Polarization properties and dispersion relations for spiral resonances of a dielectric rod

Harald G.L. Schwefel, A. Douglas Stone, Hakan E. Tureci

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


Dielectric microcavities based on cylindrical and deformed cylindrical shapes have been employed as resonators for microlasers. Such systems support spiral resonances with finite momentum along the cylinder axis. For such modes the boundary conditions do not separate, and simple TM and TE polarization states do not exist. We formulate a theory for the dispersion relations and polarization properties of such resonances for an infinite dielectric rod of arbitrary cross section and then solve for these quantities for the case of a circular cross section (cylinder). Useful analytic formulas are obtained using the eikenal (Einstein-Brillouin-Keller) method, which are shown to be excellent approximations to the exact results from the wave equation. The major finding is that the polarization of the radiation emitted into the far field is linear up to a polarization critical angle (PCA) at which it changes to elliptical. The PCA always lies between the Brewster's and total-internal-reflection angles for the dielectric, as is shown by an analysis based on the Jones matrices of the spiraling rays.

Original languageEnglish (US)
Pages (from-to)2295-2307
Number of pages13
JournalJournal of the Optical Society of America B: Optical Physics
Issue number11
StatePublished - Nov 2005
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Atomic and Molecular Physics, and Optics


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