Electromagnetic Siegert states for periodic dielectric structures

TL;DR

This paper extends Siegert states formalism to electromagnetic scattering in periodic dielectric structures, analyzing resonances, their dependence on coupling parameters, and potential for near-field amplification to enhance optical nonlinear effects.

Contribution

It introduces a formalism for electromagnetic Siegert states in periodic structures and proves a theorem on resonance control and near-field amplification via coupling parameter adjustments.

Findings

Existence of electromagnetic Siegert states in periodic dielectric arrays.

Analytic dependence of Siegert states on coupling parameters.

Potential for near-field amplification to enhance nonlinear optical effects.

Abstract

The formalism of Siegert states to describe the resonant scattering in quantum theory is extended to the resonant scattering of electromagnetic waves on periodic dielectric arrays. The excitation of electromagnetic Siegert states by an incident wave packet and their decay is studied. The formalism is applied to develop a theory of coupled electromagnetic resonances arising in the electromagnetic scattering problem for two such arrays separated by a distance 2h (or, generally, when the physical properties of the scattering array depend on a real coupling parameter h). Analytic properties of Siegert states as functions of the coupling parameter h are established by the Regular Perturbation Theorem which is an extension the Kato-Rellich theorem to the present case. By means of this theorem, it is proved that if the scattering structure admits a bound state in the radiation continuum at a certain value of the coupling parameter h, then there always exist regions within the structure in which the near field can be amplified as much as desired by adjusting the value of h. This establishes a rather general mechanism to control and amplify optical nonlinear effects in periodically structured planar structures possessing a nonlinear dielectric susceptibility.