Amorphous photonic structures - Mansha, Shampy (2018)
This thesis concerns the study of amorphous photonic crystal structures: disordered photonic lattices possessing short-range but not long-range order. In the first part of the thesis, I study amorphous structures intended for electrically-pumped random quantum cascade lasers (QCLs). Random lasers are a class of lasers which, unlike traditional lasers, have no well-defined and well-structured cavity; lasing takes place through multiple scattering from a random medium. I design and analyze amorphous lattices of dielectric rods, joined by dielectric veins, which support high quality factor (Q factor) lasing for transverse magnetic (TM) modes. Simulations show that these structures can achieve 2D Q-factors of as large as 10^5, which is not possible using previous designs based on air holes etched in dielectric slabs. In the second part, I perform a numerical study of an amorphous variant of a “photonic topological insulator” (PTI). PTIs are photonic crystal structures with band structures analogous to topological insulator materials, supporting robust electromagnetic edge states that propagate unidirectionally along the edge. Although the existence of these edge states is justified by theoretical arguments that assume long-range order, I show that similarly robust edge states exist in amorphous lattices, which possess only short-range order. This study opens new possibilities for studying disorder in PTIs. In the third and final part, I develop a computational method called "FLAME-slab", which is capable of efficiently solving the wave scattering problem for amorphous slab structures, where scattering elements are distributed within a slab with short-range order. Compared to standard finite element or finite difference methods, the FLAME-slab method allows for much coarser meshes, with as few as three grid layers spanning the thickness of the slab. Solutions are generated based on the Flexible Local Approximation Method (FLAME), using Rigorous Coupled Wave Analysis (RCWA) as a subroutine to generate local basis functions.