Optical Circulation and Isolation Based on Indirect Photonic Transitions of Guided Resonance Modes

While there has been enormous progress in meta-surface designs, most meta-surfaces are constrained by Lorentz reciprocity. Breaking reciprocity, however, enables additional functionalities and greatly expands the applications of meta-surfaces. Here, we introduce a realistic nonreciprocal meta-surface that can achieve optical circulation and isolation. This device consists of a photonic crystal slab that supports two bands of guided resonances, and upon a temporal modulation in each unit cell with a spatially varying phase, an indirect photonic transition can be induced between the guided resonances, which breaks Lorentz reciprocity without the use of magneto-optic materials. We provide direct first-principle numerical simulations, using the multifrequency finite-difference frequency-domain method, to demonstrate that this device can achieve optical circulation and isolation with no back reflection under realistic modulation frequency and modulation strength.