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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • 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)
http://dx.doi.org/10.1364/JOSAA.26.001366


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Abstract

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

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

Citation
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)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-26-6-1366


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References

  1. G. N. Vinokurov, A. A. Mak, and V. M. Mitkin, “Generating azimuthal and radial modes in optical resonators,” Kvant. Elektron. (Kiev) 8, 1890-1891 (1974) (in Russian).
  2. C.-C. Shih, “Radial polarization laser resonator,” U.S. patent 5,359,622, October 25, 1994.
  3. A. A. Tovar, “Production and propagation of cylindrical polarized Laguerre-Gaussian beams,” J. Opt. Soc. Am. A 15, 2705-2711 (1998). [CrossRef]
  4. A. Ciattoni, B. Crosignami, and P. D. Porto, “Vectorial analytical description of propagation of a highly nonparaxial beam,” Opt. Commun. 202, 17-20 (2002). [CrossRef]
  5. R. Borghi, and M. Santarsiero, “Nonparaxial propagation of spirally polarized optical beams,” J. Opt. Soc. Am. A 21, 2029-2037 (2004). [CrossRef]
  6. D. Deng, “Nonparaxial propagation of radially polarized light beams,” J. Opt. Soc. Am. B 23, 1228-1234 (2006). [CrossRef]
  7. Z. Bomzon, V. Kleiner, and E. Hasman, “Formation of radially and azimuthally polarized light using spacevariant subwavelength metal strip grating,” Appl. Phys. Lett. 79, 1587-1589 (2001). [CrossRef]
  8. D. J. Armstrong, M. C. Philips, and A. V. Smith, “Generation of radially polarized beams with an image rotating resonator,” Appl. Opt. 42, 3550-3554 (2003). [CrossRef] [PubMed]
  9. N. Passilly, R. de S. Denis, K. Aït-Ameur, F. Treussart, R. Hierle, and J.-F. Roch, “Simple interferometric technique for generation of a radially polarized light beam,” J. Opt. Soc. Am. A 22, 984-991 (2005). [CrossRef]
  10. M. S. Roth, E. W. Wyss, H. Glur, and H. P. Weber, “Generation of radially polarized beams in a Nd:YAG laser with self-adaptive overcompensation of the thermal lens,” Opt. Lett. 30, 1665-1667 (2005). [CrossRef] [PubMed]
  11. V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D 32, 1455-1461 (1999). [CrossRef]
  12. K. T. Gahagan and G. A. Swartzlander, Jr., “Simultaneous trapping of low-index and high-index microparticles observed with an optical-vortex trap,” J. Opt. Soc. Am. B 16, 533-537 (1999). [CrossRef]
  13. C. Varin and M. Piché, “Acceleration of ultra-relativistic electrons using high-intensity TM01 laser beams,” Appl. Phys. B B74, S83-S88 (2002). [CrossRef]
  14. G. Wu, Q. Lou, J. Zhou, J. Dong, and Y. Wei, “Focal shift in focused radially polarized ultrashort pulsed laser beams,” Appl. Opt. 46, 6251-6255 (2007). [CrossRef] [PubMed]
  15. L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251-5254 (2001). [CrossRef] [PubMed]
  16. N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett. 85, 6239-6241 (2004). [CrossRef]
  17. T.-C. Poon and P. P. Banerjee, Contemporary Optical Image Processing using MATLAB (Elsevier, 2001).
  18. A. Yariv and P. Yeh, Photonics, 6th ed. (Oxford Univ. Press, 2007).
  19. R. K. Luneburg, Mathematical Theory of Optics (U. California Press, 1966).
  20. D. Deng, Q. Guo, L. Wu, and X. Yang, “Propagation of radially polarized elegant light beams,” J. Opt. Soc. Am. B 24, 636-643 (2007). [CrossRef]
  21. D. Deng and Q. Guo, “Analytical vectorial structure of radially polarized light beams,” Opt. Lett. 32, 2711-2713 (2007). [CrossRef] [PubMed]
  22. H. Chen, Q. Zhan, Y. Zhang, and Y.-P. Li, “The Gouy phase shift of the highly focused radially polarized beam,” Phys. Lett. A 371, 259-261 (2007). [CrossRef]

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