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

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 towards the exact result for a perturbation describing a size reduction of the basis sphere. We then revisit the quarter-sphere perturbation treated in [Doost {\it et al.}, Phys. Rev. A {\bf 90}, 013834 (2014)], where only a single static mode per 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.

arXiv comment11 pages, 5 figures

References in corpus (7)

• Brillouin-Wigner perturbation theory in open electromagnetic systems
• Exact mode volume and Purcell factor of open optical systems
• Resonant state expansion applied to three-dimensional open optical systems
• Resonant state expansion applied to two-dimensional open optical systems
• Resonant-state expansion for open optical systems: Generalization to magnetic, chiral, and bi-anisotropic materials
• Resonant state expansion applied to planar open optical systems
• Resonant-state expansion of three-dimensional open optical systems: Light scattering

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