Design of two-dimensional photonic crystal defect states for quantum   cascade laser resonators
  Current quantum cascade lasers based upon conduction band electron transitions are predominantly TM (electrical field normal to the epitaxial direction) polarized. Here we present a study of localized defect modes, with the requisite TM polarization, in connected square and hexagonal lattice two-dimensional (2D) photonic crystals for application as quantum cascade laser resonators. A simple group-theory based analysis is used to produce an approximate description of the resonant modes supported by defects situated at different high symmetry points within the host photonic lattice. The results of this analysis are compared with 2D finite-difference time-domain (FDTD) simulations, showing a close correspondence between the two analyses, and potential applications of the analysis in quantum cascade laser design are considered. 
Kartik Srinivasan and Oskar Painter