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.

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References

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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 polarizationgratings,” 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). .
    [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,” Optics Communications 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 far-field 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,” Applied Physics Letters 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,” Optics Communications 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 lineshapes 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 (1)

2006 (1)

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,” Applied Physics Letters 89, 141105 (2006).
[Crossref]

2005 (2)

2004 (1)

2003 (2)

2002 (2)

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,” Optics Communications 209, 45 – 54 (2002).
[Crossref]

2001 (3)

2000 (2)

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

1999 (1)

1998 (2)

S. M. Norton, G. M. Morris, and T. Erdogan, “Experimental investigation of resonant-grating filter lineshapes 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,” Optics Communications 157, 13 – 16 (1998).
[Crossref]

1996 (2)

1991 (1)

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,” Optics Communications 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,” Optics Communications 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,” Applied Physics Letters 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,” Optics Communications 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,” Applied Physics Letters 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,” Optics Communications 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,” Optics Communications 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,” Optics Communications 157, 13 – 16 (1998).
[Crossref]

Gorodetski, Y.

Hasman, E.

Herzig, H. P.

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

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). .
[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). .
[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.

Kuittinen, M.

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

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,” Applied Physics Letters 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,” Applied Physics Letters 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,” Optics Communications 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). .
[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,” Applied Physics Letters 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). .
[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,” Optics Communications 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,” Applied Physics Letters 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,” Applied Physics Letters 89, 141105 (2006).
[Crossref]

Weast, R. C.

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

Wyrowski, F.

F. Wyrowski, “Upper bound of the diffraction efficiency of diffractive phase elements,” Opt. Lett. 16, 1915–1917 (1991).
[Crossref] [PubMed]

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.

Appl. Opt. (1)

Applied Physics Letters (1)

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,” Applied Physics Letters 89, 141105 (2006).
[Crossref]

J. Mod. Opt. (1)

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 (5)

Langmuir (1)

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). .
[PubMed]

Opt. Express (1)

Opt. Lett. (9)

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]

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]

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]

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

H. Lajunen, J. Tervo, and J. Turunen, “High-efficiency broadband diffractive elements based on polarizationgratings,” Opt. Lett. 29, 803–805 (2004).
[Crossref] [PubMed]

F. Gori, “Measuring Stokes parameters by means of a polarization grating,” Opt. Lett. 24, 584–586 (1999).
[Crossref]

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]

Optics Communications (2)

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,” Optics Communications 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,” Optics Communications 157, 13 – 16 (1998).
[Crossref]

Other (4)

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

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

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).

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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)

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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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