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Resonant-state expansion for periodic open optical systems

Neale, Sam Thomas 2021. Resonant-state expansion for periodic open optical systems. PhD Thesis, Cardiff University.
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The resonant-state expansion is a perturbation theory that allows the accurate calculation of the resonant states of a photonic system by using a complete set of resonant states of a basis system. This thesis pioneers a new research direction of existing rigorous perturbative theory to any periodic photonic system described by Maxwell's wave equations. This method provides new and unique tools for describing the interaction of light in periodic systems which are not available through other methods. The resonant states are found in frequency space for planar periodic systems which presents a major complication to the resonant-state expansion due to the branch cuts that are present in the frequency plane due to the dispersion relation between the frequency and the wavevector of the modes. We solve this by discretising the cuts into a series of artificial resonant states that lie along the cuts. These are then treated on equal footing with regular resonant states. Additionally, the resonant-state expansion method allows for a deeper understanding of the formation of the photonic crystal resonant states as it treats these modes as a superposition of all modes of the basis system. Specifically, we look at the bound states in the continuum, unusual modes which remain localised to the system despite existing in a strongly coupled system which contains leaky modes. The resonant-state expansion allows us to formulate mathematical conditions for these modes to form, as well as being able to distinguish between different classes of these modes.

Item Type: Thesis (PhD)
Date Type: Completion
Status: Unpublished
Schools: Physics and Astronomy
Subjects: Q Science > QC Physics
Uncontrolled Keywords: photonics, photonic crystals, resonant-state expansion, scattering matrix method, condensed matter physics, bound states in the continuum
Funders: Engineering & Physical Sciences Research Council (EPSRC)
Date of First Compliant Deposit: 23 July 2021
Last Modified: 02 Aug 2022 01:11

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