Non-Hermitian band theory of nonreciprocal transmission and amplification

The phenomenon of amplifying forward-propagating signals while blocking back-propagating ones, known as the directional or nonreciprocal amplification, is important for a wide range of applications. As open systems that exchange energy with the environment, directional amplifiers exhibit intrinsically non-Hermitian physics. General formulas for the gain and directionality, though highly desirable, have been lacking. These quantities are closely related to the Green's function whose general form has been unknown for non-Hermitan bands. In this work, we find these formulas in a compact and user-friendly form. This solution highlights intriguing connections between the directional amplification and non-Hermitian topological band theory. In particular, our formulas are based on the concept of generalized Brillouin zone, which was initially introduced as a key ingredient in understanding the non-Hermitian topology. These formulas could provide a widely applicable criterion for designing high-quality directional amplifiers, and point to new potential applications based on non-Hermitian band theory.

Reference: Wen-Tan Xue, Ming-Rui Li, Yu-Min Hu, Fei Song, Zhong Wang, arXiv:2004.09529