At least one exemplary embodiment is directed to a waveguide, which includes a three-dimensional photonic crystal including a first linear defect and a second linear defect. The first linear defect is disposed at part of columnar structures and is formed of a medium different from the columnar structures. The second linear defect is disposed at part of columnar structures extending in the longitudinal direction of the first linear defect and is formed of a medium having a refractive index different from that of the medium used for the columnar structures. The second linear defect is separated from the first linear defect by a distance of at least 0.5 times the out-of-plane lattice period of the three-dimensional photonic crystal in a direction in which layers including the columnar structures are stacked.