Trajectory eigenmodes of an orbiting wave source

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.