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Journal Articles Journal of Physics: Conference Series Year : 2020

Modal analysis of Mie resonators: Pole-expansion of scattering operators

Ross Mcphedran
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Brian Stout
Nicolas Bonod


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 omega(n) = omega(n)' + i omega(n)'', omega(n)'' 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.
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Dates and versions

hal-02905116 , version 1 (23-07-2020)





Rémi Colom, Ross Mcphedran, Brian Stout, Nicolas Bonod. Modal analysis of Mie resonators: Pole-expansion of scattering operators. Journal of Physics: Conference Series, 2020, 1461, pp.012025. ⟨10.1088/1742-6596/1461/1/012025⟩. ⟨hal-02905116⟩
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