A fundamental Lagrangian approach to transformation acoustics and spherical spacetime cloaking

Instituto de Matemática Multidisciplinar, Universitat Politècnica de València - Camino de Vera s/n, E-46022 Valencia, Spain, EU

^a mtung@mat.upv.es

Received: 9 April 2012
Accepted: 14 April 2012

Abstract

Transformation acoustics centers on the construction of advanced acoustic devices by combining mathematical transformation techniques with the engineering of acoustic metamaterials. We show how differential-geometric methods together with a variational principle form the basis of a powerful framework to control acoustic waves as desired. This formalism is required to leave the acoustic wave equation invariant under coordinate transformations and is shown to consist of a proposed acoustic Lagrangian function on a smooth spacetime manifold. As an immediate consequence, we can derive the general constitutive relations between the acoustic parameters (bulk modulus and mass-density tensor) of the physical and virtual spaces under consideration. We conclude with a practical application of this theory by presenting acoustic spherical cloaking with time dilation.