At least one exemplary embodiment is directed to a waveguide including a plurality of linear defects of a three-dimensional photonic crystal, the plurality of linear defects include a first defect formed by changing the medium of some of columnar structures to a medium different from that of the columnar structures and a second linear defect formed by shifting the position or changing the shape of some of the columnar structures extending in the same direction as the first linear defect, and the first linear defect and the second linear defect are disposed apart by 0.5 times the out-of-plane lattice period or more in the stacking direction of the three-dimensional photonic crystal.