Reflectionless excitation of arbitrary photonic structures: A general theory

TL;DR

This paper presents a comprehensive theory for achieving reflectionless excitation of arbitrary photonic structures by tuning parameters to align complex-frequency solutions called R-zeros with real frequencies, enabling perfect impedance matching.

Contribution

It introduces a general theoretical framework for reflectionless excitation in photonic structures, including conditions for tuning parameters and the role of symmetries, expanding understanding of reflectionless states.

Findings

Reflectionless states can be achieved by tuning structural parameters.

Symmetries can naturally produce reflectionless states without tuning.

The theory predicts symmetry-breaking transitions related to exceptional points.

Abstract

We outline a recently developed theory of impedance-matching, or reflectionless excitation of arbitrary finite photonic structures in any dimension. It describes the necessary and sufficient conditions for perfectly reflectionless excitation to be possible, and specifies how many physical parameters must be tuned to achieve this. In the absence of geometric symmetries the tuning of at least one structural parameter will be necessary to achieve reflectionless excitation. The theory employs a recently identified set of complex-frequency solutions of the Maxwell equations as a starting point, which are defined by having zero reflection into a chosen set of input channels, and which are referred to as R-zeros. Tuning is generically necessary in order to move an R-zero to the real-frequency axis, where it becomes a physical steady-state solution, referred to as a Reflectionless Scattering Mode (RSM). Except in single-channel systems, the RSM corresponds to a particular input wavefront, and any other wavefront will generally not be reflectionless. In a structure with parity and time-reversal symmmetry or with parity-time symmetry, generically a subset of R-zeros is real, and reflectionless states exist without structural tuning. Such systems can exhibit symmetry-breaking transitions when two RSMs meet, which corresponds to a recently identified kind of exceptional point at which the shape of the reflection and transmission resonance lineshape is flattened.