dorsal/arxiv
View SchemaPolarization properties and dispersion relations for spiral resonances of a dielectric rod
| Authors | Harald G. L. Schwefel, Hakan E. Tureci, A. Douglas Stone |
|---|---|
| Categories | |
| ArXiv ID | physics/0502057 |
| URL | https://arxiv.org/abs/physics/0502057 |
| DOI | 10.1364/JOSAB.22.002295 |
| Journal | JOSA B, Vol. 22, Issue 11, pp. 2295-2307 (2005) |
Abstract
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 and total-internal-reflection angles for the dielectric, as is shown by an analysis based on the Jones matrices of the spiraling rays.
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"abstract": "Dielectric microcavities based on cylindrical and deformed cylindrical shapes\nhave been employed as resonators for microlasers. Such systems support spiral\nresonances with finite momentum along the cylinder axis. For such modes the\nboundary conditions do not separate and simple TM and TE polarization states do\nnot exist. We formulate a theory for the dispersion relations and polarization\nproperties of such resonances for an infinite dielectric rod of arbitrary\ncross-section and then solve for these quantities for the case of a circular\ncross-section (cylinder). Useful analytic formulas are obtained using the\neikonal (Einstein-Brillouin-Keller) method which are shown to be excellent\napproximations to the exact results from the wave equation. The major finding\nis that the polarization of the radiation emitted into the far-field is linear\nup to a polarization critical angle (PCA) at which it changes to elliptical.\nThe PCA always lies between the Brewster and total-internal-reflection angles\nfor the dielectric, as is shown by an analysis based on the Jones matrices of\nthe spiraling rays.",
"arxiv_id": "physics/0502057",
"authors": [
"Harald G. L. Schwefel",
"Hakan E. Tureci",
"A. Douglas Stone"
],
"categories": [
"physics.optics",
"physics.class-ph"
],
"doi": "10.1364/JOSAB.22.002295",
"journal_ref": "JOSA B, Vol. 22, Issue 11, pp. 2295-2307 (2005)",
"title": "Polarization properties and dispersion relations for spiral resonances of a dielectric rod",
"url": "https://arxiv.org/abs/physics/0502057"
},
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