Designing Spectra in Disordered Photonic Structures

Abstract

In this chapter, we introduce the inverse design of disordered photonic structures with target spectral information. Starting from the concept of isospectrality, which originated from the old question of Can one hear the shape of a drum?, we discuss the derivation of isospectral relations between different shapes of photonic structures. Two mathematical techniques are introduced as examples of the nontrivial isospectral transformation in disordered photonics, supersymmetry and the Householder transformation, which enable the practical applications of photonic bandgap media with strong modal localization, random wave switching for binary or fuzzy logics, and inter-dimensional light transport without any loss of information.