Integrated Nonmagnetic Optical Isolators Based on Photonic Transitions $^{\ast}$

Based on the effects of photonic transitions, here we show that a linear, broadband, and nonreciprocal isolator can be accomplished by spatial-temporal refractive index modulations that simultaneously impart frequency and wave vector shifts during the photonic transition process. This paper demonstrates that on-chip isolation can be accomplished with dynamic photonic structures in standard material systems that are widely used for integrated optoelectronic applications.