Abstract

We present an original static recording method for vortex retarders (VRs) made from liquid crystal polymers (LCPs) using the superimposition of several polarized beams. VRs are birefringent plates characterized by a rotation of their fast axis about their center. The new method is based on polarization holography and photo-orientable LCP. Combining several polarized beams induces the polarization patterns required for the recording process of VRs without mechanical action. A mathematical description of the method, the outcomes of the numerical simulations, and the first experimental results are presented.

© 2013 Optical Society of America

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    [CrossRef]
  16. D. Mawet, P. Riaud, O. Absil, and J. Surdej, “Annular groove phase mask coronagraph,” Astrophys. J. 633, 1191–1200 (2005).
    [CrossRef]
  17. D. Mawet, P. Riaud, J. Surdej, and J. Baudrand, “Subwavelength surface-relief gratings for stellar coronagraphy,” Appl. Opt. 44, 7313–7321 (2005).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  26. S. R. Nersisyan, N. V. Nelson, V. Tabiryan, D. M. Steeves, and B. R. Kimball, “The promise of diffractive waveplates,” Opt. Photon. News 21, 40–45 (2010).
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2013

P. Blain, P. Piron, Y. Renotte, and S. Habraken, “An in-line shearography set-up based on circular polarization gratings,” Opt. Lasers Eng. 51, 1053–1059 (2013).
[CrossRef]

S. R. Nersisyan, N. V. Tabiryan, D. Mawet, and E. Serabyn, “Improving vector vortex waveplates for high-contrast coronagraphy,” Opt. Express 21, 8205–8213 (2013).
[CrossRef]

2012

2011

P. Piron, P. Blain, and S. Habraken, “Polarization measurement with space-variant retarders in liquid crystal polymers,” Proc. SPIE 8160, 81600Q (2011).

2010

D. Mawet, E. Serabyn, K. Liewer, R. Buruss, J. Hickey, and D. Shemo, “The vector vortex coronagraph: laboratory results, and first light at palomar observatory,” Astrophys. J. 709, 53–57 (2010).
[CrossRef]

S. R. Nersisyan, N. V. Nelson, V. Tabiryan, D. M. Steeves, and B. R. Kimball, “The promise of diffractive waveplates,” Opt. Photon. News 21, 40–45 (2010).
[CrossRef]

S.-W. Ko, C.-L. Ting, A. Y.-G. Fuh, and T.-H. Lin, “Polarization converters based on axially symmetric twisted nematic liquid crystal,” Opt. Express 18, 3601–3607 (2010).
[CrossRef]

2009

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57 (2009).
[CrossRef]

D. Mawet, E. Serabyn, K. Liewer, C. Hanot, S. McEldowney, D. Shemo, and N. O’Brien, “Optical vectorial vortex coronagraphs using liquid crystal polymers: theory, manufacturing and laboratory demonstration,” Opt. Express 17, 1902–1918 (2009).
[CrossRef]

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. 18, 1–47 (2009).
[CrossRef]

W. Chen, R. L. Nelson, D. C. Abesysinghe, and Q. Zhan, “Optimal plasmon focusing with spatial polarization engineering,” Opt. Photon. News 20, 36–41 (2009).
[CrossRef]

2008

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Spatially-variable retardation plate for efficient generation of radially- and azimuthally-polarized beams,” Opt. Commun. 281, 732–738 (2008).
[CrossRef]

G. M. Lerman and U. Levy, “Effect of radial polarization and apodization on spot size under tight focusing conditions,” Opt. Express 16, 4567–4581 (2008).
[CrossRef]

2007

2006

A. Niv, G. Biener, V. Kleiner, and E. Hasman, “Manipulation of the Pancharatnam phase in vectorial vortices,” Opt. Express 14, 4208–4220 (2006).
[CrossRef]

H. Ren, T.-H. Lin, and S.-T. Wu, “Linear to axial or radial polarization conversion using a liquid crystal gel,” Appl. Phys. Lett. 89, 051114 (2006).

2005

D. Mawet, P. Riaud, O. Absil, and J. Surdej, “Annular groove phase mask coronagraph,” Astrophys. J. 633, 1191–1200 (2005).
[CrossRef]

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

D. Mawet, P. Riaud, J. Surdej, and J. Baudrand, “Subwavelength surface-relief gratings for stellar coronagraphy,” Appl. Opt. 44, 7313–7321 (2005).
[CrossRef]

2004

2003

2002

E. J. Galvez, “Applications of geometric phase in optics,” Recent Research Developments in Optics 2, 165–182 (2002).

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]

2000

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The four-quadrant phase-mask coronagraph. I. Principle,” Publ. Astron. Soc. Pac. 112, 1479–1486 (2000).
[CrossRef]

1996

1987

M. Berry, “The adiabatic phase and Pancharatnam phase for polarized light,” J. Mod. Opt. 34, 1401–1407 (1987).
[CrossRef]

Abesysinghe, D. C.

W. Chen, R. L. Nelson, D. C. Abesysinghe, and Q. Zhan, “Optimal plasmon focusing with spatial polarization engineering,” Opt. Photon. News 20, 36–41 (2009).
[CrossRef]

Absil, O.

D. Mawet, P. Riaud, O. Absil, and J. Surdej, “Annular groove phase mask coronagraph,” Astrophys. J. 633, 1191–1200 (2005).
[CrossRef]

Baudrand, J.

Berry, M.

M. Berry, “The adiabatic phase and Pancharatnam phase for polarized light,” J. Mod. Opt. 34, 1401–1407 (1987).
[CrossRef]

Biener, G.

Blain, P.

P. Blain, P. Piron, Y. Renotte, and S. Habraken, “An in-line shearography set-up based on circular polarization gratings,” Opt. Lasers Eng. 51, 1053–1059 (2013).
[CrossRef]

P. Piron, P. Blain, and S. Habraken, “Polarization measurement with space-variant retarders in liquid crystal polymers,” Proc. SPIE 8160, 81600Q (2011).

Boccaletti, A.

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The four-quadrant phase-mask coronagraph. I. Principle,” Publ. Astron. Soc. Pac. 112, 1479–1486 (2000).
[CrossRef]

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]

Buruss, R.

D. Mawet, E. Serabyn, K. Liewer, R. Buruss, J. Hickey, and D. Shemo, “The vector vortex coronagraph: laboratory results, and first light at palomar observatory,” Astrophys. J. 709, 53–57 (2010).
[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 technique,” J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

Chen, W.

W. Chen, R. L. Nelson, D. C. Abesysinghe, and Q. Zhan, “Optimal plasmon focusing with spatial polarization engineering,” Opt. Photon. News 20, 36–41 (2009).
[CrossRef]

Cipparone, G.

Clénet, Y.

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The four-quadrant phase-mask coronagraph. I. Principle,” Publ. Astron. Soc. Pac. 112, 1479–1486 (2000).
[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 technique,” J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[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 technique,” J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

Françon, M.

M. Françon and S. Mallick, Polarization Interferometers: Applications in Microscopy and Macroscopy (Wiley-Intersciences, 1971).

Fuh, A. Y.-G.

Galvez, E. J.

E. J. Galvez, “Applications of geometric phase in optics,” Recent Research Developments in Optics 2, 165–182 (2002).

Habraken, S.

P. Blain, P. Piron, Y. Renotte, and S. Habraken, “An in-line shearography set-up based on circular polarization gratings,” Opt. Lasers Eng. 51, 1053–1059 (2013).
[CrossRef]

P. Piron, P. Blain, and S. Habraken, “Polarization measurement with space-variant retarders in liquid crystal polymers,” Proc. SPIE 8160, 81600Q (2011).

Hanot, C.

Hasman, E.

Hickey, J.

D. Mawet, E. Serabyn, K. Liewer, R. Buruss, J. Hickey, and D. Shemo, “The vector vortex coronagraph: laboratory results, and first light at palomar observatory,” Astrophys. J. 709, 53–57 (2010).
[CrossRef]

Jackel, S.

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Spatially-variable retardation plate for efficient generation of radially- and azimuthally-polarized beams,” Opt. Commun. 281, 732–738 (2008).
[CrossRef]

Kakauridze, G.

Kilosanidze, B.

Kimball, B. R.

S. R. Nersisyan, N. V. Nelson, V. Tabiryan, D. M. Steeves, and B. R. Kimball, “The promise of diffractive waveplates,” Opt. Photon. News 21, 40–45 (2010).
[CrossRef]

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. 18, 1–47 (2009).
[CrossRef]

Kleiner, V.

Ko, S.-W.

Labeyrie, A.

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The four-quadrant phase-mask coronagraph. I. Principle,” Publ. Astron. Soc. Pac. 112, 1479–1486 (2000).
[CrossRef]

Lerman, G. M.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef]

Levy, U.

Liewer, K.

D. Mawet, E. Serabyn, K. Liewer, R. Buruss, J. Hickey, and D. Shemo, “The vector vortex coronagraph: laboratory results, and first light at palomar observatory,” Astrophys. J. 709, 53–57 (2010).
[CrossRef]

D. Mawet, E. Serabyn, K. Liewer, C. Hanot, S. McEldowney, D. Shemo, and N. O’Brien, “Optical vectorial vortex coronagraphs using liquid crystal polymers: theory, manufacturing and laboratory demonstration,” Opt. Express 17, 1902–1918 (2009).
[CrossRef]

Lin, T.-H.

S.-W. Ko, C.-L. Ting, A. Y.-G. Fuh, and T.-H. Lin, “Polarization converters based on axially symmetric twisted nematic liquid crystal,” Opt. Express 18, 3601–3607 (2010).
[CrossRef]

H. Ren, T.-H. Lin, and S.-T. Wu, “Linear to axial or radial polarization conversion using a liquid crystal gel,” Appl. Phys. Lett. 89, 051114 (2006).

Lumer, Y.

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Spatially-variable retardation plate for efficient generation of radially- and azimuthally-polarized beams,” Opt. Commun. 281, 732–738 (2008).
[CrossRef]

Machavariani, G.

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Spatially-variable retardation plate for efficient generation of radially- and azimuthally-polarized beams,” Opt. Commun. 281, 732–738 (2008).
[CrossRef]

Mallick, S.

M. Françon and S. Mallick, Polarization Interferometers: Applications in Microscopy and Macroscopy (Wiley-Intersciences, 1971).

Mawet, D.

McEldowney, S.

Meir, A.

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Spatially-variable retardation plate for efficient generation of radially- and azimuthally-polarized beams,” Opt. Commun. 281, 732–738 (2008).
[CrossRef]

Moshe, I.

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Spatially-variable retardation plate for efficient generation of radially- and azimuthally-polarized beams,” Opt. Commun. 281, 732–738 (2008).
[CrossRef]

Nelson, N. V.

S. R. Nersisyan, N. V. Nelson, V. Tabiryan, D. M. Steeves, and B. R. Kimball, “The promise of diffractive waveplates,” Opt. Photon. News 21, 40–45 (2010).
[CrossRef]

Nelson, R. L.

W. Chen, R. L. Nelson, D. C. Abesysinghe, and Q. Zhan, “Optimal plasmon focusing with spatial polarization engineering,” Opt. Photon. News 20, 36–41 (2009).
[CrossRef]

Nersisyan, S. R.

S. R. Nersisyan, N. V. Tabiryan, D. Mawet, and E. Serabyn, “Improving vector vortex waveplates for high-contrast coronagraphy,” Opt. Express 21, 8205–8213 (2013).
[CrossRef]

S. R. Nersisyan, N. V. Nelson, V. Tabiryan, D. M. Steeves, and B. R. Kimball, “The promise of diffractive waveplates,” Opt. Photon. News 21, 40–45 (2010).
[CrossRef]

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. 18, 1–47 (2009).
[CrossRef]

Niv, A.

O’Brien, N.

Pagliusi, P.

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 technique,” J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

Piron, P.

P. Blain, P. Piron, Y. Renotte, and S. Habraken, “An in-line shearography set-up based on circular polarization gratings,” Opt. Lasers Eng. 51, 1053–1059 (2013).
[CrossRef]

P. Piron, P. Blain, and S. Habraken, “Polarization measurement with space-variant retarders in liquid crystal polymers,” Proc. SPIE 8160, 81600Q (2011).

Provenzano, C.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[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 technique,” J. Appl. Phys. 98, 123102 (2005).
[CrossRef]

Ren, H.

H. Ren, T.-H. Lin, and S.-T. Wu, “Linear to axial or radial polarization conversion using a liquid crystal gel,” Appl. Phys. Lett. 89, 051114 (2006).

Renotte, Y.

P. Blain, P. Piron, Y. Renotte, and S. Habraken, “An in-line shearography set-up based on circular polarization gratings,” Opt. Lasers Eng. 51, 1053–1059 (2013).
[CrossRef]

Riaud, P.

D. Mawet, P. Riaud, J. Surdej, and J. Baudrand, “Subwavelength surface-relief gratings for stellar coronagraphy,” Appl. Opt. 44, 7313–7321 (2005).
[CrossRef]

D. Mawet, P. Riaud, O. Absil, and J. Surdej, “Annular groove phase mask coronagraph,” Astrophys. J. 633, 1191–1200 (2005).
[CrossRef]

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The four-quadrant phase-mask coronagraph. I. Principle,” Publ. Astron. Soc. Pac. 112, 1479–1486 (2000).
[CrossRef]

Rouan, D.

D. Rouan, P. Riaud, A. Boccaletti, Y. Clénet, and A. Labeyrie, “The four-quadrant phase-mask coronagraph. I. Principle,” Publ. Astron. Soc. Pac. 112, 1479–1486 (2000).
[CrossRef]

Ruiz, U.

Schadt, M.

Serabyn, E.

Shemo, D.

D. Mawet, E. Serabyn, K. Liewer, R. Buruss, J. Hickey, and D. Shemo, “The vector vortex coronagraph: laboratory results, and first light at palomar observatory,” Astrophys. J. 709, 53–57 (2010).
[CrossRef]

D. Mawet, E. Serabyn, K. Liewer, C. Hanot, S. McEldowney, D. Shemo, and N. O’Brien, “Optical vectorial vortex coronagraphs using liquid crystal polymers: theory, manufacturing and laboratory demonstration,” Opt. Express 17, 1902–1918 (2009).
[CrossRef]

Stalder, M.

Steeves, D. M.

S. R. Nersisyan, N. V. Nelson, V. Tabiryan, D. M. Steeves, and B. R. Kimball, “The promise of diffractive waveplates,” Opt. Photon. News 21, 40–45 (2010).
[CrossRef]

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. 18, 1–47 (2009).
[CrossRef]

Surdej, J.

D. Mawet, P. Riaud, J. Surdej, and J. Baudrand, “Subwavelength surface-relief gratings for stellar coronagraphy,” Appl. Opt. 44, 7313–7321 (2005).
[CrossRef]

D. Mawet, P. Riaud, O. Absil, and J. Surdej, “Annular groove phase mask coronagraph,” Astrophys. J. 633, 1191–1200 (2005).
[CrossRef]

Tabiryan, N. V.

S. R. Nersisyan, N. V. Tabiryan, D. Mawet, and E. Serabyn, “Improving vector vortex waveplates for high-contrast coronagraphy,” Opt. Express 21, 8205–8213 (2013).
[CrossRef]

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. 18, 1–47 (2009).
[CrossRef]

Tabiryan, V.

S. R. Nersisyan, N. V. Nelson, V. Tabiryan, D. M. Steeves, and B. R. Kimball, “The promise of diffractive waveplates,” Opt. Photon. News 21, 40–45 (2010).
[CrossRef]

Ting, C.-L.

Wu, S.-T.

H. Ren, T.-H. Lin, and S.-T. Wu, “Linear to axial or radial polarization conversion using a liquid crystal gel,” Appl. Phys. Lett. 89, 051114 (2006).

Zhan, Q.

Adv. Opt. Photon.

Appl. Opt.

Appl. Phys. Lett.

H. Ren, T.-H. Lin, and S.-T. Wu, “Linear to axial or radial polarization conversion using a liquid crystal gel,” Appl. Phys. Lett. 89, 051114 (2006).

Astrophys. J.

D. Mawet, P. Riaud, O. Absil, and J. Surdej, “Annular groove phase mask coronagraph,” Astrophys. J. 633, 1191–1200 (2005).
[CrossRef]

D. Mawet, E. Serabyn, K. Liewer, R. Buruss, J. Hickey, and D. Shemo, “The vector vortex coronagraph: laboratory results, and first light at palomar observatory,” Astrophys. J. 709, 53–57 (2010).
[CrossRef]

J. Appl. Phys.

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

J. Mod. Opt.

M. Berry, “The adiabatic phase and Pancharatnam phase for polarized light,” J. Mod. Opt. 34, 1401–1407 (1987).
[CrossRef]

J. Nonlinear Opt. Phys.

S. R. Nersisyan, N. V. Tabiryan, D. M. Steeves, and B. R. Kimball, “Optical axis gratings in liquid crystals and their use for polarization insensitive optical switching,” J. Nonlinear Opt. Phys. 18, 1–47 (2009).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

G. Machavariani, Y. Lumer, I. Moshe, A. Meir, and S. Jackel, “Spatially-variable retardation plate for efficient generation of radially- and azimuthally-polarized beams,” Opt. Commun. 281, 732–738 (2008).
[CrossRef]

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Figures (19)

Fig. 1.
Fig. 1.

Schematic representation of the fast axis (in dashed blue) for a SR, x being the direction of variation of the fast axis in the SR and α the orientation of the fast axis.

Fig. 2.
Fig. 2.

Schematic representation of the fast axis (in dashed blue). (a) A VR with l=1 and (b) a VR with l=2, α being the orientation of the fast axis and (r, θ) the polar coordinates. The orange arrows represent the ideal electric field required to record the retarders with LCP.

Fig. 3.
Fig. 3.

Schematic representation of the local polarization ellipse. The largest (L) and the smallest (s) axis are pictured in dashed blue.

Fig. 4.
Fig. 4.

Orientation of the electric field for the superimposition of two circularly polarized beams of opposite handedness, δ being the phase retard between the two beams.

Fig. 5.
Fig. 5.

Schematic representation of the polarization overlap, the four beams possess the same incident angle on the surface.

Fig. 6.
Fig. 6.

Transmitted intensities of the half-wave plates obtained by polarization holography with several vortex centers. The smallest distance between two vortex centers will be defined as the period p, with p being a function of the incident angle and the recording wavelength, θi and λr, respectively, with λr=325nm. Our simulations were made with θi=5arcsec; therefore p=20,626λr. The value of θi was chosen due to experimental results.

Fig. 7.
Fig. 7.

Transmitted intensities of the half-wave plates obtained by polarization holography between two parallel polarizers for a size of p.

Fig. 8.
Fig. 8.

Transmitted intensities of VR of l=2 obtained by polarization holography between two parallel polarizers for a size of p. B and C are obtained by the recording a collimated beam transmitted by the intermediate plates.

Fig. 9.
Fig. 9.

Maps of Idir for the three systems.

Fig. 10.
Fig. 10.

Maps of dp for the three systems.

Fig. 11.
Fig. 11.

Maps of transmitted intensities of half-wave plates obtained with C between two parallel polarizers with an area of disorientation of the LC. The intensity in the area of disorientation is pictured by the transmitted intensity of an unpolarized beam after a linear polarizer. Thus, the area of disorientation pictured by a gray disk depend on the criterion. (a) Idir<Idir30°, (b) Idir<Idir42.5°, and (c) Idir<Idir44.9°.

Fig. 12.
Fig. 12.

Evolution of Idir along the central line. The dashed lines represent several limit values selected in our analysis: Idir30°, Idir42.5°, and Idir44.9°.

Fig. 13.
Fig. 13.

Evolution of dp along the central line. The dashed lines represent several limit values selected in our analysis: dp30°, dp42.5°, and dp44.9°, with B and C being superimposed.

Fig. 14.
Fig. 14.

Scheme of the exposing process, polarization in red and beam in blue.

Fig. 15.
Fig. 15.

Scheme of the measuring process, polarization in red and beam in blue.

Fig. 16.
Fig. 16.

(a) Transmitted intensity between two cross polarizers for a uniform retarder recorded with an ellipticaly polarized beam with an angle of 45°±2° between the axes of l1 and p1. (b) Transmitted intensity for a commercial birefringent plate in the setup. The variations of intensity in (a) are mainly due to dust on the LC layer and on small polarization aberrations due to the expanding process. The two pictures were taken with the same camera and the same exposure time and gain.

Fig. 17.
Fig. 17.

Transmitted intensities between two parallel polarizers with the largest area of disorientation for each systems with the actual experimental limit (α=43°).

Fig. 18.
Fig. 18.

Scheme of the recording process, polarization in red and beam in blue. The two recording beams possess the same intensity to record a series of linear polarization.

Fig. 19.
Fig. 19.

(a) Picture of a 1D SR between two crossed polarizers with a white source. Defects are due to dust and small oxidation spots. The retarder was recorded using the superimposition of two circularly polarized beams of opposite handedness. (b) Transmitted intensity of a uniformly linearly polarized beam after the retarder and a linear polarizer.

Tables (4)

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Table 1. Table of Idir and dp for Several Values of α

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Table 2. Table of Radii for the Resulting Intensities (in λr Units) for a Size of a Sample of 20,626λr

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Table 3. Table of Radii for the Ratio of Intensities (in λr Units) for a Size of a Sample of 20,626λr

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Table 4. Table of Radii for a Recording Polarization Obtained with an Angle of 43° between the Axis of p1 and the Axis of l1 (in λrecording Units) for a Size of a Sample of 20,626λr

Equations (16)

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l=12πϕpds.
Λλ1nIsinχ+max(nI,nIII),
A=(AxAyexp(iϕA))exp(iωt),B=(BxByexp(iϕB))exp(iδ)exp(iωt),
Σ=(Ax+Bxexp(iδ)Ayexp(iϕA)+Byexp(iϕB+iδ))exp(iωt).
R(Σ)=pcos(ωt)+qsin(ωt),
p=(Ax+Bxcos(δ)Aycos(ϕA)+Bycos(ϕB+δ))
q=(Bxsin(δ)Aysin(ϕA)+Bysin(ϕB+δ)).
I1,2=12[(px2+py2)+(qx2+qy2)]±12[(px2py2)+(qx2qy2)]2+4(pxpy+qxqy)2,sin(2θ)=2(pxpy+qxqy)[(px2py2)+(qx2qy2)]2+4(pxpy+qxqy)2,cos(2θ)=(px2py2)+(qx2qy2)[(px2py2)+(qx2qy2)]2+4(pxpy+qxqy)2.
Ax=Ay=Bx=By=2/2,ϕA=π/2,ϕB=π/2.
p=(2)/2(1+cos(δ)sin(δ)),q=(2)/2(1+sin(δ)1+cos(δ)).
I1=2,I2=0,sin(2θ)=sin(δ),cos(2θ)=cos(δ).
A=(AxAyexp(iα))exp(iδA),B=(BxByexp(iβ))exp(iδB),C=(CxCyexp(iγ))exp(iδC),D=(DxDyexp(iδ))exp(iδD)
p=(Axcos(δA)+Bxcos(δB)+Cxcos(δC)+Dxcos(δD)Aycos(α+δA)+Bycos(β+δB)+Cycos(γ+δC)+Dycos(δ+δD)),q=(Axsin(δA)+Bxsin(δB)+Cxsin(δC)+Dxsin(δD)Aysin(α+δA)+Bysin(β+δB)+Cysin(γ+δC)+Dysin(δ+δD)).
A=(01),B=(10),C=(01),D=(10).
A=(01),B=22(1i),C=(10),D=22(1i).
A=(10),B=22(11),C=(0i),D=22(11).

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