Internal and external resonances of dielectric disks

¹  Department of Mathematics, University of Bristol - Bristol BS8 1TW, UK, EU
²  Thin Film Centre, University of the West of Scotland - Paisley PA1 2BE, UK, EU
³  Department of Mathematics, University of Groningen - Nijenborgh 9, 9747 AG Groningen, The Netherlands, EU

Corresponding author: gregory.morozov@uws.ac.uk

Received: 27 March 2009
Accepted: 23 July 2009

Abstract

Circular microresonators (microdisks) are micron size dielectric disks embedded in a material of lower refractive index. They possess modes with complex eigenvalues (resonances) which are solutions of analytically given transcendental equations. The behavior of such eigenvalues in the small opening limit, i.e. when the refractive index of the cavity goes to infinity, is analyzed. This analysis allows one to clearly distinguish between internal (Feshbach) and external (shape) resonant modes for both TM and TE polarizations. This is especially important for TE polarization for which internal and external resonances can be found in the same region of the complex wave number plane. It is also shown that for both polarizations, the internal as well as external resonances can be classified by well-defined azimuthal and radial modal indices.