Computing Bessel functions of the second kind in extreme parameter regimes

Yousif, Hashim A.; Melka, Richard F.

doi:10.1016/s0010-4655(02)00697-5

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2011

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“…NAG, Maple) were not sufficient for computing many of those resonances which lie very close to the real axis. We computed the results here using the routine of Amos [2,3] with the modifications given in [47] and [48]. This is a very sensitive computation for high modal numbers m, and in some instances will have false convergences to numbers with very small but positive imaginary parts.…”

Section: Exact Solutionsmentioning

confidence: 99%

Trace formula for a dielectric microdisk with a point scatterer

Hales¹,

Sieber²,

Waalkens³

2011

J. Phys. A: Math. Theor.

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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 the present 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.

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