Boundary element analysis of dielectric waveguides

We apply the boundary element method to the analysis of optical waveguides. After summarizing constant and linear element algorithms for both two- and three-dimensional simulations, we introduce a new recursive series procedure for constructing the diagonal matrix elements. We then demonstrate that our method can be employed to minimize the reflectivity of optical waveguide antireflection coatings with both straight and angled facets.     

Multicanonical comparison of polarization-mode dispersion compensator performance

We employ a modified version of the multicanonical algorithm to evaluate the system penalties and outage probabilities of different polarization-mode dispersion compensators. The procedure determines the optimal operating conditions for each compensator architecture far more efficiently than the standard Monte Carlo algorithm.     

Propagating beam analysis of multimode waveguide tapers

We analyze both slowly and rapidly varying tapers with the aid of the propagating beam method. Our results demonstrate that while the optimal longitudinal profile for slowly varying profiles is independent of the taper length, the optimum profile of a taper which varies rapidly with respect to the inverse of the average propagation constant difference of adjacent modes must be determined computationally in each case from the given values of its length and initial and final width parameters. We also analyze the region of validity of local normal mode perturbation theory in representative taper configurations.     

Efficient beam propagation techniques

It is shown that suitable modifications of the free-space-propagation operator in the standard fast-Fourier-transform beam propagation procedure yield a far more rapid code in the context of semiconductor rib waveguide calculations. The procedure curtails the diffraction experienced by the high-order Fourier components of the electric field and mirrors the structure of the recently introduced finite-difference beam propagation algorithm. It is used to investigate the propagation losses of a Y-junction composed of single-mode rib waveguides and illuminated by its normalized guided mode     

Enhanced negative refractive index control in a 5-level system

In this paper we demonstrate that for a five-level atomic system in a dense gas interacting with two low-intensity fields by adjusting the ratio of the two magnetic amplitudes associated with the fields the effects of atomic coherence can be simply controlled. Furthermore, a negative index of refraction can be achieved over a wide wavelength range with minimal absorption.     

Fresnel studies of reflected beams

It is shown that standard numerical methods based on the Fresnel equation accurately model the reflection of a collimated TE-polarized Gaussian beam from a planar dielectric interface when the beam is incident on the interface at arbitrary nonnormal angles     

Alignment methods for biased multicanonical sampling

The efficiency of the multicanonical procedure can be significantly improved by applying an additional bias to the numerically generated sample space. However, results obtained by biasing in different sampling regions cannot in general be accurately combined, since their relative normalization coefficient is not known precisely. We demonstrate that for overlapping biasing regions a simple iterative procedure can be employed to determine the required coefficients.     

A comparison of Lanczos electric field propagation methods

The authors analyze the losses of a strongly guiding semiconductor rib waveguide Y-junction with the aid of various propagation algorithms based on Lanczos reduction. Although for the example Lanczos procedures adequately describe electric field propagation in the Fresnel approximation, the Helmholtz implementation converges unacceptably slowly. They therefore propose a finite-difference wide-angle approach which employs a power-series expansion of the forward propagation operator. The computational efficiency of the method is comparable to that of the Fresnel formalism with little or no reduction in accuracy from the Helmholtz technique     

Generalized propagation techniques-application to semiconductor ribwaveguide Y-junctions

The simulation of electric fields in strongly guiding semiconductor rib waveguide Y-junctions with a new, general operator identity which yields a series of practical and easily programmed fourth-order accurate propagation algorithms is described. While the methods require 3-6 times the computation time of standard procedures for a given propagation step, they are typically more precise by several orders of magnitude for reasonably small propagation step lengths. The exact ratio of CPU times required to achieve a given accuracy, however, is somewhat problem dependent. It is noted that the procedure has been generalized to all orders     

New approach to lossy optical waveguides

We review a method we recently developed to construct Green's function in the paraxial approximation associated with arbitrary graded-index optical elements. We then demonstrate that our formalism may be successfully applied to calculate in an extremely simple fashion the optical losses associated with bent and perturbed optical waveguides.