We established numerical methods to simulate quantum optical phenomena in photonic crystals whose refractive indices are modulated periodically to realize photonic bandgap frequencies where the presence of electromagnetic eigenmodes is forbidden. We applied those methods as well as an analytical method based on the Green function formalism to superfluorescence and quadrature-phase squeezing, and successfully evaluated their quantum aspects such as quantum localization of photons and enhancement of squeezing due to the presence of the photonic bandgap and anomalous photon group velocity. To confirm these quantum effects by experiments, two types of specimens, that is, photonic crystal slabs made of nonlinear optical materials and one-dimensional periodic structures containing rare earth ions were fabricated. Their dispersion relations, quasi phase matching, and light emission are now under investigation. On the other hand, we recently found strong localization of the electromagnetic field in certain three-dimensional fractal structures in the microwave frequency region. Its mechanism as well as application to microwave cavities and antennas are now studied.