Coupled-mode analysis of a nonreciprocal elastic wave circulator

Acoustic and elastic metamaterials with time- and space-dependent material properties have received great attention recently as a means to increase the degree of control over mechanical waves. A circulator is a device that can transmit and receive signals in a nonreciprocal fashion using a network of ports attached to a junction having either spatiotemporally varying properties or momentum bias. The work presented here considers the numerical study of an elastic wave circulator, which is composed of three elastic waveguides attached to a thin elastic ring, creating a three-port network with 3-fold rotational symmetry. Nonreciprocity is achieved for both flexural and extensional waves by modulating the elastic modulus of the ring in a rotating fashion. An approximate model based on coupled-mode theory, which makes use of a plane wave basis, is derived and implemented. Steady state solutions are found, which include the generated harmonics of the modulation frequency. The coupled-mode model is compared with a finite element approach, and conditions on the system parameters that enable a high degree of nonreciprocity are then discussed in terms of a set of characteristic dimensionless numbers. [Work supported by NSF EFRI.]