Nonreciprocal surface waves

Some surface waves have the property that a simple reversal of the direction of propagation leads to a surface wave with a different frequency. In this paper we explore the properties of such nonreciprocal waves for a variety of excitations and structures. For a semi-infinite geometry the nonreciprocity can be quite dramatic. For example in some magnetic systems, a surface wave exists for propagation in one direction, but no surface wave exists for propagation in the reverse direction. In thin films, it is generally the localization of the surface wave which is nonreciprocal. Thus a surface wave travelling along the + x axis may be localized at the upper surface of the film, while a surface wave travelling along the - x axis is localized at the lower surface of the film. We will discuss nonreciprocal surface excitations which occur in a variety of systems. The elementary properties of nonreciprocal surface plasmons, polaritons, phonons and magnons are derived. We briefly review some of the applications of nonreciprocal surface waves to practical signal processing devices. Finally we discuss the microscopic origin of nonreciprocity.