Image Processing Systems Institute of the RAS,
Samara State Aerospace University

Full text of article: Russian language.

Abstract:
Nonparaxial diffraction of Gaussian optical vortexes with initial radial polarization has been investigated. We have obtained explicit analytical expressions for radial, azimuthal, and longitudinal components of the electric vector. The simulation showed that nonparaxial formulae are more accurate than paraxial ones for areas located far from optical axis. The focal spot (area with intensity exceeding half of its maximal value) of focused Gaussian vortex field with unit topological charge and radial polarization appears to be less than that predicted by scalar theory.

Key words:
nonparaxial diffraction, radial polarization, Gaussian optical vortex, focusing of laser light.

References:

1. Bomzon, Z. Formation of radially and azimuthally polarized light using spacevariant subwavelength metal strip grating / Z. Bomzon, V. Kleiner, E. Hasman // Appl. Phys. Lett. 2001. – Vol. 79. – p. 1587-1589.
2. Armstrong, D.J. Generation of radially polarized beams with an image rotating resonator / D.J. Armstrong, M.C. Philips, A.V. Smith // Appl. Opt. 2003. – Vol. 42. – p. 3550-3554.
3. Passilly, N. Simple interferometric technique for generation of a radially polarized light beam / N. Passilly [and other] // J. Opt. Soc. Am. A 2005 22. – p. 984-991.
4. Volpe, G. Generation of cylindrical vector beams with few-mode fibers by Laguerre-Gaussian beams / G. Volpe, D. Petrov // Opt. Commun. 2004. – Vol. 237. – p. 89-95.
5. Niziev, V.G. Influence of beam polarization on laser cutting efficiency / V.G. Niziev, A.V. Nesterov // J. Phys. D 1999. – Vol. 32. – p. 1455-1461.
6. Gahagan, K.T. Simultaneous trapping of low-index and high-index microparticles observed with an optical-vortex trap / K.T. Gahagan, G.A. Swartzlander, Jr. // J. Opt. Soc. Am. B 1999. – Vol. 16. – p. 533-537.
7. Wu, G. Focal shift in focused radially polarized ultrashort pulsed laser beams / G. Wu [and other] // Appl. Opt. 2007. – Vol. 46. – p. 6251-6255.
8. Deng, D. Nonparaxial propagation of radially polarized light beams / D. Deng // J. Opt. Soc. Am. B 2006. – Vol. 23. – p. 1228-1234.
9. Banerjee, P. A q-parameter approach to analysis of propagation, focusing, and waveguiding of radially polarized Gaussian beams / P. Banerjee, G. Cook, and D. Evans // J. Opt. Soc. Am. A 2009. – Vol. 26(6) . – p. 1366-1374.
10. Kotlyar, V.V. Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate / V. Kotlyar [and other] // J. Opt. Soc. Am. A 2005. – Vol. 22. – p. 849-861.
11. Kotlyar, V.V. Diffraction of conic wave and Gaussian beam by a spiral phase plate / V.V. Kotlyar [and other] // Computer Optics. – 2005. – Vol. 28. – P. 29–36. – ISSN 0134-2452. – (in Russian).
12. Kotlyar, V.V. Diffraction of Gaussian beam by a spiral axicon / V.V. Kotlyar [and other] // Computer Optics. – 2006. – Vol. 30. – P. 30-35. – ISSN 0134-2452. – (in Russian).
13. Kovalev, A.A. Paraxial hypergeometric laser beams with singularity at the center of the waist / A.A. Kovalev [and other] // Computer Optics. – 2007. – Vol. 31(1). – P. 9-13. – ISSN 0134-2452. – (in Russian).
14. Kovalev, A.A. Nonparaxial vertorial diffraction of Gaussian beam by a spiral phase plate / A.A. Kovalev, V.V. Kotlyar // Computer Optics. – 2007. – Vol. 31(4). – P. 19-22. – ISSN 0134-2452. – (in Russian).
15. Kotlyar, V.V. Nonparaxial hypergeometric modes / V.V. Kotlyar, A.A. Kovalev // Computer Optics. – 2008. – Vol. 32(3). – P. 222-225. – ISSN 0134-2452. – (in Russian).
16. Rashid, M. Focusing of high order cylindrical vector beams / M Rashid, O M Marago, P H Jones // J. Opt. A: Pure Appl. Opt. 2009. – Vol. 11. – P. 065204 (7pp).
17. Chen, B. Tight focusing of elliptically polarized vortex beams / B. Chen, J. Pu // Appl. Opt. 2009. – Vol. 48. – p. 1288-1294.
18. Table of Integrals, Series, and Products / I.S. Gradshteyn and I.M. Ryzhik. - Elsevier, 2007.
19. Handbook of Mathematical Functions / ed. M. Abramowitz, I.A. Stegun. - National Bureau of Standards, Washington, DC, 1964.- 1044p.

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