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Abstract
Most of the resonant photonic structures behave like open cavities for light where light is trapped for some time before leaking or being absorbed. Their modes are called quasi-normal modes and are associated with complex eigenfrequencies , characterizing the rate at which the energy leaks from the structure. As a consequence, one can show that the fields of these modes diverge far away from the scatterer. This is problematic when one attempts to develop a theoretical description of the resonant interaction between light and resonant photonic stuctures in terms of their quasi-normal modes. Moreover, the existence or not of a non-resonant term in addition to these resonant contributions is still an open problem. Here, we address these two problems by deriving pole-expansions of the scattering operators of resonant optical structures. We evince the existence of a non-resonant term and we solve the problem of the divergence by studying the scattered field in the time domain and by using the causality principle. The quasi-normal mode expansion that we obtain will be of a great use to study light-matter interactions since it allows to determine the optical response of a photonic resonator both in the time and frequency domain.
Highlights
The resonant interaction between light and nanoscale photonic structures is a fundamental process in photonics
Resonances in photonics all share a common mathematical description. They can all be considered to be modes of open optical cavities often referred as quasi-normal modes or resonant states that are associated with complex eigenfrequencies ωn = ωn+iωn where ωn < 0 if the time-dependence of the fields is e−iωt
Published under licence by IOP Publishing Ltd is one of the main problems one faces when attempting to derive a theoretical description of the interaction between light and resonant photonic structures based on their quasi-normal modes
Summary
The resonant interaction between light and nanoscale photonic structures is a fundamental process in photonics. Resonances in photonics all share a common mathematical description They can all be considered to be modes of open optical cavities often referred as quasi-normal modes or resonant states that are associated with complex eigenfrequencies ωn = ωn+iωn where ωn < 0 if the time-dependence of the fields is e−iωt. These modes fulfill the outgoing boundary conditions and asymptotically behave like eiknr. Published under licence by IOP Publishing Ltd is one of the main problems one faces when attempting to derive a theoretical description of the interaction between light and resonant photonic structures based on their quasi-normal modes. The usefulness and the accuracy of the QNM analysis will be shown by studying the optical response of a dispersionless spherically symmetric scatterer
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