A photonic crystal having a structure of which the refractive index changes with a periodicity defined in a polar coordinate system is disclosed. And an optical waveguide element comprising said photonic crystal, optical inlet and outlet regions on the surface of said photonic crystal, and a defect region of incomplete photonic crystal periodicity formed within said photonic crystal is disclosed. The defect region functions as an optical waveguide path by guiding from the inlet region to the outlet region an optical signal incapable of propagating through the photonic band gap of the photonic crystal.