Abstract
The design of optical resonant systems for controlling light at the nanoscale is an exciting field of research in nanophotonics. While describing the dynamics of few resonances is a relatively well understood problem, controlling the behavior of systems with many overlapping states is considerably more difficult. In this work, we use the theory of generalized operators to formulate an exact form of spatio-temporal coupled mode theory, which retains the simplicity of traditional coupled mode theory developed for optical waveguides. We developed a fast computational method that extracts all the characteristics of optical resonators, including the full density of states, the modes quality factors, and the mode resonances and linewidths, by employing a single first principle simulation. This approach can facilitate the analytical and numerical study of complex dynamics arising from the interactions of many overlapping resonances, defined in ensembles of resonators of any geometrical shape and in materials with arbitrary responses.
Highlights
The design of optical resonant systems for controlling light at the nanoscale is an exciting field of research in nanophotonics
In the field of optical resonators, an approximate form of this approach is available in time dependent coupled mode theory32,33, which is routinely used in many applications, such as the design of efficient broadband light energy trapping systems34–36, the study of nonlinear dynamics37, and the engineering of photonic crystals and metamaterials38,39
By substituting the expression of the electromagnetic field inside each resonator region Ωn, given by Eq [10], into Eq [35] and by integrating over the volume Vn defined by the resonator region, we obtain the density of states (DOS) corresponding to the resonator region Ωn from the sum of the power density spectra of the internal modes:
Summary
The design of optical resonant systems for controlling light at the nanoscale is an exciting field of research in nanophotonics. Maxwell equations inside the resonator space Ωn are linear, and the dynamics of a(t) follow from the most general form of the linear time evolution equation for the modes am(t), with input sources corresponding to impinging waves s+: t
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