(a) We compute the transmission properties of 2-d electromagnetic TM waves that are normally incident on a Fabry-Perot structure with mirrors consisting of photonic crystals. We use a boundary integral formulation with quadratic boundary elements and utilize the Ewald representation for the Green's functions. We trace the frequencies of the Fabry-Perot cavity modes traversing the photonic bandgap as the cavity length increases and calculate corresponding Q-values. We do the computation with both lossy and lossless materials. Our results are in very good agreement with experiments performed by H. Everitt's group at Duke.
Collaborators: Mansoor Haider, NCSU; V. Papanicolaou, Nat. Tech. U. of Athens, and Wichita St. U.
(b) We derive theoretically Second Harmonic Generation in an LC circuit chain with nonlinear inductors and with capacitors that alternate in value along the chain. We use this as a discrete model of a one dimensional photonic crystal. The periodicity in the chain is used to achieve phase matching.
Collaborators: A. Georgieva, NJIT; T. Kriecherbauer, U. Munich.