We report a new computational method based on the recursive Green's function technique for a calculation of light propagation in photonic crystal (PC) structures. The method computes the Green's function of the photonic structure recursively by adding slice by slice on the basis of the Dyson's equation, that relaxes memory requirements and accelerates the computational process. The method can easily account for the infinite extension of the structure both into the air and into the space occupied by the photonic crystal by making use of the so-called "surface Green's functions". This eliminates the spurious solutions (often present in the conventional finite-difference time domain methods). The developed method has been applied to study surface modes in semi-infinite photonic crystals and their application in surface-state cavities and waveguides. Namely, we demonstrate that confining PC surface states may result in enhanced intensity of an electromagnetic field on the surface and very high Q factor of the surface state. This effect can be employed as an operational principle for surface-mode lasers and sensors. We also show a possibility of using surface states as a novel type of waveguides and discuss their applications as efficient light couplers and directional beamers.
We study the effect of boundary roughness on the resonant states broadening of the optical whispering-gallery-mode microdisk lasing cavities. We develop a new, computationally effective, and numerically stable approach based on the scattering matrix (S-matrix) technique that is capable to deal with both arbitrary complex geometry and inhomogeneous refraction index inside the two-dimensional cavity. The method presented has been applied to study the effect of surface roughness and inhomogeneity of the refraction index on Q-values of microdisk cavities for lasing applications. We demonstrate that even small surface roughness (Δr〈 λ/50) can lead to an extreme degradation of high-Q cavity modes by many orders of magnitude. The results of numerical simulation are analyzed and explained in terms of wave reflection at a curved dielectric interface combined with the examination of Poincare surfaces of section as well as Husimi distributions.