Abstract

We demonstrate a complete semiphysical and analytical model describing the angular and wavelength dependencies not only of retardance, but also its flicker, in parallel aligned liquid crystal (PA-LC) devices. It relies on the fitting of the molecules’ equivalent tilt angle as a function of applied voltage. The wide range of calculations it offers without requiring extensive characterization makes the model unique. We focus on PA-LCoS application as a polarization state generator across the visible spectrum and for a wide range of incidence angles. This approach offers novel capabilities for managing arbitrary states of both full and partial polarization. To highlight the richness of situations with PA-LCoS devices, we provide results for two different digital addressing sequences producing different levels of flicker.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (2)

A. Márquez, J. Francés, F. J. Martínez, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “Computational split-field finite-difference time-domain evaluation of simplified tilt-angle models for parallel-aligned liquid-crystal devices,” Opt. Eng. 57(03), 1 (2018).
[Crossref]

J. Francés, A. Márquez, F. J. Martínez-Guardiola, S. Bleda, S. Gallego, C. Neipp, I. Pascual, and A. Beléndez, “Simplified physical modeling of parallel-aligned liquid crystal devices at highly non-linear tilt angle profiles,” Opt. Express 26(10), 12723–12741 (2018).
[Crossref] [PubMed]

2017 (2)

I. Moreno, J. A. Davis, K. Badham, M. M. Sánchez-López, J. E. Holland, and D. M. Cottrell, “Vector Beam Polarization State Spectrum Analyzer,” Sci. Rep. 7(1), 2216 (2017).
[Crossref] [PubMed]

A. Cofré, A. Vargas, F. A. Torres-Ruiz, J. Campos, A. Lizana, M. M. Sánchez-López, and I. Moreno, “Dual polarization split lenses,” Opt. Express 25(20), 23773–23783 (2017).
[Crossref] [PubMed]

2015 (3)

X. Zheng, A. Lizana, A. Peinado, C. Ramirez, J. L. Martinez, A. Marquez, I. Moreno, and J. Campos, “Compact LCOS–SLM Based Polarization Pattern Beam Generator,” J. Lit. Technol. 33(10), 2047–2055 (2015).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Effective angular and wavelength modeling of parallel aligned liquid crystal devices,” Opt. Lasers Eng. 74, 114–121 (2015).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, I. Pascual, and A. Beléndez, “Predictive capability of average Stokes polarimetry for simulation of phase multilevel elements onto LCoS devices,” Appl. Opt. 54(6), 1379–1386 (2015).
[Crossref] [PubMed]

2014 (6)

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Averaged Stokes polarimetry applied to evaluate retardance and flicker in PA-LCoS devices,” Opt. Express 22(12), 15064–15074 (2014).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, and I. Pascual, “Extended linear polarimeter to measure retardance and flicker: application to liquid crystal on silicon devices in two working geometries,” Opt. Eng. 53(1), 014105 (2014).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Electrical dependencies of optical modulation capabilities in digitally addressed parallel aligned liquid crystal on silicon devices,” Opt. Eng. 53(6), 067104 (2014).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Retardance and flicker modeling and characterization of electro-optic linear retarders by averaged Stokes polarimetry,” Opt. Lett. 39(4), 1011–1014 (2014).
[Crossref] [PubMed]

Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light Sci. Appl. 3(10), 213 (2014).
[Crossref]

A. Dudley, G. Milione, R. R. Alfano, and A. Forbes, “All-digital wavefront sensing for structured light beams,” Opt. Express 22(11), 14031–14040 (2014).
[Crossref] [PubMed]

2013 (2)

2012 (2)

J. García-Márquez, V. López, A. González-Vega, and E. Noé, “Flicker minimization in an LCoS spatial light modulator,” Opt. Express 20(8), 8431–8441 (2012).
[Crossref] [PubMed]

A. Boutin, C. Koebele, D. Sperti, F. Verluise, G. Charlet, H. Mardoyan, L. Provost, M. Bigot-Astruc, M. Salsi, P. Tran, P. Brindel, P. Sillard, and S. Bigo, “Mode-Division Multiplexing of 2 × 100 Gb/s Channels Using an LCOS-Based Spatial Modulator,” J. Lit. Technol. 30, 618–623 (2012).

2011 (2)

A. Farré, M. Shayegan, C. López-Quesada, G. A. Blab, M. Montes-Usategui, N. R. Forde, and E. Martín-Badosa, “Positional stability of holographic optical traps,” Opt. Express 19(22), 21370–21384 (2011).
[Crossref] [PubMed]

N. Collings, T. Davey, J. Christmas, D. Chu, and B. Crossland, “The Applications and Technology of Phase-Only Liquid Crystal on Silicon Devices,” J. Disp. Technol. 7(3), 112–119 (2011).
[Crossref]

2010 (2)

2008 (2)

M. A. F. Roelens, S. Frisken, J. A. Bolger, D. Abakoumov, G. Baxter, S. Poole, and B. J. Eggleton, “Dispersion Trimming in a Reconfigurable Wavelength Selective Switch,” J. Lit. Technol. 26(1), 73–78 (2008).
[Crossref]

I A. Lizana, I. Moreno, A. Márquez, C. Iemmi, E. Fernández, J. Campos, and M. J. Yzuel, “Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics,” Opt. Express 16(21), 16711–16722 (2008).
[Crossref] [PubMed]

2006 (1)

2005 (1)

W. Osten, C. Kohler, and J. Liesener, “Evaluation and application of spatial light modulators for optical metrology,” Opt. Pura Apl. 38, 71–81 (2005).

1993 (1)

1990 (1)

A. Lien, “Extended Jones matrix representation for the twisted nematic liquid‐crystal display at oblique incidence,” Appl. Phys. Lett. 57(26), 2767–2769 (1990).
[Crossref]

1982 (1)

1972 (1)

Abakoumov, D.

M. A. F. Roelens, S. Frisken, J. A. Bolger, D. Abakoumov, G. Baxter, S. Poole, and B. J. Eggleton, “Dispersion Trimming in a Reconfigurable Wavelength Selective Switch,” J. Lit. Technol. 26(1), 73–78 (2008).
[Crossref]

Alfano, R. R.

Álvarez, M. L.

A. Márquez, J. Francés, F. J. Martínez, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “Computational split-field finite-difference time-domain evaluation of simplified tilt-angle models for parallel-aligned liquid-crystal devices,” Opt. Eng. 57(03), 1 (2018).
[Crossref]

Arias, A.

Badham, K.

I. Moreno, J. A. Davis, K. Badham, M. M. Sánchez-López, J. E. Holland, and D. M. Cottrell, “Vector Beam Polarization State Spectrum Analyzer,” Sci. Rep. 7(1), 2216 (2017).
[Crossref] [PubMed]

Baxter, G.

M. A. F. Roelens, S. Frisken, J. A. Bolger, D. Abakoumov, G. Baxter, S. Poole, and B. J. Eggleton, “Dispersion Trimming in a Reconfigurable Wavelength Selective Switch,” J. Lit. Technol. 26(1), 73–78 (2008).
[Crossref]

Beléndez, A.

J. Francés, A. Márquez, F. J. Martínez-Guardiola, S. Bleda, S. Gallego, C. Neipp, I. Pascual, and A. Beléndez, “Simplified physical modeling of parallel-aligned liquid crystal devices at highly non-linear tilt angle profiles,” Opt. Express 26(10), 12723–12741 (2018).
[Crossref] [PubMed]

A. Márquez, J. Francés, F. J. Martínez, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “Computational split-field finite-difference time-domain evaluation of simplified tilt-angle models for parallel-aligned liquid-crystal devices,” Opt. Eng. 57(03), 1 (2018).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Effective angular and wavelength modeling of parallel aligned liquid crystal devices,” Opt. Lasers Eng. 74, 114–121 (2015).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, I. Pascual, and A. Beléndez, “Predictive capability of average Stokes polarimetry for simulation of phase multilevel elements onto LCoS devices,” Appl. Opt. 54(6), 1379–1386 (2015).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Averaged Stokes polarimetry applied to evaluate retardance and flicker in PA-LCoS devices,” Opt. Express 22(12), 15064–15074 (2014).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Electrical dependencies of optical modulation capabilities in digitally addressed parallel aligned liquid crystal on silicon devices,” Opt. Eng. 53(6), 067104 (2014).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Retardance and flicker modeling and characterization of electro-optic linear retarders by averaged Stokes polarimetry,” Opt. Lett. 39(4), 1011–1014 (2014).
[Crossref] [PubMed]

Berreman, D. W.

Bigo, S.

A. Boutin, C. Koebele, D. Sperti, F. Verluise, G. Charlet, H. Mardoyan, L. Provost, M. Bigot-Astruc, M. Salsi, P. Tran, P. Brindel, P. Sillard, and S. Bigo, “Mode-Division Multiplexing of 2 × 100 Gb/s Channels Using an LCOS-Based Spatial Modulator,” J. Lit. Technol. 30, 618–623 (2012).

Bigot-Astruc, M.

A. Boutin, C. Koebele, D. Sperti, F. Verluise, G. Charlet, H. Mardoyan, L. Provost, M. Bigot-Astruc, M. Salsi, P. Tran, P. Brindel, P. Sillard, and S. Bigo, “Mode-Division Multiplexing of 2 × 100 Gb/s Channels Using an LCOS-Based Spatial Modulator,” J. Lit. Technol. 30, 618–623 (2012).

Blab, G. A.

Bleda, S.

Bolger, J. A.

M. A. F. Roelens, S. Frisken, J. A. Bolger, D. Abakoumov, G. Baxter, S. Poole, and B. J. Eggleton, “Dispersion Trimming in a Reconfigurable Wavelength Selective Switch,” J. Lit. Technol. 26(1), 73–78 (2008).
[Crossref]

Boutin, A.

A. Boutin, C. Koebele, D. Sperti, F. Verluise, G. Charlet, H. Mardoyan, L. Provost, M. Bigot-Astruc, M. Salsi, P. Tran, P. Brindel, P. Sillard, and S. Bigo, “Mode-Division Multiplexing of 2 × 100 Gb/s Channels Using an LCOS-Based Spatial Modulator,” J. Lit. Technol. 30, 618–623 (2012).

Brindel, P.

A. Boutin, C. Koebele, D. Sperti, F. Verluise, G. Charlet, H. Mardoyan, L. Provost, M. Bigot-Astruc, M. Salsi, P. Tran, P. Brindel, P. Sillard, and S. Bigo, “Mode-Division Multiplexing of 2 × 100 Gb/s Channels Using an LCOS-Based Spatial Modulator,” J. Lit. Technol. 30, 618–623 (2012).

Brown, T.

Calzado, E. M.

A. Márquez, J. Francés, F. J. Martínez, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “Computational split-field finite-difference time-domain evaluation of simplified tilt-angle models for parallel-aligned liquid-crystal devices,” Opt. Eng. 57(03), 1 (2018).
[Crossref]

Campos, J.

Charlet, G.

A. Boutin, C. Koebele, D. Sperti, F. Verluise, G. Charlet, H. Mardoyan, L. Provost, M. Bigot-Astruc, M. Salsi, P. Tran, P. Brindel, P. Sillard, and S. Bigo, “Mode-Division Multiplexing of 2 × 100 Gb/s Channels Using an LCOS-Based Spatial Modulator,” J. Lit. Technol. 30, 618–623 (2012).

Chipman, R. A.

Christmas, J.

N. Collings, T. Davey, J. Christmas, D. Chu, and B. Crossland, “The Applications and Technology of Phase-Only Liquid Crystal on Silicon Devices,” J. Disp. Technol. 7(3), 112–119 (2011).
[Crossref]

Chu, D.

Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light Sci. Appl. 3(10), 213 (2014).
[Crossref]

N. Collings, T. Davey, J. Christmas, D. Chu, and B. Crossland, “The Applications and Technology of Phase-Only Liquid Crystal on Silicon Devices,” J. Disp. Technol. 7(3), 112–119 (2011).
[Crossref]

Cofré, A.

Collings, N.

N. Collings, T. Davey, J. Christmas, D. Chu, and B. Crossland, “The Applications and Technology of Phase-Only Liquid Crystal on Silicon Devices,” J. Disp. Technol. 7(3), 112–119 (2011).
[Crossref]

Cottrell, D. M.

I. Moreno, J. A. Davis, K. Badham, M. M. Sánchez-López, J. E. Holland, and D. M. Cottrell, “Vector Beam Polarization State Spectrum Analyzer,” Sci. Rep. 7(1), 2216 (2017).
[Crossref] [PubMed]

Crossland, B.

N. Collings, T. Davey, J. Christmas, D. Chu, and B. Crossland, “The Applications and Technology of Phase-Only Liquid Crystal on Silicon Devices,” J. Disp. Technol. 7(3), 112–119 (2011).
[Crossref]

Davey, T.

N. Collings, T. Davey, J. Christmas, D. Chu, and B. Crossland, “The Applications and Technology of Phase-Only Liquid Crystal on Silicon Devices,” J. Disp. Technol. 7(3), 112–119 (2011).
[Crossref]

Davis, J. A.

I. Moreno, J. A. Davis, K. Badham, M. M. Sánchez-López, J. E. Holland, and D. M. Cottrell, “Vector Beam Polarization State Spectrum Analyzer,” Sci. Rep. 7(1), 2216 (2017).
[Crossref] [PubMed]

Dudley, A.

Eggleton, B. J.

M. A. F. Roelens, S. Frisken, J. A. Bolger, D. Abakoumov, G. Baxter, S. Poole, and B. J. Eggleton, “Dispersion Trimming in a Reconfigurable Wavelength Selective Switch,” J. Lit. Technol. 26(1), 73–78 (2008).
[Crossref]

Farré, A.

Fernández, E.

Forbes, A.

Forde, N. R.

Francés, J.

J. Francés, A. Márquez, F. J. Martínez-Guardiola, S. Bleda, S. Gallego, C. Neipp, I. Pascual, and A. Beléndez, “Simplified physical modeling of parallel-aligned liquid crystal devices at highly non-linear tilt angle profiles,” Opt. Express 26(10), 12723–12741 (2018).
[Crossref] [PubMed]

A. Márquez, J. Francés, F. J. Martínez, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “Computational split-field finite-difference time-domain evaluation of simplified tilt-angle models for parallel-aligned liquid-crystal devices,” Opt. Eng. 57(03), 1 (2018).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Effective angular and wavelength modeling of parallel aligned liquid crystal devices,” Opt. Lasers Eng. 74, 114–121 (2015).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, I. Pascual, and A. Beléndez, “Predictive capability of average Stokes polarimetry for simulation of phase multilevel elements onto LCoS devices,” Appl. Opt. 54(6), 1379–1386 (2015).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Retardance and flicker modeling and characterization of electro-optic linear retarders by averaged Stokes polarimetry,” Opt. Lett. 39(4), 1011–1014 (2014).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Electrical dependencies of optical modulation capabilities in digitally addressed parallel aligned liquid crystal on silicon devices,” Opt. Eng. 53(6), 067104 (2014).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, and I. Pascual, “Extended linear polarimeter to measure retardance and flicker: application to liquid crystal on silicon devices in two working geometries,” Opt. Eng. 53(1), 014105 (2014).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Averaged Stokes polarimetry applied to evaluate retardance and flicker in PA-LCoS devices,” Opt. Express 22(12), 15064–15074 (2014).
[Crossref] [PubMed]

Frisken, S.

M. A. F. Roelens, S. Frisken, J. A. Bolger, D. Abakoumov, G. Baxter, S. Poole, and B. J. Eggleton, “Dispersion Trimming in a Reconfigurable Wavelength Selective Switch,” J. Lit. Technol. 26(1), 73–78 (2008).
[Crossref]

Gallego, S.

A. Márquez, J. Francés, F. J. Martínez, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “Computational split-field finite-difference time-domain evaluation of simplified tilt-angle models for parallel-aligned liquid-crystal devices,” Opt. Eng. 57(03), 1 (2018).
[Crossref]

J. Francés, A. Márquez, F. J. Martínez-Guardiola, S. Bleda, S. Gallego, C. Neipp, I. Pascual, and A. Beléndez, “Simplified physical modeling of parallel-aligned liquid crystal devices at highly non-linear tilt angle profiles,” Opt. Express 26(10), 12723–12741 (2018).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Effective angular and wavelength modeling of parallel aligned liquid crystal devices,” Opt. Lasers Eng. 74, 114–121 (2015).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, I. Pascual, and A. Beléndez, “Predictive capability of average Stokes polarimetry for simulation of phase multilevel elements onto LCoS devices,” Appl. Opt. 54(6), 1379–1386 (2015).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Electrical dependencies of optical modulation capabilities in digitally addressed parallel aligned liquid crystal on silicon devices,” Opt. Eng. 53(6), 067104 (2014).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Retardance and flicker modeling and characterization of electro-optic linear retarders by averaged Stokes polarimetry,” Opt. Lett. 39(4), 1011–1014 (2014).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Averaged Stokes polarimetry applied to evaluate retardance and flicker in PA-LCoS devices,” Opt. Express 22(12), 15064–15074 (2014).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, and I. Pascual, “Extended linear polarimeter to measure retardance and flicker: application to liquid crystal on silicon devices in two working geometries,” Opt. Eng. 53(1), 014105 (2014).
[Crossref]

García-Márquez, J.

González-Vega, A.

Gu, C.

Holland, J. E.

I. Moreno, J. A. Davis, K. Badham, M. M. Sánchez-López, J. E. Holland, and D. M. Cottrell, “Vector Beam Polarization State Spectrum Analyzer,” Sci. Rep. 7(1), 2216 (2017).
[Crossref] [PubMed]

Iemmi, C.

Karakus, B.

Koebele, C.

A. Boutin, C. Koebele, D. Sperti, F. Verluise, G. Charlet, H. Mardoyan, L. Provost, M. Bigot-Astruc, M. Salsi, P. Tran, P. Brindel, P. Sillard, and S. Bigo, “Mode-Division Multiplexing of 2 × 100 Gb/s Channels Using an LCOS-Based Spatial Modulator,” J. Lit. Technol. 30, 618–623 (2012).

Kohler, C.

W. Osten, C. Kohler, and J. Liesener, “Evaluation and application of spatial light modulators for optical metrology,” Opt. Pura Apl. 38, 71–81 (2005).

Ledesma, S.

Lien, A.

A. Lien, “Extended Jones matrix representation for the twisted nematic liquid‐crystal display at oblique incidence,” Appl. Phys. Lett. 57(26), 2767–2769 (1990).
[Crossref]

Liesener, J.

W. Osten, C. Kohler, and J. Liesener, “Evaluation and application of spatial light modulators for optical metrology,” Opt. Pura Apl. 38, 71–81 (2005).

Lizana, A.

Lizana, I A.

Lobato, L.

López, V.

López-Quesada, C.

Mardoyan, H.

A. Boutin, C. Koebele, D. Sperti, F. Verluise, G. Charlet, H. Mardoyan, L. Provost, M. Bigot-Astruc, M. Salsi, P. Tran, P. Brindel, P. Sillard, and S. Bigo, “Mode-Division Multiplexing of 2 × 100 Gb/s Channels Using an LCOS-Based Spatial Modulator,” J. Lit. Technol. 30, 618–623 (2012).

Marquez, A.

X. Zheng, A. Lizana, A. Peinado, C. Ramirez, J. L. Martinez, A. Marquez, I. Moreno, and J. Campos, “Compact LCOS–SLM Based Polarization Pattern Beam Generator,” J. Lit. Technol. 33(10), 2047–2055 (2015).
[Crossref]

Márquez, A.

A. Márquez, J. Francés, F. J. Martínez, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “Computational split-field finite-difference time-domain evaluation of simplified tilt-angle models for parallel-aligned liquid-crystal devices,” Opt. Eng. 57(03), 1 (2018).
[Crossref]

J. Francés, A. Márquez, F. J. Martínez-Guardiola, S. Bleda, S. Gallego, C. Neipp, I. Pascual, and A. Beléndez, “Simplified physical modeling of parallel-aligned liquid crystal devices at highly non-linear tilt angle profiles,” Opt. Express 26(10), 12723–12741 (2018).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Effective angular and wavelength modeling of parallel aligned liquid crystal devices,” Opt. Lasers Eng. 74, 114–121 (2015).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, I. Pascual, and A. Beléndez, “Predictive capability of average Stokes polarimetry for simulation of phase multilevel elements onto LCoS devices,” Appl. Opt. 54(6), 1379–1386 (2015).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Electrical dependencies of optical modulation capabilities in digitally addressed parallel aligned liquid crystal on silicon devices,” Opt. Eng. 53(6), 067104 (2014).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Retardance and flicker modeling and characterization of electro-optic linear retarders by averaged Stokes polarimetry,” Opt. Lett. 39(4), 1011–1014 (2014).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, and I. Pascual, “Extended linear polarimeter to measure retardance and flicker: application to liquid crystal on silicon devices in two working geometries,” Opt. Eng. 53(1), 014105 (2014).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Averaged Stokes polarimetry applied to evaluate retardance and flicker in PA-LCoS devices,” Opt. Express 22(12), 15064–15074 (2014).
[Crossref] [PubMed]

A. Lizana, A. Márquez, L. Lobato, Y. Rodange, I. Moreno, C. Iemmi, and J. Campos, “The minimum Euclidean distance principle applied to improve the modulation diffraction efficiency in digitally controlled spatial light modulators,” Opt. Express 18(10), 10581–10593 (2010).
[Crossref] [PubMed]

I A. Lizana, I. Moreno, A. Márquez, C. Iemmi, E. Fernández, J. Campos, and M. J. Yzuel, “Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics,” Opt. Express 16(21), 16711–16722 (2008).
[Crossref] [PubMed]

Martín-Badosa, E.

Martinez, J. L.

X. Zheng, A. Lizana, A. Peinado, C. Ramirez, J. L. Martinez, A. Marquez, I. Moreno, and J. Campos, “Compact LCOS–SLM Based Polarization Pattern Beam Generator,” J. Lit. Technol. 33(10), 2047–2055 (2015).
[Crossref]

Martínez, F. J.

A. Márquez, J. Francés, F. J. Martínez, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “Computational split-field finite-difference time-domain evaluation of simplified tilt-angle models for parallel-aligned liquid-crystal devices,” Opt. Eng. 57(03), 1 (2018).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, I. Pascual, and A. Beléndez, “Predictive capability of average Stokes polarimetry for simulation of phase multilevel elements onto LCoS devices,” Appl. Opt. 54(6), 1379–1386 (2015).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Effective angular and wavelength modeling of parallel aligned liquid crystal devices,” Opt. Lasers Eng. 74, 114–121 (2015).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Retardance and flicker modeling and characterization of electro-optic linear retarders by averaged Stokes polarimetry,” Opt. Lett. 39(4), 1011–1014 (2014).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Electrical dependencies of optical modulation capabilities in digitally addressed parallel aligned liquid crystal on silicon devices,” Opt. Eng. 53(6), 067104 (2014).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Averaged Stokes polarimetry applied to evaluate retardance and flicker in PA-LCoS devices,” Opt. Express 22(12), 15064–15074 (2014).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, and I. Pascual, “Extended linear polarimeter to measure retardance and flicker: application to liquid crystal on silicon devices in two working geometries,” Opt. Eng. 53(1), 014105 (2014).
[Crossref]

Martínez-Guardiola, F. J.

Milione, G.

Montes-Usategui, M.

Moreno, I.

Neipp, C.

Neves, L.

Noé, E.

Ortuño, M.

Osten, W.

W. Osten, C. Kohler, and J. Liesener, “Evaluation and application of spatial light modulators for optical metrology,” Opt. Pura Apl. 38, 71–81 (2005).

Pascual, I.

A. Márquez, J. Francés, F. J. Martínez, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “Computational split-field finite-difference time-domain evaluation of simplified tilt-angle models for parallel-aligned liquid-crystal devices,” Opt. Eng. 57(03), 1 (2018).
[Crossref]

J. Francés, A. Márquez, F. J. Martínez-Guardiola, S. Bleda, S. Gallego, C. Neipp, I. Pascual, and A. Beléndez, “Simplified physical modeling of parallel-aligned liquid crystal devices at highly non-linear tilt angle profiles,” Opt. Express 26(10), 12723–12741 (2018).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Effective angular and wavelength modeling of parallel aligned liquid crystal devices,” Opt. Lasers Eng. 74, 114–121 (2015).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, I. Pascual, and A. Beléndez, “Predictive capability of average Stokes polarimetry for simulation of phase multilevel elements onto LCoS devices,” Appl. Opt. 54(6), 1379–1386 (2015).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Electrical dependencies of optical modulation capabilities in digitally addressed parallel aligned liquid crystal on silicon devices,” Opt. Eng. 53(6), 067104 (2014).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Retardance and flicker modeling and characterization of electro-optic linear retarders by averaged Stokes polarimetry,” Opt. Lett. 39(4), 1011–1014 (2014).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Averaged Stokes polarimetry applied to evaluate retardance and flicker in PA-LCoS devices,” Opt. Express 22(12), 15064–15074 (2014).
[Crossref] [PubMed]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, and I. Pascual, “Extended linear polarimeter to measure retardance and flicker: application to liquid crystal on silicon devices in two working geometries,” Opt. Eng. 53(1), 014105 (2014).
[Crossref]

Peinado, A.

X. Zheng, A. Lizana, A. Peinado, C. Ramirez, J. L. Martinez, A. Marquez, I. Moreno, and J. Campos, “Compact LCOS–SLM Based Polarization Pattern Beam Generator,” J. Lit. Technol. 33(10), 2047–2055 (2015).
[Crossref]

Poole, S.

M. A. F. Roelens, S. Frisken, J. A. Bolger, D. Abakoumov, G. Baxter, S. Poole, and B. J. Eggleton, “Dispersion Trimming in a Reconfigurable Wavelength Selective Switch,” J. Lit. Technol. 26(1), 73–78 (2008).
[Crossref]

Provost, L.

A. Boutin, C. Koebele, D. Sperti, F. Verluise, G. Charlet, H. Mardoyan, L. Provost, M. Bigot-Astruc, M. Salsi, P. Tran, P. Brindel, P. Sillard, and S. Bigo, “Mode-Division Multiplexing of 2 × 100 Gb/s Channels Using an LCOS-Based Spatial Modulator,” J. Lit. Technol. 30, 618–623 (2012).

Ramirez, C.

X. Zheng, A. Lizana, A. Peinado, C. Ramirez, J. L. Martinez, A. Marquez, I. Moreno, and J. Campos, “Compact LCOS–SLM Based Polarization Pattern Beam Generator,” J. Lit. Technol. 33(10), 2047–2055 (2015).
[Crossref]

C. Ramirez, B. Karakus, A. Lizana, and J. Campos, “Polarimetric method for liquid crystal displays characterization in presence of phase fluctuations,” Opt. Express 21(3), 3182–3192 (2013).
[Crossref] [PubMed]

Rebón, L.

Rodange, Y.

Roelens, M. A. F.

M. A. F. Roelens, S. Frisken, J. A. Bolger, D. Abakoumov, G. Baxter, S. Poole, and B. J. Eggleton, “Dispersion Trimming in a Reconfigurable Wavelength Selective Switch,” J. Lit. Technol. 26(1), 73–78 (2008).
[Crossref]

Salsi, M.

A. Boutin, C. Koebele, D. Sperti, F. Verluise, G. Charlet, H. Mardoyan, L. Provost, M. Bigot-Astruc, M. Salsi, P. Tran, P. Brindel, P. Sillard, and S. Bigo, “Mode-Division Multiplexing of 2 × 100 Gb/s Channels Using an LCOS-Based Spatial Modulator,” J. Lit. Technol. 30, 618–623 (2012).

Sánchez-López, M. M.

I. Moreno, J. A. Davis, K. Badham, M. M. Sánchez-López, J. E. Holland, and D. M. Cottrell, “Vector Beam Polarization State Spectrum Analyzer,” Sci. Rep. 7(1), 2216 (2017).
[Crossref] [PubMed]

A. Cofré, A. Vargas, F. A. Torres-Ruiz, J. Campos, A. Lizana, M. M. Sánchez-López, and I. Moreno, “Dual polarization split lenses,” Opt. Express 25(20), 23773–23783 (2017).
[Crossref] [PubMed]

Shayegan, M.

Sillard, P.

A. Boutin, C. Koebele, D. Sperti, F. Verluise, G. Charlet, H. Mardoyan, L. Provost, M. Bigot-Astruc, M. Salsi, P. Tran, P. Brindel, P. Sillard, and S. Bigo, “Mode-Division Multiplexing of 2 × 100 Gb/s Channels Using an LCOS-Based Spatial Modulator,” J. Lit. Technol. 30, 618–623 (2012).

Solís-Prosser, M. A.

Sperti, D.

A. Boutin, C. Koebele, D. Sperti, F. Verluise, G. Charlet, H. Mardoyan, L. Provost, M. Bigot-Astruc, M. Salsi, P. Tran, P. Brindel, P. Sillard, and S. Bigo, “Mode-Division Multiplexing of 2 × 100 Gb/s Channels Using an LCOS-Based Spatial Modulator,” J. Lit. Technol. 30, 618–623 (2012).

Torres-Ruiz, F. A.

Tran, P.

A. Boutin, C. Koebele, D. Sperti, F. Verluise, G. Charlet, H. Mardoyan, L. Provost, M. Bigot-Astruc, M. Salsi, P. Tran, P. Brindel, P. Sillard, and S. Bigo, “Mode-Division Multiplexing of 2 × 100 Gb/s Channels Using an LCOS-Based Spatial Modulator,” J. Lit. Technol. 30, 618–623 (2012).

Varga, J. J. M.

Vargas, A.

Verluise, F.

A. Boutin, C. Koebele, D. Sperti, F. Verluise, G. Charlet, H. Mardoyan, L. Provost, M. Bigot-Astruc, M. Salsi, P. Tran, P. Brindel, P. Sillard, and S. Bigo, “Mode-Division Multiplexing of 2 × 100 Gb/s Channels Using an LCOS-Based Spatial Modulator,” J. Lit. Technol. 30, 618–623 (2012).

Wolfe, J. E.

Yeh, P.

You, Z.

Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light Sci. Appl. 3(10), 213 (2014).
[Crossref]

Yzuel, M. J.

Zhan, Q.

Zhang, Z.

Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light Sci. Appl. 3(10), 213 (2014).
[Crossref]

Zheng, X.

X. Zheng, A. Lizana, A. Peinado, C. Ramirez, J. L. Martinez, A. Marquez, I. Moreno, and J. Campos, “Compact LCOS–SLM Based Polarization Pattern Beam Generator,” J. Lit. Technol. 33(10), 2047–2055 (2015).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

A. Lien, “Extended Jones matrix representation for the twisted nematic liquid‐crystal display at oblique incidence,” Appl. Phys. Lett. 57(26), 2767–2769 (1990).
[Crossref]

J. Disp. Technol. (1)

N. Collings, T. Davey, J. Christmas, D. Chu, and B. Crossland, “The Applications and Technology of Phase-Only Liquid Crystal on Silicon Devices,” J. Disp. Technol. 7(3), 112–119 (2011).
[Crossref]

J. Lit. Technol. (3)

M. A. F. Roelens, S. Frisken, J. A. Bolger, D. Abakoumov, G. Baxter, S. Poole, and B. J. Eggleton, “Dispersion Trimming in a Reconfigurable Wavelength Selective Switch,” J. Lit. Technol. 26(1), 73–78 (2008).
[Crossref]

A. Boutin, C. Koebele, D. Sperti, F. Verluise, G. Charlet, H. Mardoyan, L. Provost, M. Bigot-Astruc, M. Salsi, P. Tran, P. Brindel, P. Sillard, and S. Bigo, “Mode-Division Multiplexing of 2 × 100 Gb/s Channels Using an LCOS-Based Spatial Modulator,” J. Lit. Technol. 30, 618–623 (2012).

X. Zheng, A. Lizana, A. Peinado, C. Ramirez, J. L. Martinez, A. Marquez, I. Moreno, and J. Campos, “Compact LCOS–SLM Based Polarization Pattern Beam Generator,” J. Lit. Technol. 33(10), 2047–2055 (2015).
[Crossref]

J. Opt. Soc. Am. (2)

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

Light Sci. Appl. (1)

Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light Sci. Appl. 3(10), 213 (2014).
[Crossref]

Opt. Eng. (3)

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Electrical dependencies of optical modulation capabilities in digitally addressed parallel aligned liquid crystal on silicon devices,” Opt. Eng. 53(6), 067104 (2014).
[Crossref]

A. Márquez, J. Francés, F. J. Martínez, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “Computational split-field finite-difference time-domain evaluation of simplified tilt-angle models for parallel-aligned liquid-crystal devices,” Opt. Eng. 57(03), 1 (2018).
[Crossref]

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, and I. Pascual, “Extended linear polarimeter to measure retardance and flicker: application to liquid crystal on silicon devices in two working geometries,” Opt. Eng. 53(1), 014105 (2014).
[Crossref]

Opt. Express (10)

F. J. Martínez, A. Márquez, S. Gallego, M. Ortuño, J. Francés, A. Beléndez, and I. Pascual, “Averaged Stokes polarimetry applied to evaluate retardance and flicker in PA-LCoS devices,” Opt. Express 22(12), 15064–15074 (2014).
[Crossref] [PubMed]

J. Francés, A. Márquez, F. J. Martínez-Guardiola, S. Bleda, S. Gallego, C. Neipp, I. Pascual, and A. Beléndez, “Simplified physical modeling of parallel-aligned liquid crystal devices at highly non-linear tilt angle profiles,” Opt. Express 26(10), 12723–12741 (2018).
[Crossref] [PubMed]

A. Lizana, A. Márquez, L. Lobato, Y. Rodange, I. Moreno, C. Iemmi, and J. Campos, “The minimum Euclidean distance principle applied to improve the modulation diffraction efficiency in digitally controlled spatial light modulators,” Opt. Express 18(10), 10581–10593 (2010).
[Crossref] [PubMed]

J. García-Márquez, V. López, A. González-Vega, and E. Noé, “Flicker minimization in an LCoS spatial light modulator,” Opt. Express 20(8), 8431–8441 (2012).
[Crossref] [PubMed]

C. Ramirez, B. Karakus, A. Lizana, and J. Campos, “Polarimetric method for liquid crystal displays characterization in presence of phase fluctuations,” Opt. Express 21(3), 3182–3192 (2013).
[Crossref] [PubMed]

I A. Lizana, I. Moreno, A. Márquez, C. Iemmi, E. Fernández, J. Campos, and M. J. Yzuel, “Time fluctuations of the phase modulation in a liquid crystal on silicon display: characterization and effects in diffractive optics,” Opt. Express 16(21), 16711–16722 (2008).
[Crossref] [PubMed]

A. Dudley, G. Milione, R. R. Alfano, and A. Forbes, “All-digital wavefront sensing for structured light beams,” Opt. Express 22(11), 14031–14040 (2014).
[Crossref] [PubMed]

A. Farré, M. Shayegan, C. López-Quesada, G. A. Blab, M. Montes-Usategui, N. R. Forde, and E. Martín-Badosa, “Positional stability of holographic optical traps,” Opt. Express 19(22), 21370–21384 (2011).
[Crossref] [PubMed]

A. Cofré, A. Vargas, F. A. Torres-Ruiz, J. Campos, A. Lizana, M. M. Sánchez-López, and I. Moreno, “Dual polarization split lenses,” Opt. Express 25(20), 23773–23783 (2017).
[Crossref] [PubMed]

T. Brown and Q. Zhan, “Introduction: Unconventional Polarization States of Light Focus Issue,” Opt. Express 18(10), 10775–10776 (2010).
[Crossref] [PubMed]

Opt. Lasers Eng. (1)

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Effective angular and wavelength modeling of parallel aligned liquid crystal devices,” Opt. Lasers Eng. 74, 114–121 (2015).
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[Crossref]

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[Crossref]

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Figures (10)

Fig. 1
Fig. 1 Diagram for the PA-LC cell considered in the semiphysical model.
Fig. 2
Fig. 2 Tilt angle as a function of gray level obtained for the two sequence formats considered.
Fig. 3
Fig. 3 Tilt flicker for sequence formats 5-5 and 18-6, (a) as a function of gray level, and (b) as a function of average tilt angle.
Fig. 4
Fig. 4 Experiment (dots) and theoretical prediction with the proposed model (line) for sequence formats 5-5 and 18-6, for the wavelengths 473, 532 and 633 nm and for incidence at: (a) 23°; (b) 45°.
Fig. 5
Fig. 5 Experiment (dots) and theoretical prediction with the proposed model (line) for sequence formats 5-5 ((a1) and (b1)) and 18-6 ((a2) and (b2)), for the wavelengths 473, 532 and 633 nm and for incidence at 23° ((a1) and (a2)), and at 45° ((b1) and (b2)).
Fig. 6
Fig. 6 For sequence format 5-5 and for incident SOP right-handed circular, in plots (a) for the Stokes parameters and in (b) for DoP, experiment (dots) and theoretical prediction with the proposed model (line), and in plots (c) representation on the Poincaré sphere, where the dark line is simulation and gray line is experiment. Top row ((a1), (b1) and (c1)) for 633 nm and incidence at 3°; middle row ((a2), (b2) and (c2)) for 532 nm and incidence at 30°; bottom row ((a3), (b3) and (c3)) for 473 nm and incidence at 30°.
Fig. 7
Fig. 7 For sequence format 18-6 and for incident SOP right-handed circular, in plots (a) for the Stokes parameters and in (b) for DoP, experiment (dots) and theoretical prediction with the proposed model (line), and in plots (c) representation on the Poincaré sphere, where the dark line is simulation and gray line is experiment. Top row ((a1), (b1) and (c1)) for 633 nm and incidence at 3°; middle row ((a2), (b2) and (c2)) for 532 nm and incidence at 30°; bottom row ((a3), (b3) and (c3)) for 473 nm and incidence at 30°.
Fig. 8
Fig. 8 For sequence format 18-6 and for incident SOP right-handed circular, for 473 nm and at 3° incidence, in plots (a) for the Stokes parameters and in (b) for DoP, experiment (dots) and theoretical prediction with the proposed model (line), and in plots (c) representation on the Poincaré sphere, where the dark line is simulation and gray line is experiment.
Fig. 9
Fig. 9 For sequence format 5-5 and for incident SOP right-handed circular. Simulations for the spectral variation of the Stokes parameter S3 ((a1) and (a2)) and the DoP ((b1) and (b2)), for incidences at 0° ((a1) and (b1)) and at 35° ((a2) and (b2)).
Fig. 10
Fig. 10 For sequence format 5-5 and for incident SOP right-handed circular. Simulations for the variation as a function of the angle of incidence for the Stokes parameter S3 ((a1) and (a2)) and for the DoP ((b1) and (b2)), at illumination wavelengths 633 nm ((a1) and (b1)) and 473 nm ((a2) and (b2)).

Tables (3)

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Table 1 Values for the retardance in the off-state.

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Table 2 Fitted OPD and OPL obtained using the retardance values in Table 1.

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Table 3 Fitted OPD and OPL obtained for the retardance values in Table 1 with 1% uncertainty.

Equations (2)

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Γ= 2π λ OPL cos θ LC [ 1+( OPD/ OPL ) 1+( OPD/ OPL ) cos 2 ϕ 1 ]
ϕ( θ inc ,V )= π 2 +α( V ) θ LC ( θ inc )

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