Abstract

Polarization gratings are space-variant subwavelength-structured photonic devices that control electromagnetic wave propagation by local modulation of the state of polarization of light. Using electron beam lithography, we have fabricated such devices in the form of dielectric and metallic surface-relief profiles for operation in the visible wavelength region, where structural features with dimensions on the order of 100 nm are required. We provide experimental demonstrations of various laser-beam splitting elements with diffraction efficiencies exceeding values that could be achieved by diffractive elements operating in the framework of scalar optics.

© 2010 Optical Society of America

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  1. H. P. Herzig, Microoptics: Elements, Systems and Application (Taylor & Francis, London, 1997).
  2. J. Turunen, and F. Wyrowski, Diffractive Optics for Industrial and Commercial Applications (Berlin: Akademie-Verlag, 1997).
  3. F. Wyrowski, "Upper bound of the diffraction efficiency of diffractive phase elements," Opt. Lett. 16, 1915-1917 (1991).
    [CrossRef] [PubMed]
  4. J. Turunen, M. Kuittinen, and F. Wyrowski, "Diffractive optics: Electromagnetic approach," (Elsevier, 2000), chap. V, 343-388.
  5. F. Gori, "Measuring Stokes parameters by means of a polarization grating," Opt. Lett. 24, 584-586 (1999).
    [CrossRef]
  6. J. Tervo, and J. Turunen, "Paraxial-domain diffractive elements with 100% efficiency based on polarization gratings," Opt. Lett. 25, 785-786 (2000).
    [CrossRef]
  7. M. Honkanen, V. Kettunen, J. Tervo, and J. Turunen, "Paraxial-domain diffractive elements with 100% efficiency based on polarization gratings," J. Mod. Opt. 47, 2351-2359 (2000).
    [CrossRef]
  8. J. Tervo, V. Kettunen, M. Honkanen, and J. Turunen, "Design of space-variant diffractive polarization elements," J. Opt. Soc. Am. A 20, 282-289 (2003).
    [CrossRef]
  9. H. Lajunen, J. Tervo, and J. Turunen, "High-efficiency broadband diffractive elements based on polarization gratings," Opt. Lett. 29, 803-805 (2004).
    [CrossRef] [PubMed]
  10. H. Lajunen, J. Turunen, and J. Tervo, "Design of polarization gratings for broadband illumination," Opt. Express 13, 3055-3067 (2005).
    [CrossRef] [PubMed]
  11. J. A. Davis, J. Adachi, C. R. Fernández-Pousa, and I. Moreno, "Polarization beam splitters using polarization diffraction gratings," Opt. Lett. 26, 587-589 (2001).
    [CrossRef]
  12. C. R. Fernández-Pousa, I. Moreno, J. A. Davis, and J. Adachi, "Polarizing diffraction-grating triplicators," Opt. Lett. 26, 1651-1653 (2001).
    [CrossRef]
  13. L. Nikolova, T. Todorov, V. Dragostinova, T. Petrova, and N. Tomova, "Polarization reflection holographic gratings in azobenzene-containing gelatine films," Opt. Lett. 27, 92-94 (2002).
    [CrossRef]
  14. L. Nikolova, T. Todorov, M. Ivanov, F. Andruzzi, S. Hvilsted, and P. S. Ramanujam, "Polarization holographic gratings in side-chain azobenzene polyesters with linear and circular photoanisotropy," Appl. Opt. 35, 3835-3840 (1996).
    [CrossRef] [PubMed]
  15. M. Ishiguro, D. Sato, A. Shishido, and T. Ikeda, "Bragg-type polarization gratings formed in thick polymer films containing azobenzene and tolane moieties," Langmuir 23, 332-338 (2007) (PMID: 17190523.).
    [PubMed]
  16. E. Hasman, Z. Bomzon, A. Niv, G. Biener, and V. Kleiner, "Polarization beam-splitters and optical switches based on space-variant computer-generated subwavelength quasi-periodic structures," Opt. Commun. 209, 45-54 (2002).
    [CrossRef]
  17. G. M. Lerman, and U. Levy, "Generation of a radially polarized light beam using space-variant subwavelength gratings at 1064 nm," Opt. Lett. 33, 2782-2784 (2008).
    [CrossRef] [PubMed]
  18. Y. Gorodetski, G. Biener, A. Niv, V. Kleiner, and E. Hasman, "Space-variant polarization manipulation for farfield polarimetry by use of subwavelength dielectric gratings," Opt. Lett. 30, 2245-2247 (2005).
    [CrossRef] [PubMed]
  19. J. J. Wang, L. Chen, X. Liu, P. Sciortino, F. Liu, F. Walters, and X. Deng, "30-nm-wide aluminum nanowire grid for ultrahigh contrast and transmittance polarizers made by uv-nanoimprint lithography," Appl. Phys. Lett. 89, 141105 (2006).
    [CrossRef]
  20. F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. D. Fabrizio, and M. Gentili, "Analytical derivation of the optimum triplicator," Opt. Commun. 157, 13-16 (1998).
    [CrossRef]
  21. G. Biener, A. Niv, V. Kleiner, and E. Hasman, "Near-field Fourier transform polarimetry by use of a discrete space-variant subwavelength grating," J. Opt. Soc. Am. A 20, 1940-1948 (2003).
    [CrossRef]
  22. L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870-1876 (1996).
    [CrossRef]
  23. S. M. Norton, G. M. Morris, and T. Erdogan, "Experimental investigation of resonant-grating filter line-shapes in comparison with theoretical models," J. Opt. Soc. Am. A 15, 464-472 (1998).
    [CrossRef]
  24. R. C. Weast, CRC Handbook of Chemistry and Physics (CRC Press, Inc, Boca Raton, FL, 1984).
  25. G. Piquero, R. Borghi, and M. Santarsiero, "Gaussian Schell-model beams propagating through polarization gratings," J. Opt. Soc. Am. A 18, 1399-1405 (2001).
    [CrossRef]

2008

2007

M. Ishiguro, D. Sato, A. Shishido, and T. Ikeda, "Bragg-type polarization gratings formed in thick polymer films containing azobenzene and tolane moieties," Langmuir 23, 332-338 (2007) (PMID: 17190523.).
[PubMed]

2006

J. J. Wang, L. Chen, X. Liu, P. Sciortino, F. Liu, F. Walters, and X. Deng, "30-nm-wide aluminum nanowire grid for ultrahigh contrast and transmittance polarizers made by uv-nanoimprint lithography," Appl. Phys. Lett. 89, 141105 (2006).
[CrossRef]

2005

2004

2003

2002

L. Nikolova, T. Todorov, V. Dragostinova, T. Petrova, and N. Tomova, "Polarization reflection holographic gratings in azobenzene-containing gelatine films," Opt. Lett. 27, 92-94 (2002).
[CrossRef]

E. Hasman, Z. Bomzon, A. Niv, G. Biener, and V. Kleiner, "Polarization beam-splitters and optical switches based on space-variant computer-generated subwavelength quasi-periodic structures," Opt. Commun. 209, 45-54 (2002).
[CrossRef]

2001

2000

J. Tervo, and J. Turunen, "Paraxial-domain diffractive elements with 100% efficiency based on polarization gratings," Opt. Lett. 25, 785-786 (2000).
[CrossRef]

M. Honkanen, V. Kettunen, J. Tervo, and J. Turunen, "Paraxial-domain diffractive elements with 100% efficiency based on polarization gratings," J. Mod. Opt. 47, 2351-2359 (2000).
[CrossRef]

1999

1998

S. M. Norton, G. M. Morris, and T. Erdogan, "Experimental investigation of resonant-grating filter line-shapes in comparison with theoretical models," J. Opt. Soc. Am. A 15, 464-472 (1998).
[CrossRef]

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. D. Fabrizio, and M. Gentili, "Analytical derivation of the optimum triplicator," Opt. Commun. 157, 13-16 (1998).
[CrossRef]

1996

1991

Adachi, J.

Andruzzi, F.

Biener, G.

Bomzon, Z.

E. Hasman, Z. Bomzon, A. Niv, G. Biener, and V. Kleiner, "Polarization beam-splitters and optical switches based on space-variant computer-generated subwavelength quasi-periodic structures," Opt. Commun. 209, 45-54 (2002).
[CrossRef]

Borghi, R.

G. Piquero, R. Borghi, and M. Santarsiero, "Gaussian Schell-model beams propagating through polarization gratings," J. Opt. Soc. Am. A 18, 1399-1405 (2001).
[CrossRef]

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. D. Fabrizio, and M. Gentili, "Analytical derivation of the optimum triplicator," Opt. Commun. 157, 13-16 (1998).
[CrossRef]

Chen, L.

J. J. Wang, L. Chen, X. Liu, P. Sciortino, F. Liu, F. Walters, and X. Deng, "30-nm-wide aluminum nanowire grid for ultrahigh contrast and transmittance polarizers made by uv-nanoimprint lithography," Appl. Phys. Lett. 89, 141105 (2006).
[CrossRef]

Cincotti, G.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. D. Fabrizio, and M. Gentili, "Analytical derivation of the optimum triplicator," Opt. Commun. 157, 13-16 (1998).
[CrossRef]

Davis, J. A.

Deng, X.

J. J. Wang, L. Chen, X. Liu, P. Sciortino, F. Liu, F. Walters, and X. Deng, "30-nm-wide aluminum nanowire grid for ultrahigh contrast and transmittance polarizers made by uv-nanoimprint lithography," Appl. Phys. Lett. 89, 141105 (2006).
[CrossRef]

Dragostinova, V.

Erdogan, T.

Fabrizio, E. D.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. D. Fabrizio, and M. Gentili, "Analytical derivation of the optimum triplicator," Opt. Commun. 157, 13-16 (1998).
[CrossRef]

Fernández-Pousa, C. R.

Gentili, M.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. D. Fabrizio, and M. Gentili, "Analytical derivation of the optimum triplicator," Opt. Commun. 157, 13-16 (1998).
[CrossRef]

Gori, F.

F. Gori, "Measuring Stokes parameters by means of a polarization grating," Opt. Lett. 24, 584-586 (1999).
[CrossRef]

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. D. Fabrizio, and M. Gentili, "Analytical derivation of the optimum triplicator," Opt. Commun. 157, 13-16 (1998).
[CrossRef]

Gorodetski, Y.

Hasman, E.

Honkanen, M.

J. Tervo, V. Kettunen, M. Honkanen, and J. Turunen, "Design of space-variant diffractive polarization elements," J. Opt. Soc. Am. A 20, 282-289 (2003).
[CrossRef]

M. Honkanen, V. Kettunen, J. Tervo, and J. Turunen, "Paraxial-domain diffractive elements with 100% efficiency based on polarization gratings," J. Mod. Opt. 47, 2351-2359 (2000).
[CrossRef]

Hvilsted, S.

Ikeda, T.

M. Ishiguro, D. Sato, A. Shishido, and T. Ikeda, "Bragg-type polarization gratings formed in thick polymer films containing azobenzene and tolane moieties," Langmuir 23, 332-338 (2007) (PMID: 17190523.).
[PubMed]

Ishiguro, M.

M. Ishiguro, D. Sato, A. Shishido, and T. Ikeda, "Bragg-type polarization gratings formed in thick polymer films containing azobenzene and tolane moieties," Langmuir 23, 332-338 (2007) (PMID: 17190523.).
[PubMed]

Ivanov, M.

Kettunen, V.

J. Tervo, V. Kettunen, M. Honkanen, and J. Turunen, "Design of space-variant diffractive polarization elements," J. Opt. Soc. Am. A 20, 282-289 (2003).
[CrossRef]

M. Honkanen, V. Kettunen, J. Tervo, and J. Turunen, "Paraxial-domain diffractive elements with 100% efficiency based on polarization gratings," J. Mod. Opt. 47, 2351-2359 (2000).
[CrossRef]

Kleiner, V.

Lajunen, H.

Lerman, G. M.

Levy, U.

Li, L.

Liu, F.

J. J. Wang, L. Chen, X. Liu, P. Sciortino, F. Liu, F. Walters, and X. Deng, "30-nm-wide aluminum nanowire grid for ultrahigh contrast and transmittance polarizers made by uv-nanoimprint lithography," Appl. Phys. Lett. 89, 141105 (2006).
[CrossRef]

Liu, X.

J. J. Wang, L. Chen, X. Liu, P. Sciortino, F. Liu, F. Walters, and X. Deng, "30-nm-wide aluminum nanowire grid for ultrahigh contrast and transmittance polarizers made by uv-nanoimprint lithography," Appl. Phys. Lett. 89, 141105 (2006).
[CrossRef]

Moreno, I.

Morris, G. M.

Nikolova, L.

Niv, A.

Norton, S. M.

Petrova, T.

Piquero, G.

Ramanujam, P. S.

Santarsiero, M.

G. Piquero, R. Borghi, and M. Santarsiero, "Gaussian Schell-model beams propagating through polarization gratings," J. Opt. Soc. Am. A 18, 1399-1405 (2001).
[CrossRef]

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. D. Fabrizio, and M. Gentili, "Analytical derivation of the optimum triplicator," Opt. Commun. 157, 13-16 (1998).
[CrossRef]

Sato, D.

M. Ishiguro, D. Sato, A. Shishido, and T. Ikeda, "Bragg-type polarization gratings formed in thick polymer films containing azobenzene and tolane moieties," Langmuir 23, 332-338 (2007) (PMID: 17190523.).
[PubMed]

Sciortino, P.

J. J. Wang, L. Chen, X. Liu, P. Sciortino, F. Liu, F. Walters, and X. Deng, "30-nm-wide aluminum nanowire grid for ultrahigh contrast and transmittance polarizers made by uv-nanoimprint lithography," Appl. Phys. Lett. 89, 141105 (2006).
[CrossRef]

Shishido, A.

M. Ishiguro, D. Sato, A. Shishido, and T. Ikeda, "Bragg-type polarization gratings formed in thick polymer films containing azobenzene and tolane moieties," Langmuir 23, 332-338 (2007) (PMID: 17190523.).
[PubMed]

Tervo, J.

Todorov, T.

Tomova, N.

Turunen, J.

Vicalvi, S.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. D. Fabrizio, and M. Gentili, "Analytical derivation of the optimum triplicator," Opt. Commun. 157, 13-16 (1998).
[CrossRef]

Walters, F.

J. J. Wang, L. Chen, X. Liu, P. Sciortino, F. Liu, F. Walters, and X. Deng, "30-nm-wide aluminum nanowire grid for ultrahigh contrast and transmittance polarizers made by uv-nanoimprint lithography," Appl. Phys. Lett. 89, 141105 (2006).
[CrossRef]

Wang, J. J.

J. J. Wang, L. Chen, X. Liu, P. Sciortino, F. Liu, F. Walters, and X. Deng, "30-nm-wide aluminum nanowire grid for ultrahigh contrast and transmittance polarizers made by uv-nanoimprint lithography," Appl. Phys. Lett. 89, 141105 (2006).
[CrossRef]

Wyrowski, F.

Appl. Opt.

Appl. Phys. Lett.

J. J. Wang, L. Chen, X. Liu, P. Sciortino, F. Liu, F. Walters, and X. Deng, "30-nm-wide aluminum nanowire grid for ultrahigh contrast and transmittance polarizers made by uv-nanoimprint lithography," Appl. Phys. Lett. 89, 141105 (2006).
[CrossRef]

J. Mod. Opt.

M. Honkanen, V. Kettunen, J. Tervo, and J. Turunen, "Paraxial-domain diffractive elements with 100% efficiency based on polarization gratings," J. Mod. Opt. 47, 2351-2359 (2000).
[CrossRef]

J. Opt. Soc. Am. A

Langmuir

M. Ishiguro, D. Sato, A. Shishido, and T. Ikeda, "Bragg-type polarization gratings formed in thick polymer films containing azobenzene and tolane moieties," Langmuir 23, 332-338 (2007) (PMID: 17190523.).
[PubMed]

Opt. Commun.

E. Hasman, Z. Bomzon, A. Niv, G. Biener, and V. Kleiner, "Polarization beam-splitters and optical switches based on space-variant computer-generated subwavelength quasi-periodic structures," Opt. Commun. 209, 45-54 (2002).
[CrossRef]

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, G. Cincotti, E. D. Fabrizio, and M. Gentili, "Analytical derivation of the optimum triplicator," Opt. Commun. 157, 13-16 (1998).
[CrossRef]

Opt. Express

Opt. Lett.

Y. Gorodetski, G. Biener, A. Niv, V. Kleiner, and E. Hasman, "Space-variant polarization manipulation for farfield polarimetry by use of subwavelength dielectric gratings," Opt. Lett. 30, 2245-2247 (2005).
[CrossRef] [PubMed]

G. M. Lerman, and U. Levy, "Generation of a radially polarized light beam using space-variant subwavelength gratings at 1064 nm," Opt. Lett. 33, 2782-2784 (2008).
[CrossRef] [PubMed]

J. Tervo, and J. Turunen, "Paraxial-domain diffractive elements with 100% efficiency based on polarization gratings," Opt. Lett. 25, 785-786 (2000).
[CrossRef]

F. Wyrowski, "Upper bound of the diffraction efficiency of diffractive phase elements," Opt. Lett. 16, 1915-1917 (1991).
[CrossRef] [PubMed]

H. Lajunen, J. Tervo, and J. Turunen, "High-efficiency broadband diffractive elements based on polarization gratings," Opt. Lett. 29, 803-805 (2004).
[CrossRef] [PubMed]

C. R. Fernández-Pousa, I. Moreno, J. A. Davis, and J. Adachi, "Polarizing diffraction-grating triplicators," Opt. Lett. 26, 1651-1653 (2001).
[CrossRef]

L. Nikolova, T. Todorov, V. Dragostinova, T. Petrova, and N. Tomova, "Polarization reflection holographic gratings in azobenzene-containing gelatine films," Opt. Lett. 27, 92-94 (2002).
[CrossRef]

F. Gori, "Measuring Stokes parameters by means of a polarization grating," Opt. Lett. 24, 584-586 (1999).
[CrossRef]

J. A. Davis, J. Adachi, C. R. Fernández-Pousa, and I. Moreno, "Polarization beam splitters using polarization diffraction gratings," Opt. Lett. 26, 587-589 (2001).
[CrossRef]

Other

R. C. Weast, CRC Handbook of Chemistry and Physics (CRC Press, Inc, Boca Raton, FL, 1984).

H. P. Herzig, Microoptics: Elements, Systems and Application (Taylor & Francis, London, 1997).

J. Turunen, and F. Wyrowski, Diffractive Optics for Industrial and Commercial Applications (Berlin: Akademie-Verlag, 1997).

J. Turunen, M. Kuittinen, and F. Wyrowski, "Diffractive optics: Electromagnetic approach," (Elsevier, 2000), chap. V, 343-388.

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Figures (7)

Fig. 1
Fig. 1

Schematic top view of a polarization grating, illustrating the local period Λ, local fringe orientation ϕ, and the ridge width c.

Fig. 2
Fig. 2

Scanning electron micrographs of surface-relief polarization gratings: (a) blazed grating, (b) triplicator, and (c) polarimeter. In all cases only a part of one grating period d is shown (the length of the scale bar is 1 μm), but several stripes with quantized value of the local fringe orientation ϕ (x) are seen.

Fig. 3
Fig. 3

(a) Efficiency η−1 of a blazed polarization grating with thickness h = 840 nm as a function of period Λ and fill factor f. (b) Efficiencies η0 (solid line) and η±1 (dashed line) of a triplicator with period Λ = 220 nm and thickness h = 550 nm as a function of fill factor f.

Fig. 4
Fig. 4

Zero-order transmittance of TM polarized light (solid line) and extinction ratio (dotted line) as a function of wavelength for a wire-grid polarizer of period Λ = 150 nm, fill factor f = 0.5 and ridge height 160 nm.

Fig. 5
Fig. 5

Process flow for Si3N4 (a) and Aluminum (b) gratings.

Fig. 6
Fig. 6

Line detector images of intensity pattern in the far field of polarization gratings. (a) The blazed grating with different polarization states of the incident beam. Solid line: LCP. Dashed line: linear polarization. Dashed line: RCP. (b) Triplicator. (c) Polarimeter grating.

Fig. 7
Fig. 7

Intensities of the three central diffraction orders of (a) the triplicator and (b) the polarimeter grating as a function of the rotation angle of a linear polarizer with respect to the x axis.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

η 0 = 1 4 | A + B | 2 ,
η ± 1 = 1 8 | A B | 2 [ 1 ± 2 | E x | | E y | sin ( Δ θ ) | E x | 2 + | E y | 2 ] ,

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