Modes of wavechaotic dielectric resonators
Abstract
Dielectric optical microresonators and microlasers represent a realization of a wavechaotic system, where the lack of symmetry in the resonator shape leads to nonintegrable ray dynamics. Modes of such resonators display a rich spatial structure, and cannot be classified through mode indices which would require additional constants of motion in the ray dynamics. Understanding and controlling the emission properties of such resonators requires the investigation of the correspondence between classical phase space structures of the ray motion inside the resonator and resonant solutions of the wave equations. We first discuss the breakdown of the conventional eikonal approximation in the short wavelength limit, and motivate the use of phasespace ray tracing and phase space distributions. Next, we introduce an efficient numerical method to calculate the quasibound modes of dielectric resonators, which requires only two diagonalizations per N states, where N is approximately equal to the number of halfwavelengths along the perimeter. The relationship between classical phase space structures and modes is displayed via the Husimi projection technique. Observables related to the emission pattern of the resonator are calculated with high efficiency.
 Publication:

arXiv eprints
 Pub Date:
 August 2003
 arXiv:
 arXiv:physics/0308016
 Bibcode:
 2003physics...8016T
 Keywords:

 Physics  Optics;
 Condensed Matter  Mesoscopic Systems and Quantum Hall Effect;
 Nonlinear Sciences  Chaotic Dynamics;
 Quantum Physics
 EPrint:
 33 pages, 16 figures, RevTeX 4