Various optical isolator embodiments are disclosed. Embodiments comprise a waveguide section utilizing materials that induce a propagation constant shift that is propagation-direction-dependent. Embodiments are characterized by a cutoff frequency for forward propagating waves that is different than the cutoff frequency for reverse waves; the dimensions and direction of magnetization of the waveguide can be tailored so that, in a particular embodiment, the cutoff frequency for forward propagating waves is lower than the cutoff frequency for reverse waves. A particular embodiment is constructed as a single-mode waveguide on a substrate. The cross-section of the waveguide is inhomogeneous in terms of materials. At least one part of the cross-section is a non-reciprocal magneto-optic medium, which has nonzero off-diagonal permittivity tensor components. This inhomogeneity induces a propagation constant shift, which is propagation-direction-dependent. This device works as an optical isolator from the cut-off frequency of the lowest forward wave (lower frequency) to one for the lowest reverse wave (higher frequency). Various configurations consistent with the principles of the invention are disclosed.