Surface modes in photonic bandgap structures for lasing and sensing applications: the recursive Greens-function technique

In this paper, a new computational method based on the recursive Green function technique for calculation of light propagation and band structure of photonic crystal structures is reported. The advantage of this method in comparison to the conventional finite-difference time domain (FDTD) technique is that it computes Greens function of the photonic structure recursively by adding slice by slice on the basis of Dyson equation. In the present work a detailed study of the surface modes residing on a termination of a photonic crystal with a corrugated boundary is conducted. A particular attention has been paid to the effect of surface modes on the performance of a lasing cavity defined in a band-gap photonic structure. Based on the developed recursive Greens function technique we calculate a Q factor of a cavity situated in the crystal in the vicinity of a photonic structure termination