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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: G. I. Stegeman
  • Vol. 22, Iss. 11 — Nov. 1, 2005
  • pp: 2295–2307

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

Harald G. L. Schwefel, A. Douglas Stone, and Hakan E. Tureci  »View Author Affiliations

JOSA B, Vol. 22, Issue 11, pp. 2295-2307 (2005)

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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 eikonal (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.

© 2005 Optical Society of America

OCIS Codes
(060.2310) Fiber optics and optical communications : Fiber optics
(080.2720) Geometric optics : Mathematical methods (general)
(260.5430) Physical optics : Polarization
(260.5740) Physical optics : Resonance

ToC Category:
Fiber Optics and Optical Communications

Harald G. L. Schwefel, A. Douglas Stone, and Hakan E. Tureci, "Polarization properties and dispersion relations for spiral resonances of a dielectric rod," J. Opt. Soc. Am. B 22, 2295-2307 (2005)

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  1. C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nöckel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science  280, 1556–1564 (1998).
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