A semiconductor optical amplifying apparatus includes: a substrate; an active layer having a quantum well structure formed on the substrate, the active layer guiding first waveguide mode light and second waveguide mode light having a polarization direction perpendicular to that of the first waveguide mode light and amplifying the first waveguide mode light and the second waveguide mode light, the active layer having quantum wells such that projected quantization axes obtained by projecting quantization axes of the quantum wells thereof on a plane perpendicular to a light waveguide direction are inclined at 45.degree. with respect to vibration directions of electric field vectors of the first waveguide mode light and the second waveguide mode light; and an electrode for supplying a current to the active layer.