Application of resonant-state expansion to inhomogeneous and non-spherical optical resonators

Sztranyovszky, Zoltan 2022. Application of resonant-state expansion to inhomogeneous and non-spherical optical resonators. PhD Thesis, Cardiff University. Item availability restricted.

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Abstract

Resonances determine the optical properties of an object, such as its transmittance, scattering cross-section, or local field enhancement. Resonant states (RSs) provide a physically intuitive way to describe these features and a range of related physical phenomena. In this thesis I study both the resonances of dielectric optical systems and the method called resonant-state expansion (RSE). The RSE is a perturbative approach to calculate RSs, capable of treating perturbations of arbitrary arbitrary strength. It expresses the RSs of the perturbed system in the basis of the RSs of a known, unperturbed system, transforming the problem of solving Maxwell's equation to find the resonances into a linear matrix eigenvalue problem. I study the completeness of the eigenmodes, the convergence rate of the Mittag-Leffler (ML) expansion of the Green's function (GF), as well as the convergence of sum rules that the eigenmodes satisfy, establishing limits of validity. I investigate the modes of spherically symmetric, radially inhomogeneous resonators, and find that by appropriately engineering the permittivity gradient one can achieve quasi-degeneracy of the transverse-electric and transverse-magnetic whispering gallery modes. I derive, based on the RSE, a first-order perturbation theory that can treat material and shape changes of arbitrary resonators with the same formalism, and discover a remarkable phenomenon when all orders of the standard perturbation series can contribute linearly in the change of a small parameter. I apply the RSE to non-spherical systems, and reveal additional divergent terms in the ML expansion of the GF affecting the RSE convergence, which were previously unaccounted for. Finally, I also apply a RSE based approach, which links the GF to the scattering matrix, for calculation of the cross-section of cylindrical dielectric resonators. This method can potentially supersede the computational efficiency of many other existing methods, as it does not require to solve Maxwell's equation across all space, and it also does not require overlap volume integrals between the mode fields and the excitation wave, which are used in other methods.

Item Type:	Thesis (PhD)
Date Type:	Completion
Status:	Unpublished
Schools:	Physics and Astronomy
Subjects:	Q Science > QC Physics
Uncontrolled Keywords:	resonant-state expansion, optics, photonics, whispering gallery mode, perturbation theory, scattering, electromagnetism, open systems
Funders:	EPSRC, Cardiff University, PSE College
Date of First Compliant Deposit:	16 November 2022
Last Modified:	16 Nov 2023 02:30
URI:	https://orca.cardiff.ac.uk/id/eprint/154243

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