Determination of optical modes in two-dimensional finite-size photonic crystals by photonic resonance scattering

The analogy of the resonance scattering of an electron by an atom is used to investigate optical modes in two-dimensional finite-size photonic-crystal resonators. This analysis enables us to determine complex resonance energies from which we can estimate optical modes and photon lifetimes in the resonators. The threshold amplitude gain of the laser exploiting this photonic-crystal resonator is inversely proportional to the photon lifetime. This linear relation is found to remain the same irrespective of the dimensionality of the photonic crystal structure, the number of unit cells, and the size of unit cell, as long as the filling factor of the gain cell is fixed. This implies that the two-dimensional finite-size photonic-crystal resonators work well despite complicated feedback mechanisms and the absence of clear-cut cavity mirrors.