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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 20, Iss. 10 — Oct. 1, 2003
  • pp: 1974–1980

Azimuthal polarization and partial coherence

Jani Tervo  »View Author Affiliations

JOSA A, Vol. 20, Issue 10, pp. 1974-1980 (2003)

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Partially coherent fields with the electric field parallel to the azimuthal coordinate are analyzed by use of the exact angular spectrum representation. The known results for fully coherent fields are used to find the permitted forms of azimuthally polarized, partially coherent fields. The derived result is then used to show that this class of fields is severely restricted because the azimuthal polarization state is particularly sensitive to the correlation properties of the electric-field components. Two examples of azimuthally polarized fields are briefly examined. The first is a class of nondiffracting fields that retain the polarization state upon propagation, whereas the second is an example in which the azimuthal polarization is broken because the cross-spectral density function is not of the permitted form.

© 2003 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(050.1940) Diffraction and gratings : Diffraction
(260.5430) Physical optics : Polarization
(350.5500) Other areas of optics : Propagation

Original Manuscript: February 27, 2003
Revised Manuscript: May 2, 2003
Manuscript Accepted: May 2, 2003
Published: October 1, 2003

Jani Tervo, "Azimuthal polarization and partial coherence," J. Opt. Soc. Am. A 20, 1974-1980 (2003)

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  1. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  2. G. B. Arfken, H. J. Weber, Mathematical Methods for Physicists (Academic, New York, 2001).
  3. J. A. Kong, Electromagnetic Wave Theory (Wiley, New York, 1990).
  4. E. A. J. Marcatili, R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers,” Bell Syst. Tech. J. 43, 1783–1809 (1964). [CrossRef]
  5. T. Erdogan, D. G. Hall, “Circularly symmetric distributed feedback semiconductor laser: an analysis,” J. Appl. Phys. 68, 1435–1444 (1990). [CrossRef]
  6. T. Erdogan, O. King, G. W. Wicks, D. G. Hall, E. H. Anderson, M. J. Rooks, “Circularly symmetric operation of a concentric-circle-grating, surface-emitting, AlGaAs/GaAs quantum-well semiconductor laser,” Appl. Phys. Lett. 60, 1921–1923 (1992). [CrossRef]
  7. R. H. Jordan, D. G. Hall, “Free-space azimuthal wave equation: the azimuthal Bessel–Gauss beam solution,” Opt. Lett. 19, 427–429 (1994). [CrossRef] [PubMed]
  8. R. H. Jordan, D. G. Hall, “Highly directional surface emission from concentric-circle gratings on planar optical waveguides: the field expansion method,” J. Opt. Soc. Am. A 12, 84–94 (1995). [CrossRef]
  9. P. L. Greene, D. G. Hall, “Diffraction characteristics of the azimuthal Bessel–Gauss beam,” J. Opt. Soc. Am. A 13, 962–966 (1996). [CrossRef]
  10. D. G. Hall, “Vector-beam solutions of Maxwell’s wave equation,” Opt. Lett. 21, 9–11 (1996). [CrossRef] [PubMed]
  11. A. A. Tovar, G. H. Clark, “Concentric-circle-grating, surface-emitting laser beam propagation in complex optical systems,” J. Opt. Soc. Am. A 14, 3333–3340 (1997). [CrossRef]
  12. A. A. Tovar, “Production and propagation of cylindrically polarized Laguerre–Gaussian laser beams,” J. Opt. Soc. Am. A 15, 2705–2711 (1998). [CrossRef]
  13. F. Gori, G. Guattari, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987). [CrossRef]
  14. J. Tervo, P. Vahimaa, J. Turunen, “On propagation-invariant and self-imaging intensity distributions of electromagnetic fields,” J. Mod. Opt. 49, 1537–1543 (2002). [CrossRef]
  15. P. Pääkkönen, J. Tervo, P. Vahimaa, J. Turunen, F. Gori, “General vectorial decomposition of electromagnetic fields with application to propagation-invariant and rotating fields,” Opt. Express 10, 949–959 (2002). [CrossRef] [PubMed]
  16. A. Lapucci, M. Ciofini, “Polarization state modifications in the propagation of high azimuthal order annular beams,” Opt. Express 9, 603–609 (2001). [CrossRef] [PubMed]
  17. S. R. Seshadri, “Partially coherent Gaussian Schell-model electromagnetic beams,” J. Opt. Soc. Am. A 16, 1373–1380 (1999). [CrossRef]
  18. S. R. Seshadri, “Average characteristics of partially coherent electromagnetic beams,” J. Opt. Soc. Am. A 17, 780–789 (2000). [CrossRef]
  19. S. R. Seshadri, “Spatial coherence of azimuthally symmetric Gaussian electromagnetic beams,” J. Appl. Phys. 88, 6973–6980 (2000). [CrossRef]
  20. S. R. Seshadri, “Polarization properties of partially coherent Gaussian Schell-model electromagnetic beams,” J. Appl. Phys. 87, 4084–4093 (2000). [CrossRef]
  21. P. Östlund, A. T. Friberg, “Radiation efficiency of partially coherent electromagnetic beams,” J. Opt. Soc. Am. A 18, 1696–1703 (2001). [CrossRef]
  22. E. Wolf, “New theory of partial coherence in the space–frequency domain. Part I: spectra and cross spectra of steady-state sources,” J. Opt. Soc. Am. 72, 343–351 (1982). [CrossRef]
  23. E. Wolf, “Coherence properties of partially polarized electromagnetic radiation,” Nuovo Cimento 13, 2737–2753 (1959). [CrossRef]
  24. F. Gori, “Matrix treatment for partially polarized, partially coherent fields,” Opt. Lett. 23, 241–243 (1998). [CrossRef]
  25. F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Guattari, “Beam coherence-polarization matrix,” Pure Appl. Opt. 7, 941–951 (1998). [CrossRef]
  26. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995).
  27. J. Peřina, Coherence of Light (Reidel, Dordrecht, The Netherlands, 1985).
  28. E. W. Marchand, E. Wolf, “Angular correlation and thefar-zone behavior of partially coherent fields,” J. Opt. Soc. Am. 62, 379–385 (1972). [CrossRef]
  29. W. H. Carter, “Properties of electromagnetic radiation from partially correlated current distribution,” J. Opt. Soc. Am. 70, 1067–1074 (1980). [CrossRef]
  30. J. Tervo, J. Turunen, “Angular spectrum representation of partially coherent electromagnetic fields,” Opt. Commun. 209, 7–16 (2002). [CrossRef]
  31. W. H. Carter, “Electromagnetic field of a Gaussian beam with an elliptical cross section,” J. Opt. Soc. Am. 62, 1195–1201 (1972). [CrossRef]
  32. L. Raåde, B. Westergren, Mathematics Handbook for Science and Engineering (Studentlitteratur, Lund, Sweden, 1998), p. 336.
  33. G. Gbur, D. James, E. Wolf, “Energy conservation law for randomly fluctuating electromagnetic fields,” Phys. Rev. E 59, 4594–4599 (1999). [CrossRef]
  34. T. Setälä, A. Shevchenko, M. Kaivola, A. T. Friberg, “Degree of polarization for optical near fields,” Phys. Rev. E 66, 016615 (2002). [CrossRef]
  35. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987). [CrossRef]
  36. J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987). [CrossRef] [PubMed]
  37. S. R. Mishra, “A vector wave analysis of a Bessel beam,” Opt. Commun. 85, 159–161 (1991). [CrossRef]
  38. J. Turunen, A. T. Friberg, “Self-imaging and propagation-invariance in electromagnetic fields,” Pure Appl. Opt. 2, 51–60 (1993). [CrossRef]
  39. Z. Bouchal, M. Olivı́k, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995). [CrossRef]
  40. J. Turunen, A. Vasara, A. T. Friberg, “Propagation invariance and self-imaging in variable-coherence optic,” J. Opt. Soc. Am. A 8, 282–289 (1991). [CrossRef]
  41. A. V. Schegrov, E. Wolf, “Partially coherent conical beams,” Opt. Lett. 25, 141–143 (2000). [CrossRef]
  42. A. S. Ostrovsky, G. Martı́nez-Niconoff, J. C. Ramı́rez-San-Juan, “Coherent-mode representation of propagation-invariant fields,” Opt. Commun. 195, 27–34 (2001). [CrossRef]
  43. J. Turunen, “Invariant propagation of uniform-intensity Schell-model felds,” J. Mod. Opt. 49, 1795–1799 (2002). [CrossRef]
  44. L. Mandel, E. Wolf, “Complete coherence in the space–frequency domain,” Opt. Commun. 36, 247–249 (1981). [CrossRef]
  45. F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, R. Simon, “Partially polarized Gaussian Schell-model beams,” Pure Appl. Opt. 3, 1–9 (2001). [CrossRef]
  46. J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, UK, 1986), Chap. 8.
  47. W. H. Carter, E. Wolf, “Far-zone behavior of electromagnetic fields generated by fluctuating current distributions,” Phys. Rev. A 36, 1258–1269 (1987). [CrossRef] [PubMed]
  48. T. Setälä, M. Kaivola, A. T. Friberg, “Degree of polarization in near fields of thermal sources: effects of surface waves,” Phys. Rev. Lett. 88, 123902 (2002). [CrossRef] [PubMed]
  49. T. Saastamoinen, J. Tervo, J. Turunen, “Radiation from arbitrarily polarized spatially incoherent planar sources,” Opt. Commun. 221, 257–269 (2003). [CrossRef]
  50. D. F. V. James, “Change of polarization of light beams on propagation in free space,” J. Opt. Soc. Am. A 11, 1641–1643 (1994). [CrossRef]

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