Theoretical analysis of the order to disorder phase transition in random photonic crystals

The effect of structural randomness introduction into ordered photonic crystals on the behavior of the Bloch-mode and defect mode is presented. In order to induce strong localization of optical waves in nanostructures, there are two kinds of schemes: to utilize the defect mode in photonic crystals and Anderson localization modes in random structures. Recently, the intermediate state between the two above structures has been remarkably noticed. Despite its potential advantage, however, the modal characteristic of these merged structures, random photonic crystals, has not been revealed systematically yet. The aim is to figure out the appropriate degree of randomness to induce highly localized modes. We investigate an impulse response of the random photonic crystals by 2D FDTD method. We array air holes with triangular lattice shape into silicon substrate based material, and set a defect area in the center. The randomness is introduced into the structure by randomly dislocating the positions of the air holes. After the impulse illumination, we acquire the temporal evolution of the electric amplitudes over the system. By employing DFT on the sampled signals, we achieve the frequency spectrum and Q factors of the modes. We confirmed the optical phase transition of the system: with the increase of the randomness, the propagating Bloch-modes become localized and achieve higher Q factors. Slight spectrum shifts are also confirmed. The confinement efficiency of optical waves in the photonic crystals is greatly improved as well.