Nonreciprocal phase shifts in spatiotemporally varying materials

Abstract

Materials with spatiotemporally varying properties exhibit nonreciprocal wave propagation characteristics. Nonreciprocity is predominantly identified by a left-to-right (L-R) transmission amplitude that is different from the right-to-left (R-L) transmission amplitude; a significant difference in the transmitted amplitudes is often desirable in this context. We review nonreciprocal vibration transmission in discrete mechanical systems with spatiotemporally modulated elasticity. We discuss the importance of the transmitted phase in this context, specifically that the difference between the L-R and R-L transmitted phases can be the main contributor to breaking of reciprocity in short systems. We show that the formulation of the problem in terms of response envelopes provides a computationally efficient path for exploring the steady-state nonreciprocal transmission characteristics of spatiotemporally modulated materials. In particular, we use this technique to identify response regimes that are characterized by a nonreciprocal phase shift in transmitted vibrations while maintaining equal transmitted amplitudes or energies.