Accurate simulation of two-dimensional optical microcavities with uniquely solvable boundary integral equations and trigonometric Galerkin discretization

Abstract

A fast and accurate method is developed to compute the natural frequencies and scattering characteristics of arbitrary-shape two-dimensional dielectric resonators. The problem is formulated in terms of a uniquely solvable set of second-kind boundary integral equations and discretized by the Galerkin method with angular exponents as global test and trial functions. The log-singular term is extracted from one of the kernels, and closed-form expressions are derived for the main parts of all the integral operators. The resulting discrete scheme has a very high convergence rate. The method is used in the simulation of several optical microcavities for modern dense wavelength-division-multiplexed systems.

Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics

“…This is in particular advantageous if the frequency dependence of the refractive index has to be included. For the frequency domain several approaches can be applied to quasi-two-dimensional geometries, such as the finite-difference frequency-domain (FDFD) method (Shainline et al, 2009), wave-matching method (Hentschel and Richter, 2002;Nöckel and Stone, 1995), internal scattering quantization approach (Tureci et al, 2005), volume element methods (Martin et al, 1999), boundary element methods (Wiersig, 2003a;Zou et al, 2011) and related methods based on boundary integral equations (Boriskina et al, 2004). The FDFD and the volume element methods are restricted to small structures because of the limited computational power that is available today.…”

Chains of coupled square dielectric optical microcavities

“…Among the few examples are the FEM modules in the commercial package (JCMwave GmbH), and academic programs of more numerical (Sopaheluwakan 2006) (FEM) or analytical character Prkna 2004;Boriskina 2006) (circular cavities). Probably also the near field solutions at resonances (scattered field part) generated by a computational treatment of specific scattering problems (Boriskina et al 2004Pishko et al 2007), for individual, suitably shaped cavities could be used for this purpose. A third alternative would be to employ real-frequency eigensolutions for the open, leaky individual cavities with artificial gain ("lasing eigenvalue problem" Smotrova and Nosich 2004;Smotrova et al 2006).…”

Manipulation of Backscattering From a Dielectric Cylinder of Triangular Cross-Section Using the Interplay of GO-Like Ray Effects and Resonances

“…usually more attractive as demanding the discretization of only the scatterer contour instead of its area [4]- [22]. However, one should keep in mind that many forms of the boundary IEs are contaminated by the presence of spurious eigenvalues [15], [16].…”