We analyze an on-chip optical isolator based on direction dependent single-mode cutoff, which is described in 1D and 2D momentum space. Isolation is shown using 3D finite difference time domain (FDTD) where the magnetization is represented by imaginary off-diagonal permittivity tensor elements. The isolator designs are optimized using perturbation theory, which successfully predicts increased isolation for rib waveguides and structures with non-magnetic dielectric layers. Our isolators are based on bismuth iron garnet and its compatible substrates; an isolation ratio of 10.7 dB/mm is achieved for TM modes.