A photonic crystal waveguide and a homogeneous medium waveguide that can be bent sharply and placed at a free angle and have a low propagation loss. The photonic crystal waveguide (200) has a core composed of a photonic crystal (50) having a periodicity in the Y-direction. An electromagnetic wave propagates along a band on the border of the Brillouin zone of the photonic band structure of the core. The side surface parallel to the Y-direction of the core is in contact with a homogeneous medium of refractive index ns. A condition lambda0/ns>alambda/(lambda<2>/4+a<2>)<0.5> is satisfied where lambda0 is the wavelength of the electromagnetic wave in the vacuum space, a is the period of the photonic crystal, and lambda is the period in an X-Z plane direction of the wave propagating through the core. This condition is essential to prevent light from leaking from the side surface of the photonic crystal waveguide (200). Therefore, satisfying the condition confines the wave propagating through the core inside the side surface when the propagation angle phi=0 DEG .