• Open Access

Resonant-state expansion applied to three-dimensional open optical systems

M. B. Doost, W. Langbein, and E. A. Muljarov
Phys. Rev. A 90, 013834 – Published 28 July 2014

Abstract

The resonant-state expansion (RSE), a rigorous perturbative method in electrodynamics, is developed for three-dimensional open optical systems. Results are presented using the analytically solvable homogeneous dielectric sphere as unperturbed system. Since any perturbation which breaks the spherical symmetry mixes transverse electric (TE) and transverse magnetic (TM) modes, the RSE is extended here to include TM modes and a zero-frequency pole of the Green's function. We demonstrate the validity of the RSE for TM modes by verifying its convergence towards the exact result for a homogeneous perturbation of the sphere. We then apply the RSE to calculate the modes for a selection of perturbations sequentially reducing the remaining symmetry, given by a change of the dielectric constant of half-sphere and quarter-sphere shape. Since no exact solutions are known for these perturbations, we verify the RSE results by comparing them with the results of state of the art finite element method (FEM) and finite difference in time domain (FDTD) solvers. We find that for the selected perturbations, the RSE provides a significantly higher accuracy than the FEM and FDTD for a given computational effort, demonstrating its potential to supersede presently used methods. We furthermore show that in contrast to presently used methods, the RSE is able to determine the perturbation of a selected group of modes by using a limited basis local to these modes, which can further reduce the computational effort by orders of magnitude.

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  • Received 6 March 2014

DOI:https://doi.org/10.1103/PhysRevA.90.013834

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

©2014 American Physical Society

Authors & Affiliations

M. B. Doost, W. Langbein, and E. A. Muljarov*

  • School of Physics and Astronomy, Cardiff University, Cardiff CF24 3AA, United Kingdom

  • *egor.muljarov@astro.cf.ac.uk

Article Text

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Issue

Vol. 90, Iss. 1 — July 2014

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