Poles and zeros in non-Hermitian systems: Application to photonics

TL;DR

This paper introduces a contour integration method to compute poles and zeros in non-Hermitian photonic systems, facilitating device design and analysis by linking resonance features to scattering properties.

Contribution

The authors develop a novel, general approach to accurately find zeros in electromagnetic response functions, which was previously lacking in photonics research.

Findings

Applied to nanophotonic metasurfaces to identify reflection zeros

Demonstrated extraction of sensitivities for device optimization

Showed the method's applicability to other physics domains

Abstract

Resonances are essential for understanding the interactions between light and matter in photonic systems. The real frequency response of the non-Hermitian systems depends on the complex-valued resonance frequencies, which are the poles of electromagnetic response functions. The zeros of the response functions are often used for designing devices, since the zeros can be located close to the real axis, where they have significant impact on scattering properties. While methods are available to determine the locations of the poles, there is a lack of appropriate approaches to find the zeros in photonic systems. We present an approach to compute poles and zeros based on contour integration of electromagnetic quantities. This also allows to extract sensitivities with respect to geometrical or other parameters enabling efficient device design. The approach is applied to a topical example in nanophotonics, an illuminated metasurface, where the emergence of reflection zeros due to the underlying resonance poles is explored using residue-based modal expansions. The generality and simplicity of the theory allows straightforward transfer to other areas of physics. We expect that easy access to zeros will enable new computer-aided design methods in photonics and other fields.