Abstract

We have made an ultra-thin (~2.26 µm) f/2.1 lens based on the Pancharatnam phase effect using the polarization holography alignment technique. This lens exhibits a continuous phase profile, high efficiency (>97%), and is switchable from having a positive focal length to a negative one by changing the handedness of input circularly polarized light. We analyzed its optical performance and simulated it as a gradient index lens for further comparison, and to discuss its bandwidth limitation. The conditions required for improving the performance and its low-cost fabrication method is discussed. Because of the nature of Pancharatnam devices and the demonstrated fabrication method, these results are applicable to a wide size range.

© 2015 Optical Society of America

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References

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  1. S. Pancharatnam, “Generalized theory of interference, and its application,” Proc. Ind. Acad. Sci. A 44(5), 247–262 (1956).
  2. M. Martinelli and P. Vavassori, “A geometric (Pancharatnam) phase approach to the polarization and phase control in the coherent optics circuits,” Opt. Commun. 80(2), 166–176 (1990).
    [Crossref]
  3. H. H. Cheng, A. Bhowmik, and P. J. Bos, “Large angle image steering using a liquid crystal device,”SID Symp. Dig. Tech. Pap. 45(1), 739–742 (2014).
    [Crossref]
  4. M. J. Escuti, C. Oh, C. Sánchez, C. W. M. Bastiaansen, and D. J. Broer, “Simplified spectropolarimetry using reactive mesogen polarization gratings,” Proc. SPIE 6302, 630207 (2006).
    [Crossref]
  5. M. J. Escuti and W. M. Jones, “Polarization independent switching with high contrast from a liquid crystal polarization grating,” SID Symp. Dig. Tech. Papers 37, 1443–1446 (2006).
    [Crossref]
  6. M. Honma and T. Nose, “Liquid-Crystal Fresnel Zone Plate Fabricated by Microrubbing,” Jpn. J. Appl. Phys. 44(1A), 287–290 (2005).
    [Crossref]
  7. E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics,” Appl. Phys. Lett. 82(3), 328–330 (2003).
    [Crossref]
  8. Y. Gorodetski, G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Optical properties of polarization-dependent geometric phase elements with partially polarized light,” Opt. Commun. 266(2), 365–375 (2006).
    [Crossref]
  9. T. Todorov, L. Nikolova, and N. Tomova, “Polarization holography. 2: Polarization holographic gratings in photoanisotropic materials with and without intrinsic birefringence,” Appl. Opt. 23(24), 4588–4591 (1984).
    [Crossref] [PubMed]
  10. G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005).
    [Crossref]
  11. H. Sarkissian, S. V. Serak, N. V. Tabiryan, L. B. Glebov, V. Rotar, and B. Y. Zeldovich, “Polarization-controlled switching between diffraction orders in transverse-periodically aligned nematic liquid crystals,” Opt. Lett. 31(15), 2248–2250 (2006).
    [Crossref] [PubMed]
  12. C. Oh, “Broadband Polarization Gratings for Efficient Liquid Crystal Display, Beam Steering, Spectropolarimetry, and Fresnel Zone Plate,” Ph. D. Thesis, North Carolina State University (2009).
  13. C. Oh and M. J. Escuti, “Achromatic diffraction from polarization gratings with high efficiency,” Opt. Lett. 33(20), 2287–2289 (2008).
    [Crossref] [PubMed]
  14. C. Oh and M. J. Escuti, “Achromatic polarization gratings as highly efficient thin-film polarizing beamsplitters for broadband light,” Proc. SPIE 6682, 668211 (2007).
    [Crossref]
  15. K. Hirayama, E. N. Glytsis, T. K. Gaylord, and D. W. Wilson, “Rigorous electromagnetic analysis of diffractive cylindrical lenses,” J. Opt. Soc. Am. A 13(11), 2219–2231 (1996).
    [Crossref]
  16. E. Hecht, Optics, 2nd ed. (Addison Wesley, 1987).
  17. R. K. Komanduri and M. J. Escuti, “Elastic continuum analysis of the liquid crystal polarization grating,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2), 021701 (2007).
    [Crossref] [PubMed]
  18. C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76(4), 043815 (2007).
    [Crossref]

2014 (1)

H. H. Cheng, A. Bhowmik, and P. J. Bos, “Large angle image steering using a liquid crystal device,”SID Symp. Dig. Tech. Pap. 45(1), 739–742 (2014).
[Crossref]

2008 (1)

2007 (3)

C. Oh and M. J. Escuti, “Achromatic polarization gratings as highly efficient thin-film polarizing beamsplitters for broadband light,” Proc. SPIE 6682, 668211 (2007).
[Crossref]

R. K. Komanduri and M. J. Escuti, “Elastic continuum analysis of the liquid crystal polarization grating,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2), 021701 (2007).
[Crossref] [PubMed]

C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76(4), 043815 (2007).
[Crossref]

2006 (3)

H. Sarkissian, S. V. Serak, N. V. Tabiryan, L. B. Glebov, V. Rotar, and B. Y. Zeldovich, “Polarization-controlled switching between diffraction orders in transverse-periodically aligned nematic liquid crystals,” Opt. Lett. 31(15), 2248–2250 (2006).
[Crossref] [PubMed]

M. J. Escuti, C. Oh, C. Sánchez, C. W. M. Bastiaansen, and D. J. Broer, “Simplified spectropolarimetry using reactive mesogen polarization gratings,” Proc. SPIE 6302, 630207 (2006).
[Crossref]

Y. Gorodetski, G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Optical properties of polarization-dependent geometric phase elements with partially polarized light,” Opt. Commun. 266(2), 365–375 (2006).
[Crossref]

2005 (2)

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005).
[Crossref]

M. Honma and T. Nose, “Liquid-Crystal Fresnel Zone Plate Fabricated by Microrubbing,” Jpn. J. Appl. Phys. 44(1A), 287–290 (2005).
[Crossref]

2003 (1)

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics,” Appl. Phys. Lett. 82(3), 328–330 (2003).
[Crossref]

1996 (1)

1990 (1)

M. Martinelli and P. Vavassori, “A geometric (Pancharatnam) phase approach to the polarization and phase control in the coherent optics circuits,” Opt. Commun. 80(2), 166–176 (1990).
[Crossref]

1984 (1)

1956 (1)

S. Pancharatnam, “Generalized theory of interference, and its application,” Proc. Ind. Acad. Sci. A 44(5), 247–262 (1956).

Bastiaansen, C. W. M.

M. J. Escuti, C. Oh, C. Sánchez, C. W. M. Bastiaansen, and D. J. Broer, “Simplified spectropolarimetry using reactive mesogen polarization gratings,” Proc. SPIE 6302, 630207 (2006).
[Crossref]

Bhowmik, A.

H. H. Cheng, A. Bhowmik, and P. J. Bos, “Large angle image steering using a liquid crystal device,”SID Symp. Dig. Tech. Pap. 45(1), 739–742 (2014).
[Crossref]

Biener, G.

Y. Gorodetski, G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Optical properties of polarization-dependent geometric phase elements with partially polarized light,” Opt. Commun. 266(2), 365–375 (2006).
[Crossref]

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics,” Appl. Phys. Lett. 82(3), 328–330 (2003).
[Crossref]

Bos, P. J.

H. H. Cheng, A. Bhowmik, and P. J. Bos, “Large angle image steering using a liquid crystal device,”SID Symp. Dig. Tech. Pap. 45(1), 739–742 (2014).
[Crossref]

Broer, D. J.

M. J. Escuti, C. Oh, C. Sánchez, C. W. M. Bastiaansen, and D. J. Broer, “Simplified spectropolarimetry using reactive mesogen polarization gratings,” Proc. SPIE 6302, 630207 (2006).
[Crossref]

Callan-Jones, A.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005).
[Crossref]

Cheng, H. H.

H. H. Cheng, A. Bhowmik, and P. J. Bos, “Large angle image steering using a liquid crystal device,”SID Symp. Dig. Tech. Pap. 45(1), 739–742 (2014).
[Crossref]

Crawford, G. P.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005).
[Crossref]

Eakin, J. N.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005).
[Crossref]

Escuti, M. J.

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

C. Oh and M. J. Escuti, “Achromatic polarization gratings as highly efficient thin-film polarizing beamsplitters for broadband light,” Proc. SPIE 6682, 668211 (2007).
[Crossref]

R. K. Komanduri and M. J. Escuti, “Elastic continuum analysis of the liquid crystal polarization grating,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2), 021701 (2007).
[Crossref] [PubMed]

C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76(4), 043815 (2007).
[Crossref]

M. J. Escuti, C. Oh, C. Sánchez, C. W. M. Bastiaansen, and D. J. Broer, “Simplified spectropolarimetry using reactive mesogen polarization gratings,” Proc. SPIE 6302, 630207 (2006).
[Crossref]

Gaylord, T. K.

Glebov, L. B.

Glytsis, E. N.

Gorodetski, Y.

Y. Gorodetski, G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Optical properties of polarization-dependent geometric phase elements with partially polarized light,” Opt. Commun. 266(2), 365–375 (2006).
[Crossref]

Hasman, E.

Y. Gorodetski, G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Optical properties of polarization-dependent geometric phase elements with partially polarized light,” Opt. Commun. 266(2), 365–375 (2006).
[Crossref]

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics,” Appl. Phys. Lett. 82(3), 328–330 (2003).
[Crossref]

Hirayama, K.

Honma, M.

M. Honma and T. Nose, “Liquid-Crystal Fresnel Zone Plate Fabricated by Microrubbing,” Jpn. J. Appl. Phys. 44(1A), 287–290 (2005).
[Crossref]

Kleiner, V.

Y. Gorodetski, G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Optical properties of polarization-dependent geometric phase elements with partially polarized light,” Opt. Commun. 266(2), 365–375 (2006).
[Crossref]

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics,” Appl. Phys. Lett. 82(3), 328–330 (2003).
[Crossref]

Komanduri, R. K.

R. K. Komanduri and M. J. Escuti, “Elastic continuum analysis of the liquid crystal polarization grating,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2), 021701 (2007).
[Crossref] [PubMed]

Martinelli, M.

M. Martinelli and P. Vavassori, “A geometric (Pancharatnam) phase approach to the polarization and phase control in the coherent optics circuits,” Opt. Commun. 80(2), 166–176 (1990).
[Crossref]

Nikolova, L.

Niv, A.

Y. Gorodetski, G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Optical properties of polarization-dependent geometric phase elements with partially polarized light,” Opt. Commun. 266(2), 365–375 (2006).
[Crossref]

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics,” Appl. Phys. Lett. 82(3), 328–330 (2003).
[Crossref]

Nose, T.

M. Honma and T. Nose, “Liquid-Crystal Fresnel Zone Plate Fabricated by Microrubbing,” Jpn. J. Appl. Phys. 44(1A), 287–290 (2005).
[Crossref]

Oh, C.

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

C. Oh and M. J. Escuti, “Achromatic polarization gratings as highly efficient thin-film polarizing beamsplitters for broadband light,” Proc. SPIE 6682, 668211 (2007).
[Crossref]

C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76(4), 043815 (2007).
[Crossref]

M. J. Escuti, C. Oh, C. Sánchez, C. W. M. Bastiaansen, and D. J. Broer, “Simplified spectropolarimetry using reactive mesogen polarization gratings,” Proc. SPIE 6302, 630207 (2006).
[Crossref]

Pancharatnam, S.

S. Pancharatnam, “Generalized theory of interference, and its application,” Proc. Ind. Acad. Sci. A 44(5), 247–262 (1956).

Pelcovits, R. A.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005).
[Crossref]

Radcliffe, M. D.

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005).
[Crossref]

Rotar, V.

Sánchez, C.

M. J. Escuti, C. Oh, C. Sánchez, C. W. M. Bastiaansen, and D. J. Broer, “Simplified spectropolarimetry using reactive mesogen polarization gratings,” Proc. SPIE 6302, 630207 (2006).
[Crossref]

Sarkissian, H.

Serak, S. V.

Tabiryan, N. V.

Todorov, T.

Tomova, N.

Vavassori, P.

M. Martinelli and P. Vavassori, “A geometric (Pancharatnam) phase approach to the polarization and phase control in the coherent optics circuits,” Opt. Commun. 80(2), 166–176 (1990).
[Crossref]

Wilson, D. W.

Zeldovich, B. Y.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics,” Appl. Phys. Lett. 82(3), 328–330 (2003).
[Crossref]

J. Appl. Phys. (1)

G. P. Crawford, J. N. Eakin, M. D. Radcliffe, A. Callan-Jones, and R. A. Pelcovits, “Liquid-crystal diffraction gratings using polarization holography alignment techniques,” J. Appl. Phys. 98(12), 123102 (2005).
[Crossref]

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

Jpn. J. Appl. Phys. (1)

M. Honma and T. Nose, “Liquid-Crystal Fresnel Zone Plate Fabricated by Microrubbing,” Jpn. J. Appl. Phys. 44(1A), 287–290 (2005).
[Crossref]

Opt. Commun. (2)

Y. Gorodetski, G. Biener, A. Niv, V. Kleiner, and E. Hasman, “Optical properties of polarization-dependent geometric phase elements with partially polarized light,” Opt. Commun. 266(2), 365–375 (2006).
[Crossref]

M. Martinelli and P. Vavassori, “A geometric (Pancharatnam) phase approach to the polarization and phase control in the coherent optics circuits,” Opt. Commun. 80(2), 166–176 (1990).
[Crossref]

Opt. Lett. (2)

Phys. Rev. A (1)

C. Oh and M. J. Escuti, “Numerical analysis of polarization gratings using the finite-difference time-domain method,” Phys. Rev. A 76(4), 043815 (2007).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

R. K. Komanduri and M. J. Escuti, “Elastic continuum analysis of the liquid crystal polarization grating,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(2), 021701 (2007).
[Crossref] [PubMed]

Proc. Ind. Acad. Sci. A (1)

S. Pancharatnam, “Generalized theory of interference, and its application,” Proc. Ind. Acad. Sci. A 44(5), 247–262 (1956).

Proc. SPIE (2)

M. J. Escuti, C. Oh, C. Sánchez, C. W. M. Bastiaansen, and D. J. Broer, “Simplified spectropolarimetry using reactive mesogen polarization gratings,” Proc. SPIE 6302, 630207 (2006).
[Crossref]

C. Oh and M. J. Escuti, “Achromatic polarization gratings as highly efficient thin-film polarizing beamsplitters for broadband light,” Proc. SPIE 6682, 668211 (2007).
[Crossref]

SID Symp. Dig. Tech. Pap. (1)

H. H. Cheng, A. Bhowmik, and P. J. Bos, “Large angle image steering using a liquid crystal device,”SID Symp. Dig. Tech. Pap. 45(1), 739–742 (2014).
[Crossref]

Other (3)

M. J. Escuti and W. M. Jones, “Polarization independent switching with high contrast from a liquid crystal polarization grating,” SID Symp. Dig. Tech. Papers 37, 1443–1446 (2006).
[Crossref]

E. Hecht, Optics, 2nd ed. (Addison Wesley, 1987).

C. Oh, “Broadband Polarization Gratings for Efficient Liquid Crystal Display, Beam Steering, Spectropolarimetry, and Fresnel Zone Plate,” Ph. D. Thesis, North Carolina State University (2009).

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Figures (7)

Fig. 1
Fig. 1 (a) The schematic of full optical setup for holographic exposure. (ND: neutral density; BE: beam expander; M: magnification; LP: linear polarizer; BS: beam splitter; QWP: quarter-wave plate;) (b) Direct observation of interference pattern from the CCD coupled with 20x objective lens.
Fig. 2
Fig. 2 (a) The Pancharatnam Lens observed under an interference filter using polarized microscope, with magnified pictures (b) around the center; (c) at 0.5 mm radius (d) at 1 mm radius (e) at 1.5 mm radius (f) at 2 mm radius; (g) close to the edge. Figures (b) and (g) are from the areas designated by boxes in figure (a)
Fig. 3
Fig. 3 The comparison of OPD of aspherical lens used in holographic exposure and the Pancharatnam lens with polynomial fit shown in red dash line.
Fig. 4
Fig. 4 (a) Characterization of PSF and (b) MTF of Pancharatnam lens under 2 mm aperture and 632 nm wavelength. The bars show the range of data points acquired from three cross sections of each of 3 PSF measurements.
Fig. 5
Fig. 5 (a) Characterization of PSF and (b) MTF of Pancharatnam lens under 4 mm aperture and 632 nm wavelength. The bars show the range of data points acquired from three cross sections of each of 3 PSF measurements.
Fig. 6
Fig. 6 This Pancharatnam lens was attached to CCD (a) with 2 mm aperture; (b) with 3 mm aperture; (c) with 4 mm aperture; (d) with 5 mm aperture for imaging tests using 11.5 nm FWHM of interference filter.
Fig. 7
Fig. 7 The MTF/2 bandwidth limit (as defined in the text) vs. f-number of a diffraction-limited Pancharatnam lens.

Equations (5)

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Γ( r )= sin 1 ( I( r ) I 0 )+ Γ o ,
OPD'= Γ 2π λ~ r 2 2f .
n(r)= n o + n r 1 r+ n r 2 r 2 ,
OPD'= Γ 2π λ=2m(r)λ=n(r)d,
f= π r 2 2β( r )λ .

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