Resonant-state expansion applied to three-dimensional open optical systems: Complete set of static modes

Lobanov, S. V. ORCID: https://orcid.org/0000-0002-3126-1903, Langbein, W. ORCID: https://orcid.org/0000-0001-9786-1023 and Muljarov, E. A. ORCID: https://orcid.org/0000-0002-2878-4148 2019. Resonant-state expansion applied to three-dimensional open optical systems: Complete set of static modes. Physical Review A 100 (6) , -. 10.1103/PhysRevA.100.063811

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Abstract

We present two alternative complete sets of static modes of a homogeneous dielectric sphere, for their use in the resonant-state expansion (RSE), a rigorous perturbative method in electrodynamics. Physically, these modes are needed to correctly describe the static electric field of a charge redistribution within the optical system due to a perturbation of the permittivity. We demonstrate the convergence of the RSE toward the exact result for a perturbation describing a size reduction of the basis sphere. We then revisit the quarter-sphere perturbation treated by Doost et al. [Phys. Rev. A 90, 013834 (2014)], where only a single static mode for each angular momentum was introduced, and show that using a complete set of static modes leads to a small though non-negligible correction of the RSE result, improving the agreement with finite-element simulations. As another example of applying the RSE with a complete set of static modes, we calculate the resonant states of a dielectric cylinder, also comparing the result with a finite-element simulation.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Physics and Astronomy
Publisher:	American Physical Society
ISSN:	2469-9926
Date of First Compliant Deposit:	22 January 2020
Date of Acceptance:	6 December 2019
Last Modified:	02 May 2023 21:01
URI:	https://orca.cardiff.ac.uk/id/eprint/128940

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