Generalized Maxwell projections for multi-mode network Photonics

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 systems with 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 that 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, 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 in ensembles of resonators of any geometrical shape defined in materials with arbitrary responses.

Broadband vectorial ultra-flat optics with experimental efficiency up to 99% in the visible via universal approximators

“…Figure 1c represents the input-output relationship of the system, obtained from the generalized scattering theory, which provides an equivalent formulation of Maxwell equations based on an intuitive division of the space into propagation and resonant effects [40,62,63]. A detailed demonstration of this result is presented in [62,63], while here we summarize the main aspects.…”

“…Figure 1c represents the input-output relationship of the system, obtained from the generalized scattering theory, which provides an equivalent formulation of Maxwell equations based on an intuitive division of the space into propagation and resonant effects [40,62,63]. A detailed demonstration of this result is presented in [62,63], while here we summarize the main aspects. In this representation, space is partitioned into two main sets: the resonant nanostructures (resonances space) and the remaining space composing the external environment (propagation space).…”