Optical Isolation based on Space-time Engineered Asymmetric Photonic   Bandgaps
  Nonreciprocal electromagnetic devices play an important role in modern optical and microwave technologies. Conventional methods for realizing such systems are incompatible with integrated circuits. With recent advances in integrated photonics, the need for efficient on-chip magnetless nonreciprocal devices is more urgent than ever. This paper leverages space-time engineered asymmetric photonic bandgaps to generate optical isolation. It is shown that a properly designed space-time modulated slab is highly reflective/transparent for opposite directions of propagation. The proposed method requires a low modulation frequency, is magnetless and can achieve very high isolation levels. Experimental proof of concept at microwave frequencies is provided. 
Nima Chamanara, Sajjad Taravati, Zo\'e-Lise Deck-L\'eger, and   Christophe Caloz
physics.optics