abstract

Dyadic Green's functions for inhomogeneous parallel-plate waveguides are considered. The usual residue series form of the Green's function is examined in the case of modal degeneracies, where second-order poles are encountered. The corresponding second-order residue contributions are properly interpreted as representing "associated functions" of the structure by constructing a new dyadic root function representation of the Hertzian potential Green's dyadic. The dyadic root functions include both eigenfunctions (corresponding to first-order residues) and associated functions, analogous to the idea of Jordan chains in finite-dimensional spaces. Numerical results are presented for the case of a two-layer parallel-plate waveguide

Mathematical analysis of the generalized natural modes of an inhomogeneous optical fiber

The eigenvalue problem for generalized natural modes of an inhomogeneous optical fiber without a sharp boundary is formulated as a problem for the set of time-harmonic Maxwell equations with the Reichardt condition at infinity in the cross-sectional plane. The generalized eigenvalues (including, as subsets, the well-known guided and leaky modes) of this problem are the complex propagation constants on a logarithmic Riemann surface. A theorem on spectrum localization is proved, and then the original problem is reduced to a nonlinear spectral problem with a compact integral operator. It is proved that the set of all eigenvalues of the original problem can only be a set of isolated points on the Riemann surface, and it is also proved that each eigenvalue depends continuously on the frequency and refraction index and can appear and disappear only at the boundary of the Riemann surface. © 2005 Society for Industrial and Applied Mathematics

Green's function expansions in dyadic root functions for shielded layered waveguides

Dyadic Green's functions for inhomogeneous parallel-plate waveguides are considered. The usual residue series form of the Green's function is examined in the case of modal degeneracies, where secondorder poles are encountered. The corresponding second-order residue contributions are properly interpreted as representing "associated functions" of the structure by constructing a new dyadic root function representation of the Hertzian potential Green's dyadic. The dyadic root functions include both eigenfunctions (corresponding to first-order residues) and associated functions, analogous to the idea of Jordan chains in finite-dimensional spaces. Numerical results are presented for the case of a two-layer parallel-plate waveguide

A radiation condition for uniqueness in a wave propagation problem for 2-D open waveguides

We study the uniqueness of solutions of Helmholtz equation for a problem that concerns wave propagation in waveguides. The classical radiation condition does not apply to our problem because the inhomogeneity of the index of refraction extends to infinity in one direction. Also, because of the presence of a waveguide, some waves propagate in one direction with different propagation constants and without decaying in amplitude. Our main result provides an explicit condition for uniqueness which takes into account the physically significant components, corresponding to guided and non-guided waves; this condition reduces to the classical Sommerfeld-Rellich condition in the relevant cases. Finally, we also show that our condition is satisfied by a solution, already present in literature, of the problem under consideration

Convergence of the galerkin method for numerical calculation of the guided modes of an integrated optical guide

The Galerkin method for numerical calculation of the natural modes of an integrated optical guide is proposed and the convergence of the Galerkin method is proved

Convergence of the galerkin method for numerical calculation of the guided modes of an integrated optical guide

The Galerkin method for numerical calculation of the natural modes of an integrated optical guide is proposed and the convergence of the Galerkin method is proved

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Mathematical analysis of the guided modes of an integrated optical guide

© 2002 IEEE. The eigenvalue problem for guided modes of an integrated optical guide is reduced to a strongly-singular domain integral equation. It is proved that the operator of the domain integral equation is a Fredholm operator with zero index. It is also proved that the spectrum of the original problem can only be a set of isolated points

Mathematical analysis of the guided modes of an integrated optical guide

© 2002 IEEE. The eigenvalue problem for guided modes of an integrated optical guide is reduced to a strongly-singular domain integral equation. It is proved that the operator of the domain integral equation is a Fredholm operator with zero index. It is also proved that the spectrum of the original problem can only be a set of isolated points