Abstract

Near-field focusing properties of perfect black Fresnel zone plates are analyzed by solving Maxwell equations using the vectorial angular spectrum representation and the equivalent Rayleigh diffraction formulae of the first kind given by the Luneburg vector diffraction theory. Linear and circular polarizations are compared. As a result, an exact analytical expression for axial intensity is obtained showing that, in the near field, the shift of focal length is inherent in the diffraction process and independent of incident field polarization. The numerical intensity distribution of the electromagnetic field is also obtained, which allows us to demonstrate that when vectorial analysis of the system is performed, subwavelength focusing cannot be achieved for very short focal distances. This result is valid for linearly and circularly polarized incident fields. Finally, it is shown that symmetry of the focalized field is strongly dependent on the polarization of the incident field and that the vectorial diffraction theory can be a good alternative to finite-difference time-domain methods.

© 2011 IEEE

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  1. R. Merlin, "Radiationless electromagnetic interference: Evanescent-field lenses and perfect focusing," Science 317, 927-929 (2007).
  2. A. Grbic, L. Jiang, R. Merlin, "Near-field plates: Subdiffraction focusing with patterned surfaces," Science 320, 511-513 (2008).
  3. Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, X. G. Luo, "Plasmonic microzone plate: Superfocusing at visible regime," Appl. Phys. Lett. 91, 061124-1-061124-3 (2007).
  4. R. G. Mote, S. F. Yu, B. K. Ng, W. Zhou, S. P. Lau, "Near-field focusing properties of zone plates in visible regime—New insights," Opt. Exp. 16, 9554-9564 (2008).
  5. R. G. Mote, S. F. Yu, W. Zhou, S. F. Li, "Subwavelength focusing behavior of high numerical-aperture phase Fresnel zone plates under various polarization states," Appl. Phys. Lett. 95, 191113-1-191113-3 (2009).
  6. H. C. Kim, H. Ko, M. S. Cheng, "High efficient optical focusing of a zone plate composed of metal/dielectric multilayer," Opt. Exp. 17, 3078-3083 (2009).
  7. J. H. Li, Y. W. Cheng, Y. C. Chue, C. H. Lin, T. W. H. Sheu, "The influence of propagating and evanescent waves on the focusing properties of zone plate structures," Opt. Exp. 17, 18462-18468 (2009).
  8. M. Perez-Molina, L. Carretero, P. Acebal, S. Blaya, "Optical singularities and power flux in the near-field region of planar evanescent-field superlenses," J. Opt. Soc. Amer. A, Opt. Image Sci. Vis. 25, 2865-2874 (2008).
  9. R. K. Luneburg, Mathematical Theory of Optics (Univ. California Press, 1964).
  10. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).
  11. J. Guo, X. Zhao, Y. Min, "The general integral expressions for on axis nonparaxial vectorial spherical waves diffracted at a circular aperture," Opt. Commun. 282, 1511-1515 (2009).
  12. L. Carretero, P. Acebal, S. Blaya, C. Garcia, A. Fimia, R. Madrigal, A. Murciano, "Nonparaxial diffraction analysis of Airy and SAiry beams," Opt. Exp. 17, 22432-22441 (2009).
  13. G. D. Gillen, C. M. Seck, S. Guha, "Analytical beam propagation model for clipped focused-Gaussian beams using vector diffraction theory," Opt. Exp. 18, 4023-4040 (2010).
  14. J. A. Romero, L. Hernandez, "Vectorial approach to Huygens's principle for plane waves: Circular aperture and zone plates," J. Opt. Soc. Amer. A, Opt. Image Sci. Vis. 23, 1141-1145 (2006).
  15. I. S. Gradshteyn, I. Ryzhik, Table of Integrals, Series and Products (Academic, 1994).
  16. H. Q. Tang, X. G. Li, G. Q. Zhou, K. C. Zhu, "Vectorial structure of helical hollow Gaussian beams in the far field," Opt. Commun. 282, 478-481 (2009).
  17. S. Quabis, R. Dorn, M. Eberler, O. Glockl, G. Leuchs, "The focus of light-theoretical calculation and experimental tomographic reconstruction," Appl. Phys. B 72, 109-113 (2001).
  18. R. Dorn, S. Quabis, G. Leuchs, "The focus of light-linear polarization breaks the rotational symmetry of the focal spot," J. Modern Opt. 50, 1917-1926 (2003).
  19. M. Born, E. Wolf, Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1984).

2010 (1)

G. D. Gillen, C. M. Seck, S. Guha, "Analytical beam propagation model for clipped focused-Gaussian beams using vector diffraction theory," Opt. Exp. 18, 4023-4040 (2010).

2009 (6)

J. Guo, X. Zhao, Y. Min, "The general integral expressions for on axis nonparaxial vectorial spherical waves diffracted at a circular aperture," Opt. Commun. 282, 1511-1515 (2009).

L. Carretero, P. Acebal, S. Blaya, C. Garcia, A. Fimia, R. Madrigal, A. Murciano, "Nonparaxial diffraction analysis of Airy and SAiry beams," Opt. Exp. 17, 22432-22441 (2009).

H. Q. Tang, X. G. Li, G. Q. Zhou, K. C. Zhu, "Vectorial structure of helical hollow Gaussian beams in the far field," Opt. Commun. 282, 478-481 (2009).

R. G. Mote, S. F. Yu, W. Zhou, S. F. Li, "Subwavelength focusing behavior of high numerical-aperture phase Fresnel zone plates under various polarization states," Appl. Phys. Lett. 95, 191113-1-191113-3 (2009).

H. C. Kim, H. Ko, M. S. Cheng, "High efficient optical focusing of a zone plate composed of metal/dielectric multilayer," Opt. Exp. 17, 3078-3083 (2009).

J. H. Li, Y. W. Cheng, Y. C. Chue, C. H. Lin, T. W. H. Sheu, "The influence of propagating and evanescent waves on the focusing properties of zone plate structures," Opt. Exp. 17, 18462-18468 (2009).

2008 (3)

M. Perez-Molina, L. Carretero, P. Acebal, S. Blaya, "Optical singularities and power flux in the near-field region of planar evanescent-field superlenses," J. Opt. Soc. Amer. A, Opt. Image Sci. Vis. 25, 2865-2874 (2008).

A. Grbic, L. Jiang, R. Merlin, "Near-field plates: Subdiffraction focusing with patterned surfaces," Science 320, 511-513 (2008).

R. G. Mote, S. F. Yu, B. K. Ng, W. Zhou, S. P. Lau, "Near-field focusing properties of zone plates in visible regime—New insights," Opt. Exp. 16, 9554-9564 (2008).

2007 (2)

R. Merlin, "Radiationless electromagnetic interference: Evanescent-field lenses and perfect focusing," Science 317, 927-929 (2007).

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, X. G. Luo, "Plasmonic microzone plate: Superfocusing at visible regime," Appl. Phys. Lett. 91, 061124-1-061124-3 (2007).

2006 (1)

J. A. Romero, L. Hernandez, "Vectorial approach to Huygens's principle for plane waves: Circular aperture and zone plates," J. Opt. Soc. Amer. A, Opt. Image Sci. Vis. 23, 1141-1145 (2006).

2003 (1)

R. Dorn, S. Quabis, G. Leuchs, "The focus of light-linear polarization breaks the rotational symmetry of the focal spot," J. Modern Opt. 50, 1917-1926 (2003).

2001 (1)

S. Quabis, R. Dorn, M. Eberler, O. Glockl, G. Leuchs, "The focus of light-theoretical calculation and experimental tomographic reconstruction," Appl. Phys. B 72, 109-113 (2001).

Appl. Phys. B (1)

S. Quabis, R. Dorn, M. Eberler, O. Glockl, G. Leuchs, "The focus of light-theoretical calculation and experimental tomographic reconstruction," Appl. Phys. B 72, 109-113 (2001).

Appl. Phys. Lett. (1)

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, X. G. Luo, "Plasmonic microzone plate: Superfocusing at visible regime," Appl. Phys. Lett. 91, 061124-1-061124-3 (2007).

Appl. Phys. Lett. (1)

R. G. Mote, S. F. Yu, W. Zhou, S. F. Li, "Subwavelength focusing behavior of high numerical-aperture phase Fresnel zone plates under various polarization states," Appl. Phys. Lett. 95, 191113-1-191113-3 (2009).

J. Modern Opt. (1)

R. Dorn, S. Quabis, G. Leuchs, "The focus of light-linear polarization breaks the rotational symmetry of the focal spot," J. Modern Opt. 50, 1917-1926 (2003).

J. Opt. Soc. Amer. A, Opt. Image Sci. Vis. (2)

J. A. Romero, L. Hernandez, "Vectorial approach to Huygens's principle for plane waves: Circular aperture and zone plates," J. Opt. Soc. Amer. A, Opt. Image Sci. Vis. 23, 1141-1145 (2006).

M. Perez-Molina, L. Carretero, P. Acebal, S. Blaya, "Optical singularities and power flux in the near-field region of planar evanescent-field superlenses," J. Opt. Soc. Amer. A, Opt. Image Sci. Vis. 25, 2865-2874 (2008).

Opt. Exp. (1)

H. C. Kim, H. Ko, M. S. Cheng, "High efficient optical focusing of a zone plate composed of metal/dielectric multilayer," Opt. Exp. 17, 3078-3083 (2009).

Opt. Commun. (2)

J. Guo, X. Zhao, Y. Min, "The general integral expressions for on axis nonparaxial vectorial spherical waves diffracted at a circular aperture," Opt. Commun. 282, 1511-1515 (2009).

H. Q. Tang, X. G. Li, G. Q. Zhou, K. C. Zhu, "Vectorial structure of helical hollow Gaussian beams in the far field," Opt. Commun. 282, 478-481 (2009).

Opt. Exp. (4)

L. Carretero, P. Acebal, S. Blaya, C. Garcia, A. Fimia, R. Madrigal, A. Murciano, "Nonparaxial diffraction analysis of Airy and SAiry beams," Opt. Exp. 17, 22432-22441 (2009).

G. D. Gillen, C. M. Seck, S. Guha, "Analytical beam propagation model for clipped focused-Gaussian beams using vector diffraction theory," Opt. Exp. 18, 4023-4040 (2010).

J. H. Li, Y. W. Cheng, Y. C. Chue, C. H. Lin, T. W. H. Sheu, "The influence of propagating and evanescent waves on the focusing properties of zone plate structures," Opt. Exp. 17, 18462-18468 (2009).

R. G. Mote, S. F. Yu, B. K. Ng, W. Zhou, S. P. Lau, "Near-field focusing properties of zone plates in visible regime—New insights," Opt. Exp. 16, 9554-9564 (2008).

Science (2)

R. Merlin, "Radiationless electromagnetic interference: Evanescent-field lenses and perfect focusing," Science 317, 927-929 (2007).

A. Grbic, L. Jiang, R. Merlin, "Near-field plates: Subdiffraction focusing with patterned surfaces," Science 320, 511-513 (2008).

Other (4)

R. K. Luneburg, Mathematical Theory of Optics (Univ. California Press, 1964).

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, 1995).

I. S. Gradshteyn, I. Ryzhik, Table of Integrals, Series and Products (Academic, 1994).

M. Born, E. Wolf, Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1984).

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