Two-dimensional dielectric microcavities are of widespread use in microoptics applications. Recently, a trace formula has been established for dielectric cavities which relates their resonance spectrum to the periodic rays inside the cavity. In this paper, we extend this trace formula to a dielectric disk with a small scatterer. This system has been introduced for microlaser applications, because it has long-lived resonances with strongly directional far field. We show that its resonance spectrum contains signatures not only of periodic rays but also of diffractive rays that occur in Keller's geometrical theory of diffraction. We compare our results with those for a closed cavity with Dirichlet boundary conditions.
|Translated title of the contribution||Trace formula for a dielectric microdisk with a point scatterer|
|Number of pages||33|
|Journal||Journal of Physics A: Mathematical and Theoretical|
|Publication status||Published - 15 Apr 2011|
Bibliographical notePublisher: IOP
Hales, RFM., Sieber, MMA., & Waalkens, H. (2011). Trace formula for a dielectric microdisk with a point scatterer. Journal of Physics A: Mathematical and Theoretical, 44(15), . https://doi.org/10.1088/1751-8113/44/15/155305