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Dielectric microcavities based on cylindrical and deformed cylindrical shapeshave been employed as resonators for microlasers. Such systems support spiralresonances with finite momentum along the cylinder axis. For such modes theboundary conditions do not separate and simple TM and TE polarization states donot exist. We formulate a theory for the dispersion relations and polarizationproperties of such resonances for an infinite dielectric rod of arbitrarycross-section and then solve for these quantities for the case of a circularcross-section (cylinder). Useful analytic formulas are obtained using theeikonal (Einstein-Brillouin-Keller) method which are shown to be excellentapproximations to the exact results from the wave equation. The major findingis that the polarization of the radiation emitted into the far-field is linearup to a polarization critical angle (PCA) at which it changes to elliptical.The PCA always lies between the Brewster and total-internal-reflection anglesfor the dielectric, as is shown by an analysis based on the Jones matrices ofthe spiraling rays.Comment: submitted to JOSA

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