Linear broadband nonreciprocity in waveguides using distributed feed forward control

Abstract

Nonreciprocal waveguides can exhibit different properties depending on the direction, amplitude, and frequency content of an incident wave. These systems are the focus of intense recent research activity in engineering and in acoustics in particular driven by exciting applications such as cloaking, subwavelength anechoic termination, and full-duplex communication. In biology, nonreciprocity has been identified in cochlear mechanics and is hypothesized to play a role in its filtering and nonlinear processing of sound. Although there has been a surge in the study of unidirectional energy propagation in acoustic media, most of the work has been limited to non-linear effects and/or narrowband non-reciprocity. However, nonlinear effects generate additional harmonics, complicating the approach, and narrowband non-reciprocity constrains the bandwidth that can be used. We have developed the theory for linear nonreciprocal broadband acoustic waveguides using a distributed feed forward control scheme that exhibits significant broadband, nonreciprocity while maintaining stability. We discuss the different systems for which the paradigm may be adopted along with the theoretical formalism to predict the stability and dispersion relations for this class of waveguides.