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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 26, Iss. 6 — Jun. 1, 2009
  • pp: 1366–1374

A q-parameter approach to analysis of propagation, focusing, and waveguiding of radially polarized Gaussian beams

Partha P. Banerjee, Gary Cook, and Dean R. Evans  »View Author Affiliations

JOSA A, Vol. 26, Issue 6, pp. 1366-1374 (2009)

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The q-parameter of a Gaussian beam is a convenient way to determine its paraxial propagation in a medium as well as in an optical system under external or induced lensing. The assumption is that the Gaussian beam either is scalar or has a linear polarization. It is shown that propagation of radially polarized Gaussian beams in a medium and/or under lensing can be readily analyzed rather simply by knowing the q-transformation of the underlying scalar Gaussian beam. The exact profiles of the longitudinal and transverse components of initially radially polarized lowest-order Laguerre–Gaussian beams are derived and compared with those of the linearly polarized Gaussian beam. It can be readily shown that the longitudinal component of the polarization does not contribute to real power flow at the focal plane. The focal shift and the Guoy phase during lensing are calculated, again based on the underlying q-parameter. The methodology for extension to higher-order Laguerre–Gaussians is also developed. Finally, waveguiding of radially polarized beams in a graded index square law medium is analyzed, and conditions for the existence of radially or longitudinally polarized modes are derived.

© 2009 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(260.1960) Physical optics : Diffraction theory
(260.5430) Physical optics : Polarization

ToC Category:
Physical Optics

Original Manuscript: January 30, 2009
Revised Manuscript: March 23, 2009
Manuscript Accepted: March 26, 2009
Published: May 14, 2009

Partha P. Banerjee, Gary Cook, and Dean R. Evans, "A q-parameter approach to analysis of propagation, focusing, and waveguiding of radially polarized Gaussian beams," J. Opt. Soc. Am. A 26, 1366-1374 (2009)

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