Theoretical research of the control of radiation fields in photonic crystals

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The following three projects were targeted at the start of this research project ; (1) to develop powerful analytical means to estimate the quality of the photonic crystals fabricated by the experimental teams, (2) to examine fundamental problems of photonic crystals which remain to be solved and (3) to propose new optical phenomena which will encourage the experimental teams to pave a new way to the future development of photonic crystals.For (1), we developed the theoretical methods for the calculations of the following three topics ; (1-1) the density of states of photonic bands of slab type photonic crystals and the lifetime of them induced by the leak of photons out of photonic crystals, (1-2) the frequencies of the photonic bands of defected photonic crystals and the optical response from them and (1-3) the band structures of photonic crystals of arbitrary shapes of unit cell.For (2), theoretical investigations were carried out successfully in the following three items ; (2-1) how to estimate the threshold population-inversion for the laser oscillation from atoms in photonic crystals, (2-2) what are the new features of photonic crystals in the phenomena of quantum optics such as superradiance, Rabi oscillation, nonlinear photon mixing and so on.For (3), we investigated fully the cross section of photon emission from a charge running near the surface of a photonic crystal. This calculation stimulated the experiments of several groups including the team of Dr. Segawa of this research project.