Trajectory eigenmodes of an orbiting wave source

¹ Institut Langevin, ESPCI ParisTech and Université Paris Diderot, CNRS UMR 7587 - 10 rue Vauquelin, 75231 Paris cedex 05, France, EU
² Matières et Systèmes Complexes, Université Paris 7 Denis Diderot, CNRS - UMR 7057 - Bâtiment Condorcet, 10 rue Alice Domon et éonie Duquet, 75205 Paris cedex 13, France, EU

Received: 8 January 2013
Accepted: 22 March 2013

Abstract

Resonances usually result from wave superpositions in cavities where they are due to the wave spatio-temporal folding imposed by the boundaries. These energy accumulations are the signature of the cavity eigenmodes. Here we study a situation in which wave superposition results from the motion of a source emitting sustained overlapping waves. It is found that resonances can be produced in an unbounded space, the boundary conditions being now defined by the trajectory. When periodic trajectories are investigated, it is found that for a discrete subset of orbits, resonant wave modes are excited. Trajectory eigenmodes thus emerge. These modes have three attributes. Their associated resonant wave fields are the Fourier transform of the source's trajectory. They are non-radiative and they satisfy the perimeter Bohr-Sommerfeld quantization rule.