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Carretero L, Acebal P, Blaya S. Diffraction of convergent spherical waves with all possible polarization states using the Luneburg integral method. J Opt Soc Am A Opt Image Sci Vis. 2013;30(4):733-40doi: 10.1364/JOSAA.30.000733.
Carretero, L., Acebal, P., & Blaya, S. (2013). Diffraction of convergent spherical waves with all possible polarization states using the Luneburg integral method. Journal of the Optical Society of America. A, Optics, image science, and vision, 30(4), 733-40. https://doi.org/10.1364/JOSAA.30.000733
Carretero, Luis, et al. "Diffraction of convergent spherical waves with all possible polarization states using the Luneburg integral method." Journal of the Optical Society of America. A, Optics, image science, and vision vol. 30,4 (2013): 733-40. doi: https://doi.org/10.1364/JOSAA.30.000733
Carretero L, Acebal P, Blaya S. Diffraction of convergent spherical waves with all possible polarization states using the Luneburg integral method. J Opt Soc Am A Opt Image Sci Vis. 2013 Apr 01;30(4):733-40. doi: 10.1364/JOSAA.30.000733. PMID: 23595335.
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J Opt Soc Am A Opt Image Sci Vis. 2013 Apr 01;30(4):733-40. doi: 10.1364/JOSAA.30.000733.

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

Journal of the Optical Society of America. A, Optics, image science, and vision

Luis Carretero, Pablo Acebal, Salvador Blaya

Affiliations

  1. Universidad Miguel Hernández, Departamento de Ciencia de Materiales Óptica y Tecnología electrónica, Alicante, Spain. [email protected]

PMID: 23595335 DOI: 10.1364/JOSAA.30.000733

Abstract

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.

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