Abstract
The resonant state expansion, a recently developed method in electrodynamics, is generalized here to planar open optical systems with non-normal incidence of light. The method is illustrated and verified on exactly solvable examples, such as a dielectric slab and a Bragg reflector microcavity, for which explicit analytic formulas are developed. This comparison demonstrates the accuracy and convergence of the method. Interestingly, the spectral analysis of a dielectric slab in terms of resonant states reveals an influence of waveguide modes in the transmission. These modes, which on resonance do not couple to external light, surprisingly do couple to external light for off-resonant excitation.
Highlights
Optical waveguides (WGs) are a basic building block for optical technology owing to their lossless guiding of light, enabled, for example, by total internal reflection
We study the role of resonant states (RSs) in the transmission of a dielectric slab and, in particular, the influence of the WG modes on the slab transmission
Using the resonant-state expansion (RSE), in particular, Eqs. (20) and (22), we calculate the perturbed eigenvalues ν for the simplest perturbation, which is constant across the slab, and compare the RSE results with the available exact solution
Summary
Optical waveguides (WGs) are a basic building block for optical technology owing to their lossless guiding of light, enabled, for example, by total internal reflection. The method of eliminating the cut presented here can be applied to fiber WGs, generalizing our recent paper on cylindrical resonators [8] to non-normal incidence and will be the subject of a future paper It enables treating planar photonic crystals and cavities, which have important applications.
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