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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 30, Iss. 4 — Apr. 1, 2013
  • pp: 733–740

Diffraction of convergent spherical waves with all possible polarization states using the Luneburg integral method

Luis Carretero, Pablo Acebal, and Salvador Blaya  »View Author Affiliations

JOSA A, Vol. 30, Issue 4, pp. 733-740 (2013)

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We present a complete electromagnetic study, which includes electric, magnetic, and Poynting vector fields of diffracted convergent spherical waves under all possible polarization states compatible with Maxwell’s equations. Exit pupil boundary conditions for these polarizations were obtained by means of Hertz potentials. Using these boundary conditions, two-dimensional Luneburg diffraction integrals for the three components of electric and magnetic fields were formulated, and after some approximations, we showed that the complete electromagnetic description of the inhomogeneous polarization states of spherical waves is reduced to the knowledge of seven one-dimensional integrals. The consistency of the method was tested by comparison with other previously reported methods for linearly polarized (LP), TE, and TM polarizations, while the versatility of the method was showed with the study of nonstandard polarization states, for example, that resulting from the superposition of TE and TM dephased spherical waves, which shows a helicoidal behavior of the Poynting vector at the focalization region, or the inhomogeneous LP state that exhibits a ring structure for the Poynting vector at the focal plane.

© 2013 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(260.2110) Physical optics : Electromagnetic optics
(350.5500) Other areas of optics : Propagation

ToC Category:
Diffraction and Gratings

Original Manuscript: November 15, 2012
Revised Manuscript: January 21, 2013
Manuscript Accepted: February 22, 2013
Published: March 27, 2013

Luis Carretero, Pablo Acebal, and Salvador Blaya, "Diffraction of convergent spherical waves with all possible polarization states using the Luneburg integral method," J. Opt. Soc. Am. A 30, 733-740 (2013)

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