A three-dimensional photonic crystal has periodic-refractive-index
structures including a first layer having a periodic structure based on a
first rectangular lattice having a period of A along a first axis and a
period of B along a second axis orthogonal to the first axis in the plane
direction, a second layer having a periodic structure disposed at a
position shifted by +3B/8 along the second axis with respect to the
position of the first rectangular lattice, a third layer having a
periodic structure disposed at a position shifted by A/2 along the first
axis and B/2 along the second axis with respect to the position of the
periodic structure in the first layer, and a fourth layer having a
periodic structure disposed at the same position as the periodic
structure in the second layer.