Abstract

We propose specially designed double anisotropic polarization diffraction gratings capable of producing a selective number of diffraction orders and with selective different states of polarization. Different polarization diffraction gratings are demonstrated, including linear polarization with horizontal, vertical and ± 45° orientations, and circular R and L polarization outputs. When illuminated with an arbitrary state of polarization, the system acts as a complete polarimeter where the intensities of the diffraction orders allow measurement of the Stokes parameters with a single shot. Experimental proof-of-concept is presented using a parallel-aligned liquid crystal display operating in a double pass architecture.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
  4. G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40(9), 1980–1983 (2015).
    [Crossref] [PubMed]
  5. L. Zhang, B. Liu, and X. Xin, “Secure coherent optical multi-carrier system with four-dimensional modulation space and Stokes vector scrambling,” Opt. Lett. 40(12), 2858–2861 (2015).
    [Crossref] [PubMed]
  6. S. E. Temple, J. E. McGregor, C. Miles, L. Graham, J. Miller, J. Buck, N. E. Scott-Samuel, and N. W. Roberts, “Perceiving polarization with the naked eye: characterization of human polarization sensitivity,” Proc. Biol. Sci. 282(1811), 20150338 (2015).
    [Crossref] [PubMed]
  7. G. Cincotti, “Polarization gratings: Design and applications,” IEEE J. Quantum Electron. 39(12), 1645–1652 (2003).
    [Crossref]
  8. T. Todorov and L. Nikolova, “Spectrophotopolarimeter: fast simultaneous real-time measurement of light parameters,” Opt. Lett. 17(5), 358–359 (1992).
    [Crossref] [PubMed]
  9. F. Gori, “Measuring Stokes parameters by means of a polarization grating,” Opt. Lett. 24(9), 584–586 (1999).
    [Crossref] [PubMed]
  10. J. Tervo and J. Turunen, “Paraxial-domain diffractive elements with 100% efficiency based on polarization gratings,” Opt. Lett. 25(11), 785–786 (2000).
    [Crossref] [PubMed]
  11. C. Oh and M. J. Escuti, “Achromatic diffraction from polarization gratings with high efficiency,” Opt. Lett. 33(20), 2287–2289 (2008).
    [Crossref] [PubMed]
  12. I. Vartiainen, J. Tervo, J. Turunen, and M. Kuittinen, “Surface-relief polarization gratings for visible light,” Opt. Express 18(22), 22850–22858 (2010).
    [Crossref] [PubMed]
  13. M. Beresna and P. G. Kazansky, “Polarization diffraction grating produced by femtosecond laser nanostructuring in glass,” Opt. Lett. 35(10), 1662–1664 (2010).
    [Crossref] [PubMed]
  14. M. Le Docen and P. Pellat-Finet, “Polarization properties and diffraction efficiencies of binary anisotropic gratings: general study and experiments on ferroelectric liquid crystals,” Opt. Commun. 151(4-6), 321–330 (1998).
    [Crossref]
  15. A. Martínez-García, I. Moreno, M. M. Sánchez-López, and P. García-Martínez, “Operational modes of a ferroelectric LCoS modulator for displaying binary polarization, amplitude, and phase diffraction gratings,” Appl. Opt. 48(15), 2903–2914 (2009).
    [Crossref] [PubMed]
  16. J. A. Davis, J. Adachi, C. R. Fernández-Pousa, and I. Moreno, “Polarization beam splitters using polarization diffraction gratings,” Opt. Lett. 26(9), 587–589 (2001).
    [Crossref] [PubMed]
  17. C. R. Fernández-Pousa, I. Moreno, J. A. Davis, and J. Adachi, “Polarizing diffraction-grating triplicators,” Opt. Lett. 26(21), 1651–1653 (2001).
    [Crossref] [PubMed]
  18. Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Spatial Fourier-transform polarimetry using space-variant subwavelength metal-stripe polarizers,” Opt. Lett. 26(21), 1711–1713 (2001).
    [Crossref] [PubMed]
  19. I. Moreno, J. A. Davis, T. M. Hernandez, D. M. Cottrell, and D. Sand, “Complete polarization control of light from a liquid crystal spatial light modulator,” Opt. Express 20(1), 364–376 (2012).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  21. L. A. Romero and F. M. Dickey, “The mathematical theory of laser beam-splitting gratings,” Prog. Optics 54, 319–386 (2010).
    [Crossref]
  22. J. Albero, I. Moreno, J. A. Davis, D. M. Cottrell, and D. Sand, “Generalized phase diffraction gratings with tailored intensity,” Opt. Lett. 37(20), 4227–4229 (2012).
    [Crossref] [PubMed]
  23. J. Albero, J. A. Davis, D. M. Cottrell, C. E. Granger, K. R. McCormick, and I. Moreno, “Generalized diffractive optical elements with asymmetric harmonic response and phase control,” Appl. Opt. 52(15), 3637–3644 (2013).
    [Crossref] [PubMed]
  24. J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38(6), 1051 (1999).
    [Crossref]
  25. http://support.microsoft.com/kb/214115

2015 (3)

2013 (2)

J. Albero, J. A. Davis, D. M. Cottrell, C. E. Granger, K. R. McCormick, and I. Moreno, “Generalized diffractive optical elements with asymmetric harmonic response and phase control,” Appl. Opt. 52(15), 3637–3644 (2013).
[Crossref] [PubMed]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

2012 (3)

2010 (3)

2009 (1)

2008 (1)

2007 (1)

2006 (1)

2003 (1)

G. Cincotti, “Polarization gratings: Design and applications,” IEEE J. Quantum Electron. 39(12), 1645–1652 (2003).
[Crossref]

2001 (3)

2000 (1)

1999 (2)

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38(6), 1051 (1999).
[Crossref]

F. Gori, “Measuring Stokes parameters by means of a polarization grating,” Opt. Lett. 24(9), 584–586 (1999).
[Crossref] [PubMed]

1998 (1)

M. Le Docen and P. Pellat-Finet, “Polarization properties and diffraction efficiencies of binary anisotropic gratings: general study and experiments on ferroelectric liquid crystals,” Opt. Commun. 151(4-6), 321–330 (1998).
[Crossref]

1992 (1)

Adachi, J.

Ahmed, N.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Albero, J.

Alfano, R. R.

Amako, J.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38(6), 1051 (1999).
[Crossref]

Beresna, M.

Biener, G.

Bomzon, Z.

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Buck, J.

S. E. Temple, J. E. McGregor, C. Miles, L. Graham, J. Miller, J. Buck, N. E. Scott-Samuel, and N. W. Roberts, “Perceiving polarization with the naked eye: characterization of human polarization sensitivity,” Proc. Biol. Sci. 282(1811), 20150338 (2015).
[Crossref] [PubMed]

Chenault, D. B.

Cincotti, G.

G. Cincotti, “Polarization gratings: Design and applications,” IEEE J. Quantum Electron. 39(12), 1645–1652 (2003).
[Crossref]

Cottrell, D. M.

Davis, J. A.

Dickey, F. M.

L. A. Romero and F. M. Dickey, “The mathematical theory of laser beam-splitting gratings,” Prog. Optics 54, 319–386 (2010).
[Crossref]

L. A. Romero and F. M. Dickey, “Theory of optimal beam splitting by phase gratings. I. One-dimensional gratings,” J. Opt. Soc. Am. A 24(8), 2280–2295 (2007).
[Crossref] [PubMed]

Dolinar, S.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Escuti, M. J.

Fazal, I. M.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Fernández-Pousa, C. R.

García-Martínez, P.

Goldstein, D. L.

Gori, F.

Graham, L.

S. E. Temple, J. E. McGregor, C. Miles, L. Graham, J. Miller, J. Buck, N. E. Scott-Samuel, and N. W. Roberts, “Perceiving polarization with the naked eye: characterization of human polarization sensitivity,” Proc. Biol. Sci. 282(1811), 20150338 (2015).
[Crossref] [PubMed]

Granger, C. E.

Hasman, E.

Hernandez, T. M.

Huang, H.

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40(9), 1980–1983 (2015).
[Crossref] [PubMed]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Karimi, E.

Kazansky, P. G.

Kleiner, V.

Kristensen, P.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Kuittinen, M.

Lavery, M. P. J.

Le Docen, M.

M. Le Docen and P. Pellat-Finet, “Polarization properties and diffraction efficiencies of binary anisotropic gratings: general study and experiments on ferroelectric liquid crystals,” Opt. Commun. 151(4-6), 321–330 (1998).
[Crossref]

Liu, B.

Marrucci, L.

Martínez-García, A.

McCormick, K. R.

McGregor, J. E.

S. E. Temple, J. E. McGregor, C. Miles, L. Graham, J. Miller, J. Buck, N. E. Scott-Samuel, and N. W. Roberts, “Perceiving polarization with the naked eye: characterization of human polarization sensitivity,” Proc. Biol. Sci. 282(1811), 20150338 (2015).
[Crossref] [PubMed]

Miles, C.

S. E. Temple, J. E. McGregor, C. Miles, L. Graham, J. Miller, J. Buck, N. E. Scott-Samuel, and N. W. Roberts, “Perceiving polarization with the naked eye: characterization of human polarization sensitivity,” Proc. Biol. Sci. 282(1811), 20150338 (2015).
[Crossref] [PubMed]

Milione, G.

Miller, J.

S. E. Temple, J. E. McGregor, C. Miles, L. Graham, J. Miller, J. Buck, N. E. Scott-Samuel, and N. W. Roberts, “Perceiving polarization with the naked eye: characterization of human polarization sensitivity,” Proc. Biol. Sci. 282(1811), 20150338 (2015).
[Crossref] [PubMed]

Moreno, I.

Nguyen, T. A.

Nikolova, L.

Nolan, D. A.

Oh, C.

Pellat-Finet, P.

M. Le Docen and P. Pellat-Finet, “Polarization properties and diffraction efficiencies of binary anisotropic gratings: general study and experiments on ferroelectric liquid crystals,” Opt. Commun. 151(4-6), 321–330 (1998).
[Crossref]

Ramachandran, S.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Ren, Y.

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40(9), 1980–1983 (2015).
[Crossref] [PubMed]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Roberts, N. W.

S. E. Temple, J. E. McGregor, C. Miles, L. Graham, J. Miller, J. Buck, N. E. Scott-Samuel, and N. W. Roberts, “Perceiving polarization with the naked eye: characterization of human polarization sensitivity,” Proc. Biol. Sci. 282(1811), 20150338 (2015).
[Crossref] [PubMed]

Romero, L. A.

L. A. Romero and F. M. Dickey, “The mathematical theory of laser beam-splitting gratings,” Prog. Optics 54, 319–386 (2010).
[Crossref]

L. A. Romero and F. M. Dickey, “Theory of optimal beam splitting by phase gratings. I. One-dimensional gratings,” J. Opt. Soc. Am. A 24(8), 2280–2295 (2007).
[Crossref] [PubMed]

Sánchez-López, M. M.

Sand, D.

Scott-Samuel, N. E.

S. E. Temple, J. E. McGregor, C. Miles, L. Graham, J. Miller, J. Buck, N. E. Scott-Samuel, and N. W. Roberts, “Perceiving polarization with the naked eye: characterization of human polarization sensitivity,” Proc. Biol. Sci. 282(1811), 20150338 (2015).
[Crossref] [PubMed]

Shaw, J. A.

Sonehara, T.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38(6), 1051 (1999).
[Crossref]

Temple, S. E.

S. E. Temple, J. E. McGregor, C. Miles, L. Graham, J. Miller, J. Buck, N. E. Scott-Samuel, and N. W. Roberts, “Perceiving polarization with the naked eye: characterization of human polarization sensitivity,” Proc. Biol. Sci. 282(1811), 20150338 (2015).
[Crossref] [PubMed]

Tervo, J.

Todorov, T.

Tsai, P.

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38(6), 1051 (1999).
[Crossref]

Tur, M.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Turunen, J.

Tyo, J. S.

Vartiainen, I.

Wang, J.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Willner, A. E.

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40(9), 1980–1983 (2015).
[Crossref] [PubMed]

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Xie, G.

Xin, X.

Yan, Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Yang, J.-Y.

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Yue, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Zhang, L.

Appl. Opt. (3)

IEEE J. Quantum Electron. (1)

G. Cincotti, “Polarization gratings: Design and applications,” IEEE J. Quantum Electron. 39(12), 1645–1652 (2003).
[Crossref]

J. Opt. Soc. Am. A (1)

Nat. Photonics (1)

J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012).
[Crossref]

Opt. Commun. (1)

M. Le Docen and P. Pellat-Finet, “Polarization properties and diffraction efficiencies of binary anisotropic gratings: general study and experiments on ferroelectric liquid crystals,” Opt. Commun. 151(4-6), 321–330 (1998).
[Crossref]

Opt. Eng. (1)

J. A. Davis, P. Tsai, D. M. Cottrell, T. Sonehara, and J. Amako, “Transmission variations in liquid crystal spatial light modulators caused by interference and diffraction effects,” Opt. Eng. 38(6), 1051 (1999).
[Crossref]

Opt. Express (2)

Opt. Lett. (11)

M. Beresna and P. G. Kazansky, “Polarization diffraction grating produced by femtosecond laser nanostructuring in glass,” Opt. Lett. 35(10), 1662–1664 (2010).
[Crossref] [PubMed]

J. A. Davis, J. Adachi, C. R. Fernández-Pousa, and I. Moreno, “Polarization beam splitters using polarization diffraction gratings,” Opt. Lett. 26(9), 587–589 (2001).
[Crossref] [PubMed]

C. R. Fernández-Pousa, I. Moreno, J. A. Davis, and J. Adachi, “Polarizing diffraction-grating triplicators,” Opt. Lett. 26(21), 1651–1653 (2001).
[Crossref] [PubMed]

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Spatial Fourier-transform polarimetry using space-variant subwavelength metal-stripe polarizers,” Opt. Lett. 26(21), 1711–1713 (2001).
[Crossref] [PubMed]

G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, and A. E. Willner, “4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer,” Opt. Lett. 40(9), 1980–1983 (2015).
[Crossref] [PubMed]

L. Zhang, B. Liu, and X. Xin, “Secure coherent optical multi-carrier system with four-dimensional modulation space and Stokes vector scrambling,” Opt. Lett. 40(12), 2858–2861 (2015).
[Crossref] [PubMed]

T. Todorov and L. Nikolova, “Spectrophotopolarimeter: fast simultaneous real-time measurement of light parameters,” Opt. Lett. 17(5), 358–359 (1992).
[Crossref] [PubMed]

F. Gori, “Measuring Stokes parameters by means of a polarization grating,” Opt. Lett. 24(9), 584–586 (1999).
[Crossref] [PubMed]

J. Tervo and J. Turunen, “Paraxial-domain diffractive elements with 100% efficiency based on polarization gratings,” Opt. Lett. 25(11), 785–786 (2000).
[Crossref] [PubMed]

C. Oh and M. J. Escuti, “Achromatic diffraction from polarization gratings with high efficiency,” Opt. Lett. 33(20), 2287–2289 (2008).
[Crossref] [PubMed]

J. Albero, I. Moreno, J. A. Davis, D. M. Cottrell, and D. Sand, “Generalized phase diffraction gratings with tailored intensity,” Opt. Lett. 37(20), 4227–4229 (2012).
[Crossref] [PubMed]

Proc. Biol. Sci. (1)

S. E. Temple, J. E. McGregor, C. Miles, L. Graham, J. Miller, J. Buck, N. E. Scott-Samuel, and N. W. Roberts, “Perceiving polarization with the naked eye: characterization of human polarization sensitivity,” Proc. Biol. Sci. 282(1811), 20150338 (2015).
[Crossref] [PubMed]

Prog. Optics (1)

L. A. Romero and F. M. Dickey, “The mathematical theory of laser beam-splitting gratings,” Prog. Optics 54, 319–386 (2010).
[Crossref]

Science (1)

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340(6140), 1545–1548 (2013).
[Crossref] [PubMed]

Other (1)

http://support.microsoft.com/kb/214115

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Figures (6)

Fig. 1
Fig. 1

Scheme of the optical system to generate a PDG. LP: linear polarizer; NPBS: non-polarizing beam splitter; SLM: spatial light modulator; QWP: quarter-wave plate; L1 and L2: converging lenses; R: mirror reflector.

Fig. 2
Fig. 2

PDG beam splitter producing orders + 1 and −1 with vertical and horizontal linear polarizations. (a) Image addressed to the SLM and grating phase profiles. (b) Experimental results captured at the CCD plane for different analyzers indicated on the top of the figure.

Fig. 3
Fig. 3

PDG producing orders + 2, + 1, −1, and −2 with vertical linear, RCP, LCP and horizontal linear polarizations. (a) Image addressed to the SLM and grating phase profiles. (b) Experimental results captures at the CCD plane for different analyzers indicated on the top.

Fig. 4
Fig. 4

PDG producing orders + 3, + 1, −1, and −3 with linear 135, RCP, linear 45 and LCP polarizations. (a) Image addressed to the SLM and grating phase profiles. (b) Experimental results captures at the CCD plane for different analyzers indicated on the top.

Fig. 5
Fig. 5

PDG producing orders + 3, + 2, + 1, −1, −2, and −3 with polarization states RCP, linear horizontal, linear 135°, LCP, linear vertical and linear 45°. (a) Image addressed to the SLM and phase profiles. (b) Experimental results captured at the CCD plane for different analyzers indicated on the top.

Fig. 6
Fig. 6

Diffraction orders generated when different input polarizations are launched to the PDG sextuplicator with a final linear analyzer oriented at 45°. The intensities of + 3, + 2, + 1, −1, −2, −3 orders are proportional to the LCP, L0, L135, RCP, L90 and L45 polarization components. The input polarization is verified by the absence of the diffraction order with orthogonal PSA.

Tables (3)

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Table 1 Numerical constants of the phase only gratings in Fig. 3.

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Table 2 Numerical constants of the phase only gratings in Fig. 4.

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Table 3 Numerical constants of the phase only gratings in Fig. 5.

Equations (5)

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s( x )= k μ k exp( i α k ) exp( ikγx ),
exp[ iφ( x ) ]= s( x ) | s( x ) | .
exp[ iφ( x ) ]= m= + c m exp( imγx ) ,
c m = 1 2π/γ π/γ +π/γ exp[ iφ( x ) ] exp( imγx )dx,
η= k | c k | 2 m= + | c m | 2

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