ABSTRACT
In this chapter, we describe various approaches to computing
the spectra of photonic quasicrystals (PQCs). We focus on a
recently developed super-space method for computing the spectra and eigenstates of PQCs defined by the standard cut-and-project
construction, that involves directly solving Maxwell’s equations
in higher dimensions, where a generalization of Bloch’s theorem
applies. We emphasize the conceptual and practical differences
between super-space and supercell methods, which involve computing the eigenfrequencies and/or local density of states to an
approximation of the true aperiodic structure.
