A photonic crystal waveguide and a homogeneous medium waveguide for enabling a steep bend and arrangement at an arbitrary angle with low propagation loss. A photonic crystal waveguide has a core formed by a photonic crystal having periodicity in the Y-direction. Electromagnetic wave is propagated by a band on the Brillouin zone boundary of the photonic band structure of the core. A side face of the core parallel to the Y-direction is in contact with a homogeneous medium having a refractive index of n.sub.s, and the condition of .lamda..sub.0/n.sub.s>a.lamda./(.lamda..sup.2/4+a.sup.2).sup.0.5 is satisfied when the wavelength in vacuum of the electromagnetic wave is represented by .lamda..sub.0, the period of the photonic crystal is represented by a, and the period in the XZ-plane direction of the wave propagated through the core is represented by .lamda..