Abstract

In recent works, we demonstrated the accuracy and physical relevance of a highly simplified reverse-engineering analytical model for a parallel-aligned liquid crystal on silicon devices (PA-LCoS). Both experimental measurements and computational simulations applying the rigorous split-field finite difference time domain (SF-FDTD) technique led to this conclusion in the low applied voltages range. In this paper, we develop a complete rigorous validation covering the full range of possible applied voltages, including highly non-linear liquid crystal (LC) tilt angle profiles. We demonstrate the applicability of the model for spectral and angular retardation calculations, of interest in spatial light modulation applications. We also show that our analytical model enables the calculation of the retardance for novel PA-LC devices as a function of the LC compound and cell gap, becoming an appealing alternative to the usual numerical approaches for PA-LC devices design.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  29. A. Lizana, N. Martín, M. Estapé, E. Fernández, I. Moreno, A. Márquez, C. Iemmi, J. Campos, and M. J. Yzuel, “Influence of the incident angle in the performance of Liquid Crystal on Silicon displays,” Opt. Express 17(10), 8491–8505 (2009).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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2018 (1)

A. Márquez, J. Francés, F. J. Martínez-Guardiola, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “Computational SF-FDTD evaluation of simplified tilt-angle models for parallel aligned liquid crystal devices,” Opt. Eng. 57, 037110 (2018).
[Crossref]

2017 (2)

A. Márquez, J. Francés, F. J. Martínez-Guardiola, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “SF-FDTD analysis of a predictive physical model for parallel aligned liquid crystal devices,” Proc. SPIE 10395, 1039509 (2017).

M. Wang, L. Zong, L. Mao, A. Marquez, Y. Ye, H. Zhao, and F. J. Vaquero, “LCoS SLM Study and Its Application in Wavelength Selective Switch,” Photonics 4(22), 1–16 (2017).

2015 (5)

2014 (5)

2013 (1)

J. Francés, S. Bleda, M. L. Lázara, F. J. Martínez, A. Márquez, C. Neipp, and A. Beléndez, “Acceleration of split-field finite difference time-domain method for anisotropic media by means of graphics processing unit computing,” Opt. Eng. 53(1), 011005 (2013).
[Crossref]

2012 (2)

M. N. Miskiewicz, P. T. Bowen, and M. J. Escuti, “Efficient 3D FDTD analysis of arbitrary birefringent and dichroic media with obliquely incident sources,” Proc. SPIE 8255, 82550W (2012).
[Crossref]

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]

2011 (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]

2010 (2)

I. Abdulhalim and D. Menashe, “Approximate analytic solutions for the director profile of homogeneously aligned nematic liquid crystals,” Liq. Cryst. 37(2), 233–239 (2010).
[Crossref]

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

2009 (2)

A. Lizana, N. Martín, M. Estapé, E. Fernández, I. Moreno, A. Márquez, C. Iemmi, J. Campos, and M. J. Yzuel, “Influence of the incident angle in the performance of Liquid Crystal on Silicon displays,” Opt. Express 17(10), 8491–8505 (2009).
[Crossref] [PubMed]

A. Lizana, I. Moreno, A. Márquez, E. Also, C. Iemmi, J. Campos, and M. J. Yzuel, “Influence of the temporal fluctuations phenomena on the ECB LCoS performance,” Proc. SPIE 7442, 74420G (2009).
[Crossref]

2007 (1)

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystal based micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007).
[Crossref]

2006 (2)

C. Oh and M. J. Escuti, “Time-domain analysis of periodic anisotropic media at oblique incidence: an efficient FDTD implementation,” Opt. Express 14(24), 11870–11884 (2006).
[Crossref] [PubMed]

A. Márquez, I. Moreno, J. Campos, and M. J. Yzuel, “Analysis of Fabry–Perot interference effects on the modulation properties of liquid crystal displays,” Opt. Commun. 265(1), 84–94 (2006).
[Crossref]

2005 (1)

J. Li, C.-H. Wen, S. Gauza, R. Lu, and S.-T. Wu, “Refractive Indices of Liquid Crystals for Display Applications,” J. Disp. Technol. 1(1), 51–61 (2005).
[Crossref]

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]

1983 (1)

Abdulhalim, I.

I. Abdulhalim and D. Menashe, “Approximate analytic solutions for the director profile of homogeneously aligned nematic liquid crystals,” Liq. Cryst. 37(2), 233–239 (2010).
[Crossref]

Also, E.

A. Lizana, I. Moreno, A. Márquez, E. Also, C. Iemmi, J. Campos, and M. J. Yzuel, “Influence of the temporal fluctuations phenomena on the ECB LCoS performance,” Proc. SPIE 7442, 74420G (2009).
[Crossref]

Álvarez, M. L.

A. Márquez, J. Francés, F. J. Martínez-Guardiola, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “Computational SF-FDTD evaluation of simplified tilt-angle models for parallel aligned liquid crystal devices,” Opt. Eng. 57, 037110 (2018).
[Crossref]

A. Márquez, J. Francés, F. J. Martínez-Guardiola, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “SF-FDTD analysis of a predictive physical model for parallel aligned liquid crystal devices,” Proc. SPIE 10395, 1039509 (2017).

F. J. Martínez, R. Fernández, A. Márquez, S. Gallego, M. L. Álvarez, I. Pascual, and A. Beléndez, “Exploring binary and ternary modulations on a PA-LCoS device for holographic data storage in a PVA/AA photopolymer,” Opt. Express 23(16), 20459–20479 (2015).
[Crossref] [PubMed]

Beléndez, A.

A. Márquez, J. Francés, F. J. Martínez-Guardiola, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “Computational SF-FDTD evaluation of simplified tilt-angle models for parallel aligned liquid crystal devices,” Opt. Eng. 57, 037110 (2018).
[Crossref]

A. Márquez, J. Francés, F. J. Martínez-Guardiola, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “SF-FDTD analysis of a predictive physical model for parallel aligned liquid crystal devices,” Proc. SPIE 10395, 1039509 (2017).

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

F. J. Martínez, R. Fernández, A. Márquez, S. Gallego, M. L. Álvarez, I. Pascual, and A. Beléndez, “Exploring binary and ternary modulations on a PA-LCoS device for holographic data storage in a PVA/AA photopolymer,” Opt. Express 23(16), 20459–20479 (2015).
[Crossref] [PubMed]

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, “Averaged Stokes polarimetry applied to evaluate retardance and flicker in PA-LCoS devices,” Opt. Express 22(12), 15064–15074 (2014).
[Crossref] [PubMed]

J. Francés, S. Bleda, M. L. Lázara, F. J. Martínez, A. Márquez, C. Neipp, and A. Beléndez, “Acceleration of split-field finite difference time-domain method for anisotropic media by means of graphics processing unit computing,” Opt. Eng. 53(1), 011005 (2013).
[Crossref]

Bleda, S.

J. Francés, J. Tervo, S. Gallego, S. Bleda, C. Neipp, and A. Márquez, “Split-field finite-difference time-domain method for second-harmonic generation in two-dimensionally periodic structures,” J. Opt. Soc. Am. B 32(4), 664–669 (2015).
[Crossref]

J. Francés, S. Bleda, M. L. Lázara, F. J. Martínez, A. Márquez, C. Neipp, and A. Beléndez, “Acceleration of split-field finite difference time-domain method for anisotropic media by means of graphics processing unit computing,” Opt. Eng. 53(1), 011005 (2013).
[Crossref]

Blümel, T.

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystal based micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007).
[Crossref]

Bowen, P. T.

M. N. Miskiewicz, P. T. Bowen, and M. J. Escuti, “Efficient 3D FDTD analysis of arbitrary birefringent and dichroic media with obliquely incident sources,” Proc. SPIE 8255, 82550W (2012).
[Crossref]

Brown, T. G.

Calzado, E. M.

A. Márquez, J. Francés, F. J. Martínez-Guardiola, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “Computational SF-FDTD evaluation of simplified tilt-angle models for parallel aligned liquid crystal devices,” Opt. Eng. 57, 037110 (2018).
[Crossref]

A. Márquez, J. Francés, F. J. Martínez-Guardiola, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “SF-FDTD analysis of a predictive physical model for parallel aligned liquid crystal devices,” Proc. SPIE 10395, 1039509 (2017).

Campos, J.

Carrión, J. V.

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), 1–10 (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]

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]

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]

del Mar Sánchez-López, M.

Escuti, M. J.

M. N. Miskiewicz, P. T. Bowen, and M. J. Escuti, “Efficient 3D FDTD analysis of arbitrary birefringent and dichroic media with obliquely incident sources,” Proc. SPIE 8255, 82550W (2012).
[Crossref]

C. Oh and M. J. Escuti, “Time-domain analysis of periodic anisotropic media at oblique incidence: an efficient FDTD implementation,” Opt. Express 14(24), 11870–11884 (2006).
[Crossref] [PubMed]

Estapé, M.

Fernández, E.

Fernández, R.

Francés, J.

A. Márquez, J. Francés, F. J. Martínez-Guardiola, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “Computational SF-FDTD evaluation of simplified tilt-angle models for parallel aligned liquid crystal devices,” Opt. Eng. 57, 037110 (2018).
[Crossref]

A. Márquez, J. Francés, F. J. Martínez-Guardiola, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “SF-FDTD analysis of a predictive physical model for parallel aligned liquid crystal devices,” Proc. SPIE 10395, 1039509 (2017).

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

J. Francés, J. Tervo, S. Gallego, S. Bleda, C. Neipp, and A. Márquez, “Split-field finite-difference time-domain method for second-harmonic generation in two-dimensionally periodic structures,” J. Opt. Soc. Am. B 32(4), 664–669 (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, “Averaged Stokes polarimetry applied to evaluate retardance and flicker in PA-LCoS devices,” Opt. Express 22(12), 15064–15074 (2014).
[Crossref] [PubMed]

J. Francés, S. Bleda, M. L. Lázara, F. J. Martínez, A. Márquez, C. Neipp, and A. Beléndez, “Acceleration of split-field finite difference time-domain method for anisotropic media by means of graphics processing unit computing,” Opt. Eng. 53(1), 011005 (2013).
[Crossref]

Gallego, S.

A. Márquez, J. Francés, F. J. Martínez-Guardiola, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “Computational SF-FDTD evaluation of simplified tilt-angle models for parallel aligned liquid crystal devices,” Opt. Eng. 57, 037110 (2018).
[Crossref]

A. Márquez, J. Francés, F. J. Martínez-Guardiola, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “SF-FDTD analysis of a predictive physical model for parallel aligned liquid crystal devices,” Proc. SPIE 10395, 1039509 (2017).

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Effective angular and wavelength modelling 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, R. Fernández, A. Márquez, S. Gallego, M. L. Álvarez, I. Pascual, and A. Beléndez, “Exploring binary and ternary modulations on a PA-LCoS device for holographic data storage in a PVA/AA photopolymer,” Opt. Express 23(16), 20459–20479 (2015).
[Crossref] [PubMed]

J. Francés, J. Tervo, S. Gallego, S. Bleda, C. Neipp, and A. Márquez, “Split-field finite-difference time-domain method for second-harmonic generation in two-dimensionally periodic structures,” J. Opt. Soc. Am. B 32(4), 664–669 (2015).
[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, 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]

García-Márquez, J.

García-Martínez, P.

Gauza, S.

J. Li, C.-H. Wen, S. Gauza, R. Lu, and S.-T. Wu, “Refractive Indices of Liquid Crystals for Display Applications,” J. Disp. Technol. 1(1), 51–61 (2005).
[Crossref]

González-Vega, A.

Hermerschmidt, A.

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystal based micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007).
[Crossref]

Iemmi, C.

A. Lizana, I. Moreno, A. Márquez, E. Also, C. Iemmi, J. Campos, and M. J. Yzuel, “Influence of the temporal fluctuations phenomena on the ECB LCoS performance,” Proc. SPIE 7442, 74420G (2009).
[Crossref]

A. Lizana, N. Martín, M. Estapé, E. Fernández, I. Moreno, A. Márquez, C. Iemmi, J. Campos, and M. J. Yzuel, “Influence of the incident angle in the performance of Liquid Crystal on Silicon displays,” Opt. Express 17(10), 8491–8505 (2009).
[Crossref] [PubMed]

Krüger, S.

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystal based micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007).
[Crossref]

Lázara, M. L.

J. Francés, S. Bleda, M. L. Lázara, F. J. Martínez, A. Márquez, C. Neipp, and A. Beléndez, “Acceleration of split-field finite difference time-domain method for anisotropic media by means of graphics processing unit computing,” Opt. Eng. 53(1), 011005 (2013).
[Crossref]

Li, J.

J. Li, C.-H. Wen, S. Gauza, R. Lu, and S.-T. Wu, “Refractive Indices of Liquid Crystals for Display Applications,” J. Disp. Technol. 1(1), 51–61 (2005).
[Crossref]

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]

Lizana, A.

López, V.

Lu, R.

J. Li, C.-H. Wen, S. Gauza, R. Lu, and S.-T. Wu, “Refractive Indices of Liquid Crystals for Display Applications,” J. Disp. Technol. 1(1), 51–61 (2005).
[Crossref]

Mao, L.

M. Wang, L. Zong, L. Mao, A. Marquez, Y. Ye, H. Zhao, and F. J. Vaquero, “LCoS SLM Study and Its Application in Wavelength Selective Switch,” Photonics 4(22), 1–16 (2017).

Marquez, A.

M. Wang, L. Zong, L. Mao, A. Marquez, Y. Ye, H. Zhao, and F. J. Vaquero, “LCoS SLM Study and Its Application in Wavelength Selective Switch,” Photonics 4(22), 1–16 (2017).

Márquez, A.

A. Márquez, J. Francés, F. J. Martínez-Guardiola, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “Computational SF-FDTD evaluation of simplified tilt-angle models for parallel aligned liquid crystal devices,” Opt. Eng. 57, 037110 (2018).
[Crossref]

A. Márquez, J. Francés, F. J. Martínez-Guardiola, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “SF-FDTD analysis of a predictive physical model for parallel aligned liquid crystal devices,” Proc. SPIE 10395, 1039509 (2017).

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

X. Zheng, A. Lizana, A. Peinado, C. Ramírez, J. L. Martínez, A. Márquez, I. Moreno, and J. Campos, “Compact LCOS-SLM based polarization pattern beam generator,” J. Lightwave Technol. 33(10), 2047–2055 (2015).
[Crossref]

F. J. Martínez, R. Fernández, A. Márquez, S. Gallego, M. L. Álvarez, I. Pascual, and A. Beléndez, “Exploring binary and ternary modulations on a PA-LCoS device for holographic data storage in a PVA/AA photopolymer,” Opt. Express 23(16), 20459–20479 (2015).
[Crossref] [PubMed]

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]

J. Francés, J. Tervo, S. Gallego, S. Bleda, C. Neipp, and A. Márquez, “Split-field finite-difference time-domain method for second-harmonic generation in two-dimensionally periodic structures,” J. Opt. Soc. Am. B 32(4), 664–669 (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, “Averaged Stokes polarimetry applied to evaluate retardance and flicker in PA-LCoS devices,” Opt. Express 22(12), 15064–15074 (2014).
[Crossref] [PubMed]

J. Francés, S. Bleda, M. L. Lázara, F. J. Martínez, A. Márquez, C. Neipp, and A. Beléndez, “Acceleration of split-field finite difference time-domain method for anisotropic media by means of graphics processing unit computing,” Opt. Eng. 53(1), 011005 (2013).
[Crossref]

A. Lizana, I. Moreno, A. Márquez, E. Also, C. Iemmi, J. Campos, and M. J. Yzuel, “Influence of the temporal fluctuations phenomena on the ECB LCoS performance,” Proc. SPIE 7442, 74420G (2009).
[Crossref]

A. Lizana, N. Martín, M. Estapé, E. Fernández, I. Moreno, A. Márquez, C. Iemmi, J. Campos, and M. J. Yzuel, “Influence of the incident angle in the performance of Liquid Crystal on Silicon displays,” Opt. Express 17(10), 8491–8505 (2009).
[Crossref] [PubMed]

A. Márquez, I. Moreno, J. Campos, and M. J. Yzuel, “Analysis of Fabry–Perot interference effects on the modulation properties of liquid crystal displays,” Opt. Commun. 265(1), 84–94 (2006).
[Crossref]

Martín, N.

Martínez, F. J.

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Effective angular and wavelength modelling 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, R. Fernández, A. Márquez, S. Gallego, M. L. Álvarez, I. Pascual, and A. Beléndez, “Exploring binary and ternary modulations on a PA-LCoS device for holographic data storage in a PVA/AA photopolymer,” Opt. Express 23(16), 20459–20479 (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, “Averaged Stokes polarimetry applied to evaluate retardance and flicker in PA-LCoS devices,” Opt. Express 22(12), 15064–15074 (2014).
[Crossref] [PubMed]

J. Francés, S. Bleda, M. L. Lázara, F. J. Martínez, A. Márquez, C. Neipp, and A. Beléndez, “Acceleration of split-field finite difference time-domain method for anisotropic media by means of graphics processing unit computing,” Opt. Eng. 53(1), 011005 (2013).
[Crossref]

Martínez, J. L.

Martínez-Guardiola, F. J.

A. Márquez, J. Francés, F. J. Martínez-Guardiola, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “Computational SF-FDTD evaluation of simplified tilt-angle models for parallel aligned liquid crystal devices,” Opt. Eng. 57, 037110 (2018).
[Crossref]

A. Márquez, J. Francés, F. J. Martínez-Guardiola, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “SF-FDTD analysis of a predictive physical model for parallel aligned liquid crystal devices,” Proc. SPIE 10395, 1039509 (2017).

Menashe, D.

I. Abdulhalim and D. Menashe, “Approximate analytic solutions for the director profile of homogeneously aligned nematic liquid crystals,” Liq. Cryst. 37(2), 233–239 (2010).
[Crossref]

Miskiewicz, M. N.

M. N. Miskiewicz, P. T. Bowen, and M. J. Escuti, “Efficient 3D FDTD analysis of arbitrary birefringent and dichroic media with obliquely incident sources,” Proc. SPIE 8255, 82550W (2012).
[Crossref]

Moreno, I.

Neipp, C.

J. Francés, J. Tervo, S. Gallego, S. Bleda, C. Neipp, and A. Márquez, “Split-field finite-difference time-domain method for second-harmonic generation in two-dimensionally periodic structures,” J. Opt. Soc. Am. B 32(4), 664–669 (2015).
[Crossref]

J. Francés, S. Bleda, M. L. Lázara, F. J. Martínez, A. Márquez, C. Neipp, and A. Beléndez, “Acceleration of split-field finite difference time-domain method for anisotropic media by means of graphics processing unit computing,” Opt. Eng. 53(1), 011005 (2013).
[Crossref]

Noé, E.

Oh, C.

Ortuño, M.

Osten, S.

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystal based micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007).
[Crossref]

Pascual, I.

A. Márquez, J. Francés, F. J. Martínez-Guardiola, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “Computational SF-FDTD evaluation of simplified tilt-angle models for parallel aligned liquid crystal devices,” Opt. Eng. 57, 037110 (2018).
[Crossref]

A. Márquez, J. Francés, F. J. Martínez-Guardiola, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “SF-FDTD analysis of a predictive physical model for parallel aligned liquid crystal devices,” Proc. SPIE 10395, 1039509 (2017).

F. J. Martínez, A. Márquez, S. Gallego, J. Francés, I. Pascual, and A. Beléndez, “Effective angular and wavelength modelling 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, R. Fernández, A. Márquez, S. Gallego, M. L. Álvarez, I. Pascual, and A. Beléndez, “Exploring binary and ternary modulations on a PA-LCoS device for holographic data storage in a PVA/AA photopolymer,” Opt. Express 23(16), 20459–20479 (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, “Averaged Stokes polarimetry applied to evaluate retardance and flicker in PA-LCoS devices,” Opt. Express 22(12), 15064–15074 (2014).
[Crossref] [PubMed]

Peinado, A.

Ramírez, C.

Sánchez-López, M. M.

Southwell, W. H.

Tervo, J.

Vaquero, F. J.

M. Wang, L. Zong, L. Mao, A. Marquez, Y. Ye, H. Zhao, and F. J. Vaquero, “LCoS SLM Study and Its Application in Wavelength Selective Switch,” Photonics 4(22), 1–16 (2017).

Vargas, A.

Wang, M.

M. Wang, L. Zong, L. Mao, A. Marquez, Y. Ye, H. Zhao, and F. J. Vaquero, “LCoS SLM Study and Its Application in Wavelength Selective Switch,” Photonics 4(22), 1–16 (2017).

Wen, C.-H.

J. Li, C.-H. Wen, S. Gauza, R. Lu, and S.-T. Wu, “Refractive Indices of Liquid Crystals for Display Applications,” J. Disp. Technol. 1(1), 51–61 (2005).
[Crossref]

Wu, S.-T.

J. Li, C.-H. Wen, S. Gauza, R. Lu, and S.-T. Wu, “Refractive Indices of Liquid Crystals for Display Applications,” J. Disp. Technol. 1(1), 51–61 (2005).
[Crossref]

Ye, Y.

M. Wang, L. Zong, L. Mao, A. Marquez, Y. Ye, H. Zhao, and F. J. Vaquero, “LCoS SLM Study and Its Application in Wavelength Selective Switch,” Photonics 4(22), 1–16 (2017).

You, Z.

Z. Zhang, Z. You, and D. Chu, “Fundamentals of phase-only liquid crystal on silicon (LCOS) devices,” Light Sci. Appl. 3(10), 1–10 (2014).
[Crossref]

Yzuel, M. J.

A. Lizana, I. Moreno, A. Márquez, E. Also, C. Iemmi, J. Campos, and M. J. Yzuel, “Influence of the temporal fluctuations phenomena on the ECB LCoS performance,” Proc. SPIE 7442, 74420G (2009).
[Crossref]

A. Lizana, N. Martín, M. Estapé, E. Fernández, I. Moreno, A. Márquez, C. Iemmi, J. Campos, and M. J. Yzuel, “Influence of the incident angle in the performance of Liquid Crystal on Silicon displays,” Opt. Express 17(10), 8491–8505 (2009).
[Crossref] [PubMed]

A. Márquez, I. Moreno, J. Campos, and M. J. Yzuel, “Analysis of Fabry–Perot interference effects on the modulation properties of liquid crystal displays,” Opt. Commun. 265(1), 84–94 (2006).
[Crossref]

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), 1–10 (2014).
[Crossref]

Zhao, H.

M. Wang, L. Zong, L. Mao, A. Marquez, Y. Ye, H. Zhao, and F. J. Vaquero, “LCoS SLM Study and Its Application in Wavelength Selective Switch,” Photonics 4(22), 1–16 (2017).

Zheng, X.

Zong, L.

M. Wang, L. Zong, L. Mao, A. Marquez, Y. Ye, H. Zhao, and F. J. Vaquero, “LCoS SLM Study and Its Application in Wavelength Selective Switch,” Photonics 4(22), 1–16 (2017).

Appl. Opt. (1)

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. (2)

J. Li, C.-H. Wen, S. Gauza, R. Lu, and S.-T. Wu, “Refractive Indices of Liquid Crystals for Display Applications,” J. Disp. Technol. 1(1), 51–61 (2005).
[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]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (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), 1–10 (2014).
[Crossref]

Liq. Cryst. (1)

I. Abdulhalim and D. Menashe, “Approximate analytic solutions for the director profile of homogeneously aligned nematic liquid crystals,” Liq. Cryst. 37(2), 233–239 (2010).
[Crossref]

Opt. Commun. (1)

A. Márquez, I. Moreno, J. Campos, and M. J. Yzuel, “Analysis of Fabry–Perot interference effects on the modulation properties of liquid crystal displays,” Opt. Commun. 265(1), 84–94 (2006).
[Crossref]

Opt. Eng. (2)

A. Márquez, J. Francés, F. J. Martínez-Guardiola, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “Computational SF-FDTD evaluation of simplified tilt-angle models for parallel aligned liquid crystal devices,” Opt. Eng. 57, 037110 (2018).
[Crossref]

J. Francés, S. Bleda, M. L. Lázara, F. J. Martínez, A. Márquez, C. Neipp, and A. Beléndez, “Acceleration of split-field finite difference time-domain method for anisotropic media by means of graphics processing unit computing,” Opt. Eng. 53(1), 011005 (2013).
[Crossref]

Opt. Express (7)

J. L. Martínez, I. Moreno, M. del Mar Sánchez-López, A. Vargas, and P. García-Martínez, “Analysis of multiple internal reflections in a parallel aligned liquid crystal on silicon SLM,” Opt. Express 22(21), 25866–25879 (2014).
[Crossref] [PubMed]

A. Lizana, N. Martín, M. Estapé, E. Fernández, I. Moreno, A. Márquez, C. Iemmi, J. Campos, and M. J. Yzuel, “Influence of the incident angle in the performance of Liquid Crystal on Silicon displays,” Opt. Express 17(10), 8491–8505 (2009).
[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]

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

C. Oh and M. J. Escuti, “Time-domain analysis of periodic anisotropic media at oblique incidence: an efficient FDTD implementation,” Opt. Express 14(24), 11870–11884 (2006).
[Crossref] [PubMed]

F. J. Martínez, R. Fernández, A. Márquez, S. Gallego, M. L. Álvarez, I. Pascual, and A. Beléndez, “Exploring binary and ternary modulations on a PA-LCoS device for holographic data storage in a PVA/AA photopolymer,” Opt. Express 23(16), 20459–20479 (2015).
[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]

Opt. Lasers Eng. (1)

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

Opt. Lett. (3)

Photonics (1)

M. Wang, L. Zong, L. Mao, A. Marquez, Y. Ye, H. Zhao, and F. J. Vaquero, “LCoS SLM Study and Its Application in Wavelength Selective Switch,” Photonics 4(22), 1–16 (2017).

Proc. SPIE (4)

A. Hermerschmidt, S. Osten, S. Krüger, and T. Blümel, “Wave front generation using a phase-only modulating liquid-crystal based micro-display with HDTV resolution,” Proc. SPIE 6584, 65840E (2007).
[Crossref]

A. Lizana, I. Moreno, A. Márquez, E. Also, C. Iemmi, J. Campos, and M. J. Yzuel, “Influence of the temporal fluctuations phenomena on the ECB LCoS performance,” Proc. SPIE 7442, 74420G (2009).
[Crossref]

M. N. Miskiewicz, P. T. Bowen, and M. J. Escuti, “Efficient 3D FDTD analysis of arbitrary birefringent and dichroic media with obliquely incident sources,” Proc. SPIE 8255, 82550W (2012).
[Crossref]

A. Márquez, J. Francés, F. J. Martínez-Guardiola, S. Gallego, M. L. Álvarez, E. M. Calzado, I. Pascual, and A. Beléndez, “SF-FDTD analysis of a predictive physical model for parallel aligned liquid crystal devices,” Proc. SPIE 10395, 1039509 (2017).

Other (7)

F. Abeles, Optics of Thin Films in Advanced Optical Techniques (North-Holland Publishing Co, 1967).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).

V. G. Chigrinov, H. S. Kwok, D. A. Yakovlev, G. V. Simonenko, and V. I. Tsoy, “LCD Optimization and Modeling,” in SID 04 DIGEST (2014), pp. 982–985.

G. Lazarev, A. Hermerschmidt, S. Krüger, and S. Osten, “LCOS spatial light modulators: trends and applications,” in Optical Imaging and Metrology: Advanced Technologies, W. Osten and N. Reingand, eds. (John Wiley & Sons Inc, 2012).

P. Yeh and C. Gu, Optics of Liquid Crystal Displays (John Wiley & Sons Inc, 1999).

S. T. Wu and D. K. Yang, Reflective Liquid Crystal Displays (John Wiley & Sons Inc, 2005).

V. G. Chigrinov, Liquid Crystal Devices: Physics and Applications (Artech House, 1999).

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Figures (20)

Fig. 1
Fig. 1 Diagram for the PA-LC cell considered in the model proposed.
Fig. 2
Fig. 2 LC director tilt angle profiles across the thickness of the cell and for various voltages.
Fig. 3
Fig. 3 Retardance measurements obtained in the SF-FDTD simulated experiment for 18 wavelengths and 61 voltages and the incidence angles: (a) 3°, (b) 25°, (c) 35°, and (d) 45°.
Fig. 4
Fig. 4 Retardance simulated measurements for the various incidence angles (in the legend) and for the wavelengths: (a) 633 nm, (b) 532 nm, and (c) 473 nm.
Fig. 5
Fig. 5 SF-FDTD experiment (dots) and theoretical fitting with the proposed simplified model (continuous line) for the wavelengths 633, 532 and 473 nm and for incidence at: (a) 3°; (b) 35°.
Fig. 6
Fig. 6 Tilt angle as a function of voltage.
Fig. 7
Fig. 7 Difference between theoretical and SF-FDTD-experimental retardance normalized by the theoretical value for wavelengths 633, 532 and 473 nm and for incidence at: (a) 3°, and (b) 35°.
Fig. 8
Fig. 8 SF-FDTD experiment (dots) and prediction with the proposed simplified model (continuous line) for the wavelengths 633, 532 and 473 nm and for incidence at: (a) 25°; (b) 45°.
Fig. 9
Fig. 9 Difference between predicted and SF-FDTD experimental retardance normalized by the predicted value for wavelengths 633, 532 and 473 nm and for incidence at: (a) 25°, and (b) 45°.
Fig. 10
Fig. 10 Relation for α max (sine profile), (a) vs. tilt angle of an equivalent homogenous slab and, (b) vs. voltage.
Fig. 11
Fig. 11 Comparison between the realistic and the sine tilt profiles for a series of voltages.
Fig. 12
Fig. 12 Tilt angle as a function of gray level for the commercial PA-LCoS in [14].
Fig. 13
Fig. 13 From the experimental data for the commercial PA-LCoS in [14]. Relation between (sine profile), (a) vs. tilt angle of an equivalent homogenous slab and, (b) vs. gray level (applied voltage).
Fig. 14
Fig. 14 Sine tilt profiles as a function of the gray level.
Fig. 15
Fig. 15 Proposed simplified model (continuous line) and SF-FDTD experimental (dots) retardance versus wavelength and for three incidences. (a) Maximum and (b) minimum retardance values.
Fig. 16
Fig. 16 Retardance dynamic range. Proposed simplified model (continuous line) and SF-FDTD experimental (dots) retardance versus wavelength and for three incidences.
Fig. 17
Fig. 17 With the simplified model, usage of the true OPL to calculate the retardance. Normalized retardance difference in the: (a) Off-state, against the true off-state retardance, and (b) On-state, for an angle of incidence of 45°, against the calculation using the fitted OPL.
Fig. 18
Fig. 18 Values for OPD, in (a), and OPL, in (b), for two LC compounds and two temperatures, for a cell gap of 2 µm. Data points in the plots are the sample values use to fit the extended Cauchy relation across the visible.
Fig. 19
Fig. 19 Using the proposed simplified model, simulated retardance at 633 nm, at incidence angles: (a) 0°; (b) 45°.
Fig. 20
Fig. 20 Using the proposed simplified model, simulated retardance at 473 nm, at incidence angles: (a) 0°; (b) 45°.

Tables (5)

Tables Icon

Table 1 Values for the parameters used to simulate the performance of the PA-LC cell.

Tables Icon

Table 2 Values for the retardance in the off-state.

Tables Icon

Table 3 True OPD and OPL parameters calculated from the cell gap and the indices of refraction in Table 1.

Tables Icon

Table 4 Fitted OPD and OPL values for different values for nLC, and values for the figures of merit for the off-state χ2 and for the on-state MSE comparison between theoretical and experimental results.

Tables Icon

Table 5 OPD and OPL parameters obtained for the commercial PA-LCoS in [14].

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

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 ),
α sin = α max sin( πz/d ),
ΔΓ= 2π λ ( OPL/d ) cos θ LC ( 1+( OPD/ OPL ) 1+( OPD/ OPL ) cos 2 ϕ 1 )Δz.
Γ total hom ( θ inc , α hom )= 2π λ ( OPL cos θ LC ( θ inc ) [ 1+( OPD/ OPL ) 1+( OPD/ OPL ) cos 2 ϕ( θ inc , α hom ) + 1+( OPD/ OPL ) 1+( OPD/ OPL ) cos 2 ϕ( θ inc , α hom ) 2 ] ).
Γ total sin ( θ inc , α max )= 2π λ OPL cos θ LC ( θ inc ) ... ... 0 1 ( 1+( OPD/ OPL ) 1+( OPD/ OPL ) cos 2 ϕ( θ inc , α sin ( α max ,z' ) ) + 1+( OPD/ OPL ) 1+( OPD/ OPL ) cos 2 ϕ( θ inc , α sin ( α max ,z' ) ) 2 )d z ,
Γ total sin ( θ inc , α max )= Γ total hom ( θ inc , α hom ),

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