Analogue Transformations in Physics and their Application to Acoustics

TL;DR

This paper introduces a universal transformation method based on analogue spacetimes, enabling advanced control of waves in various physical systems like acoustics and quantum fluids, surpassing previous limitations.

Contribution

It develops a new transformation approach using analogue spacetimes, allowing transformations involving space-time mixing and moving media in wave control applications.

Findings

Designed a spacetime compressor for acoustic waves

Created a carpet cloak for a moving aircraft

Demonstrated the method's versatility across physics domains

Abstract

Transformation optics has shaped up a revolutionary electromagnetic design paradigm, enabling scientists to build astonishing devices such as invisibility cloaks. Unfortunately, the application of transformation techniques to other branches of physics is often constrained by the structure of the field equations. We develop here a complete transformation method using the idea of analogue spacetimes. The method is general and could be considered as a new paradigm for controlling waves in different branches of physics, from acoustics in quantum fluids to graphene electronics. As an application, we derive an "analogue transformation acoustics" formalism that naturally allows the use of transformations mixing space and time or involving moving fluids, both of which were impossible with the standard approach. To demonstrate the power of our method, we give an explicit design of a spacetime compressor for acoustic waves and a carpet cloak for a moving aircraft.