A Framework to Compute Resonances Arising from Multiple Scattering

Numerous natural and technological phenomena are governed by
resonances. In nanophotonics, resonances often result from the interaction of
several optical elements. Controlling these resonances is an excellent
opportunity to provide light with properties on demand for applications
ranging from sensing to quantum technologies. The inverse design of large,
distributed resonators, however, is typically challenged by high computational
costs when discretizing the entire system in space. Here, this limitation is
overcome by harnessing prior knowledge about the individual scatterers that
form the resonator and their interaction. In particular, a transition matrix multi-scattering framework is coupled with the state-of-the-art adaptive Antoulas–Anderson (AAA) algorithm to identify complex poles of the optical response function. A sample refinement strategy suitable for accurately locating a large number of poles is introduced. The AAA algorithm is tied into an automatic differentiation framework to efficiently differentiate multi-scattering resonance calculations. The resulting resonance solver allows for efficient gradient-based optimization, demonstrated here by the inverse design of an integrated exciton-polariton cavity. ... mehrThis contribution serves as an
important step towards efficient resonance calculations in a variety of multi-scattering scenarios, such as inclusions in stratified media, periodic lattices, and scatterers with arbitrary shapes.