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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 10, Iss. 18 — Sep. 9, 2002
  • pp: 949–959

General vectorial decomposition of electromagnetic fields with application to propagation-invariant and rotating fields

Pertti Pääkkönen, Jani Tervo, Pasi Vahimaa, Jari Turunen, and Franco Gori  »View Author Affiliations

Optics Express, Vol. 10, Issue 18, pp. 949-959 (2002)

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A novel decomposition of the transversal part of the electric field vector of a general non-paraxial electromagnetic field is presented, which is an extension of the radial/aximuthal decomposition and is known as γζ decomposition. Purely γ and ζ polarized fields are examined and the decomposition is applied to propagation-invariant, rotating, and self-imaging electromagnetic fields. An experimental example on the effect of state of polarization in the propagation characteristics of the field: its is shown that a simple modification of the polarization conditions of the angular spectrum converts a self-imaging field into a propagation-invariant field.

© 2002 Optical Society of America

OCIS Codes
(260.5430) Physical optics : Polarization
(350.5500) Other areas of optics : Propagation

ToC Category:
Research Papers

Original Manuscript: July 31, 2002
Revised Manuscript: August 30, 2002
Published: September 9, 2002

Pertti Paakkonen, Jani Tervo, Pasi Vahimaa, Jari Turunen, and Franco Gori, "General vectorial decomposition of electromagnetic fields with application to propagation-invariant and rotating fields," Opt. Express 10, 949-959 (2002)

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  1. W. D. Montgomery, ???Self-imaging objects of in.nite aperture,??? J. Opt. Soc. Am. 57, 772???778 (1967). [CrossRef]
  2. K. Patorski, ???The self-imaging phenomenon and its applications,??? in Progress in Optics Vol. XXVII, E. Wolf, ed. (Elsevier, Amsterdam, 1989), Chap. 1.
  3. J. Durnin, ???Exact solutions for nondifiracting beams. I. The scalar theory,??? J. Opt. Soc. Am. A 4, 651???654 (1987). [CrossRef]
  4. J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, ???Diffraction-free beams,??? Phys. Rev. Lett. 58, 1499???1501 (1987). [CrossRef] [PubMed]
  5. Y. Y. Schechner, R. Piestun, and J. Shamir, ???Wave propagating with rotating intensity distributions,??? Phys. Rev. E 54, R50???R53 (1996). [CrossRef]
  6. S. Chavez-Cerda, G. S. McDonald, and G. H. S. New, ???Nondiffracting Beams: travelling, standing, rotating and spiral waves,??? Opt. Commun. 123, 225???233 (1996). [CrossRef]
  7. C. Paterson and R. Smith, ???Higher-order Bessel waves produced by axicon-type computergenerated holograms,??? Opt. Commun. 124, 121???130 (1996). [CrossRef]
  8. S. R. Mishra, ???A vector wave analysis of a Bessel beam,??? Opt. Commun. 85, 159???161 (1991). [CrossRef]
  9. J. Turunen and A. T. Friberg, ???Self-imaging and propagation-invariance in electromagnetic fields,??? Pure Appl. Opt. 2, 51???60 (1993). [CrossRef]
  10. Z. Bouchal and M. Olivýk, ???Non-diffractive vector Bessel beams,??? J. Mod. Opt. 42, 1555???1566 (1995). [CrossRef]
  11. Z. Bouchal, R. Horak and J. Wagner, ???Propagation-invariant electromagnetic fields,??? J. Mod. Opt. 43, 1905???1920 (1996). [CrossRef]
  12. J. Tervo and J. Turunen, ???Rotating scale-invariant electromagnetic fields,??? Opt. Express 9, 9???15 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-1-9">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-1-9</a>. [CrossRef] [PubMed]
  13. P. Paakkonen, J. Lautanen, M. Honkanen, M. Kuittinen, J. Turunen, S. N. Khonina, V. V. Kotlyar, V. A. Soifer and A. T. Friberg, ???Rotating optical fields: experimental demonstration with diffractive optics,??? J. Mod. Opt. 46, 2355???2369 (1998). [CrossRef]
  14. F. Gori, ???Polarization basis for vortex beams,??? J. Opt. Soc. Am. A 18, 1612???1617 (2001). [CrossRef]
  15. L. Mandel, and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995), Sect. 3.2.
  16. G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Academic Press, New York, 2001), p. 681.
  17. R. H. Jordan and 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]
  18. J. Tervo, P. Vahimaa, and J. Turunen, ???On propagation-invariant and self-imaging intensity distributions of electromagnetic fields,??? J. Mod. Opt. 49, 1537???1543 (2002). [CrossRef]
  19. A. Lapucci and M. Ciofini, ???Polarization state modifications in the propagation of high azimuthal order annular beams,??? Opt. Express 9, 603???609 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-12-603">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-12-603</a>. [CrossRef] [PubMed]
  20. J. Tervo and J. Turunen, ???Self-imaging of electromagnetic fields,??? Opt. Express 9, 622???630 (2001), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-12-622">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-9-12-622</a>. [CrossRef] [PubMed]
  21. J. Tervo and J. Turunen, ???Generation of vectorial propagation-invariant fields by polarizationgrating axicons,??? Opt. Commun. 192, 13???18 (2001). [CrossRef]

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