Abstract

The polarization state of light transmitted through a polymer-dispersed liquid-crystal film with small, spherical, nonabsorbing, partially oriented nematic droplets is theoretically investigated. The model used is based on the effective medium approach. Scattering properties of a single droplet are described by the Rayleigh–Gans approximation. Propagation of coherent light is described within the framework of the Twersky theory. To describe the orientation of liquid-crystal molecules inside droplets and liquid-crystal droplets in a sample, the concept of multilevel order parameters is employed. Conditions for circular and linear polarization of the transmitted light are determined and investigated.

© 2009 Optical Society of America

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    [CrossRef]
  3. P. S. Drzaic and A. M. Gonzales, “Refractive index gradients and light scattering in polymer-dispersed liquid crystal films,” Appl. Phys. Lett. 62, 1332-1334 (1993).
    [CrossRef]
  4. L. McKenna, L. S. Miller, and I. R. Peterson, “Polymer dispersed liquid crystal films for modulating infra-red radiation,” Polymer 45, 6977-6984 (2004).
    [CrossRef]
  5. S. Zumer, A. Golemme, and J. W. Doane, “Light extinction in a dispersion of small nematic droplets,” J. Opt. Soc. Am. A 6, 403-411 (1989).
    [CrossRef]
  6. P. J. W. Hands, A. K. Kirby, and G. D. Love, “Phase modulation with polymer-dispersed liquid crystals,” Proc. SPIE 5894, 193-200 (2005).
    [CrossRef]
  7. S. Matsumoto, M. Houlbert, T. Hayashi, and K.-i. Kubodera, “Fine droplets of liquid crystals in a transparent polymer and their response to an electric field,” Appl. Phys. Lett. 69, 1044-1046 (1996).
    [CrossRef]
  8. V. A. Loiko, A. V. Konkolovich, and P. G. Maksimenko, “Polarization and phase of light transmitted through polymer-dispersed liquid crystal film,” J. Soc. Inf. Disp. 14, 595-601(2006).
    [CrossRef]
  9. H. Ren, Y.-H. Fan, and S.-T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83, 1515-1517 (2003).
    [CrossRef]
  10. V. A. Loiko and A. V. Konkolovich, “Focusing of light by polymer-dispersed liquid-crystal films with nanosized droplets,” JETP 103, 935-943 (2006).
    [CrossRef]
  11. H. Ren, Y.-H. Fan, Y.-H. Lin, and S.-T. Wu, “Tunable-focus microlens arrays using nanosized polymer-dispersed liquid crystal droplets,” Opt. Commun. 247, 101-106 (2005).
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    [CrossRef]
  13. C. Levallois, V. Verbrugge, L. Dupont, J.-L. de Bougrenet de la Tocnaye, B. Caillaud, A. Le Corre, O. Dehaese, H. Folliot, and S. Loualiche, “1.55-μm optically pumped tunable VCSEL based on a nano-polymer dispersive liquid crystal phase modulator,” Proc. SPIE 6185, 61850W (2006).
    [CrossRef]
  14. F. Simoni, Nonlinear Optical Properties of Liquid Crystals (World Scientific, 1997).
  15. J. R. Kelly and P. Palffy-Muhoray, “The optical response of polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. 243, 11-29 (1994).
    [CrossRef]
  16. A. D. Kiselev, O. V. Yaroshchuk, and L. O. Dolgov, “Ordering of droplets and light scattering in polymer dispersed liquid crystal films,” J. Phys. Condens. Matter 16, 7183-7197 (2004).
    [CrossRef]
  17. A. Mertelj and M. Copic, “Anisotropic diffusion of light in polymer dispersed liquid crystals,” Phys. Rev. E 75, 011705 (2007).
    [CrossRef]
  18. F. Bloisi, C. Ruocchio, P. Terrecuso, and L. Vicari, “Optoelectronic polarizer by PDLC,” Liq. Cryst. 20, 377-379 (1996).
    [CrossRef]
  19. I. Amimori, N. V. Priezjev, R. A. Pelcovits, and G. P. Crawford, “Optomechanical properties of stretched polymer dispersed liquid crystal films for scattering polarizer applications,” J. Appl. Phys. 93, 3248-3252 (2003).
    [CrossRef]
  20. V. A. Loiko and A. V. Konkolovich, “Phase change of a plane wave propagating through a polymer film with encapsulated nanodimensional nematic liquid crystal particles,” JETP 96, 489-495 (2003).
    [CrossRef]
  21. V. A. Loiko, A. V. Konkolovich, A. A. Miskevich, and P. G. Maksimenko, “Propagation of light in the polymer dispersed liquid-crystal film with nanosized nematic droplets,” Proc. SPIE 6023, 49-58 (2005).
    [CrossRef]
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  24. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge U. Press, 2006).
  25. V. A. Loiko, P. G. Maksimenko, and A. V. Konkolovich, “A method for calculating the light extinction coefficients of a polymer layer with small nematic liquid-crystal droplets,” Opt. Spectrosc. 105, 791-797 (2008).
    [CrossRef]
  26. F. Basile, F. Bloisi, L. Vicari, and F. Simoni, “Optical phase shift of polymer-dispersed liquid crystals,” Phys. Rev. E 48, 432-438 (1993).
    [CrossRef]
  27. A. P. Ivanov, V. A. Loiko, and V. P. Dick, Light Propagation in Densely Packed Disperse Media (Science & Technics, 1988).
  28. S. Zumer and J. W. Doane, “Light scattering from a small nematic droplet,” Phys. Rev. A 34, 3373-3386 (1986).
    [CrossRef] [PubMed]

2008

V. A. Loiko, P. G. Maksimenko, and A. V. Konkolovich, “A method for calculating the light extinction coefficients of a polymer layer with small nematic liquid-crystal droplets,” Opt. Spectrosc. 105, 791-797 (2008).
[CrossRef]

2007

A. Mertelj and M. Copic, “Anisotropic diffusion of light in polymer dispersed liquid crystals,” Phys. Rev. E 75, 011705 (2007).
[CrossRef]

2006

V. A. Loiko, A. V. Konkolovich, and P. G. Maksimenko, “Polarization and phase of light transmitted through polymer-dispersed liquid crystal film,” J. Soc. Inf. Disp. 14, 595-601(2006).
[CrossRef]

V. A. Loiko and A. V. Konkolovich, “Focusing of light by polymer-dispersed liquid-crystal films with nanosized droplets,” JETP 103, 935-943 (2006).
[CrossRef]

C. Levallois, V. Verbrugge, L. Dupont, J.-L. de Bougrenet de la Tocnaye, B. Caillaud, A. Le Corre, O. Dehaese, H. Folliot, and S. Loualiche, “1.55-μm optically pumped tunable VCSEL based on a nano-polymer dispersive liquid crystal phase modulator,” Proc. SPIE 6185, 61850W (2006).
[CrossRef]

2005

H. Ren, Y.-H. Fan, Y.-H. Lin, and S.-T. Wu, “Tunable-focus microlens arrays using nanosized polymer-dispersed liquid crystal droplets,” Opt. Commun. 247, 101-106 (2005).
[CrossRef]

P. J. W. Hands, A. K. Kirby, and G. D. Love, “Phase modulation with polymer-dispersed liquid crystals,” Proc. SPIE 5894, 193-200 (2005).
[CrossRef]

V. A. Loiko, A. V. Konkolovich, A. A. Miskevich, and P. G. Maksimenko, “Propagation of light in the polymer dispersed liquid-crystal film with nanosized nematic droplets,” Proc. SPIE 6023, 49-58 (2005).
[CrossRef]

2004

A. D. Kiselev, O. V. Yaroshchuk, and L. O. Dolgov, “Ordering of droplets and light scattering in polymer dispersed liquid crystal films,” J. Phys. Condens. Matter 16, 7183-7197 (2004).
[CrossRef]

S. Gottardo, S. Cavalieri, O. V. Yaroshchuk, and D. S. Wiersma, “Quasi-two-dimensional diffusive random laser action,” Phys. Rev. Lett. 93, 263901 (2004).
[CrossRef]

L. McKenna, L. S. Miller, and I. R. Peterson, “Polymer dispersed liquid crystal films for modulating infra-red radiation,” Polymer 45, 6977-6984 (2004).
[CrossRef]

2003

H. Ren, Y.-H. Fan, and S.-T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83, 1515-1517 (2003).
[CrossRef]

I. Amimori, N. V. Priezjev, R. A. Pelcovits, and G. P. Crawford, “Optomechanical properties of stretched polymer dispersed liquid crystal films for scattering polarizer applications,” J. Appl. Phys. 93, 3248-3252 (2003).
[CrossRef]

V. A. Loiko and A. V. Konkolovich, “Phase change of a plane wave propagating through a polymer film with encapsulated nanodimensional nematic liquid crystal particles,” JETP 96, 489-495 (2003).
[CrossRef]

1996

F. Bloisi, C. Ruocchio, P. Terrecuso, and L. Vicari, “Optoelectronic polarizer by PDLC,” Liq. Cryst. 20, 377-379 (1996).
[CrossRef]

S. Matsumoto, M. Houlbert, T. Hayashi, and K.-i. Kubodera, “Fine droplets of liquid crystals in a transparent polymer and their response to an electric field,” Appl. Phys. Lett. 69, 1044-1046 (1996).
[CrossRef]

1994

J. R. Kelly and P. Palffy-Muhoray, “The optical response of polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. 243, 11-29 (1994).
[CrossRef]

1993

F. Basile, F. Bloisi, L. Vicari, and F. Simoni, “Optical phase shift of polymer-dispersed liquid crystals,” Phys. Rev. E 48, 432-438 (1993).
[CrossRef]

P. S. Drzaic and A. M. Gonzales, “Refractive index gradients and light scattering in polymer-dispersed liquid crystal films,” Appl. Phys. Lett. 62, 1332-1334 (1993).
[CrossRef]

1989

B.-G. Wu, J. H. Erdman, and J. W. Doane, “Response times and voltages for PDLC shutters,” Liq. Cryst. 5, 1453-1465 (1989).
[CrossRef]

S. Zumer, A. Golemme, and J. W. Doane, “Light extinction in a dispersion of small nematic droplets,” J. Opt. Soc. Am. A 6, 403-411 (1989).
[CrossRef]

1986

S. Zumer and J. W. Doane, “Light scattering from a small nematic droplet,” Phys. Rev. A 34, 3373-3386 (1986).
[CrossRef] [PubMed]

Amimori, I.

I. Amimori, N. V. Priezjev, R. A. Pelcovits, and G. P. Crawford, “Optomechanical properties of stretched polymer dispersed liquid crystal films for scattering polarizer applications,” J. Appl. Phys. 93, 3248-3252 (2003).
[CrossRef]

Basile, F.

F. Basile, F. Bloisi, L. Vicari, and F. Simoni, “Optical phase shift of polymer-dispersed liquid crystals,” Phys. Rev. E 48, 432-438 (1993).
[CrossRef]

Bloisi, F.

F. Bloisi, C. Ruocchio, P. Terrecuso, and L. Vicari, “Optoelectronic polarizer by PDLC,” Liq. Cryst. 20, 377-379 (1996).
[CrossRef]

F. Basile, F. Bloisi, L. Vicari, and F. Simoni, “Optical phase shift of polymer-dispersed liquid crystals,” Phys. Rev. E 48, 432-438 (1993).
[CrossRef]

Caillaud, B.

C. Levallois, V. Verbrugge, L. Dupont, J.-L. de Bougrenet de la Tocnaye, B. Caillaud, A. Le Corre, O. Dehaese, H. Folliot, and S. Loualiche, “1.55-μm optically pumped tunable VCSEL based on a nano-polymer dispersive liquid crystal phase modulator,” Proc. SPIE 6185, 61850W (2006).
[CrossRef]

Cavalieri, S.

S. Gottardo, S. Cavalieri, O. V. Yaroshchuk, and D. S. Wiersma, “Quasi-two-dimensional diffusive random laser action,” Phys. Rev. Lett. 93, 263901 (2004).
[CrossRef]

Copic, M.

A. Mertelj and M. Copic, “Anisotropic diffusion of light in polymer dispersed liquid crystals,” Phys. Rev. E 75, 011705 (2007).
[CrossRef]

Crawford, G. P.

I. Amimori, N. V. Priezjev, R. A. Pelcovits, and G. P. Crawford, “Optomechanical properties of stretched polymer dispersed liquid crystal films for scattering polarizer applications,” J. Appl. Phys. 93, 3248-3252 (2003).
[CrossRef]

de Bougrenet de la Tocnaye, J.-L.

C. Levallois, V. Verbrugge, L. Dupont, J.-L. de Bougrenet de la Tocnaye, B. Caillaud, A. Le Corre, O. Dehaese, H. Folliot, and S. Loualiche, “1.55-μm optically pumped tunable VCSEL based on a nano-polymer dispersive liquid crystal phase modulator,” Proc. SPIE 6185, 61850W (2006).
[CrossRef]

Dehaese, O.

C. Levallois, V. Verbrugge, L. Dupont, J.-L. de Bougrenet de la Tocnaye, B. Caillaud, A. Le Corre, O. Dehaese, H. Folliot, and S. Loualiche, “1.55-μm optically pumped tunable VCSEL based on a nano-polymer dispersive liquid crystal phase modulator,” Proc. SPIE 6185, 61850W (2006).
[CrossRef]

Dick, V. P.

A. P. Ivanov, V. A. Loiko, and V. P. Dick, Light Propagation in Densely Packed Disperse Media (Science & Technics, 1988).

Doane, J. W.

S. Zumer, A. Golemme, and J. W. Doane, “Light extinction in a dispersion of small nematic droplets,” J. Opt. Soc. Am. A 6, 403-411 (1989).
[CrossRef]

B.-G. Wu, J. H. Erdman, and J. W. Doane, “Response times and voltages for PDLC shutters,” Liq. Cryst. 5, 1453-1465 (1989).
[CrossRef]

S. Zumer and J. W. Doane, “Light scattering from a small nematic droplet,” Phys. Rev. A 34, 3373-3386 (1986).
[CrossRef] [PubMed]

Dolgov, L. O.

A. D. Kiselev, O. V. Yaroshchuk, and L. O. Dolgov, “Ordering of droplets and light scattering in polymer dispersed liquid crystal films,” J. Phys. Condens. Matter 16, 7183-7197 (2004).
[CrossRef]

Drzaic, P. S.

P. S. Drzaic and A. M. Gonzales, “Refractive index gradients and light scattering in polymer-dispersed liquid crystal films,” Appl. Phys. Lett. 62, 1332-1334 (1993).
[CrossRef]

P. S. Drzaic, Liquid Crystal Dispersions (World Scientific, 1995).

Dupont, L.

C. Levallois, V. Verbrugge, L. Dupont, J.-L. de Bougrenet de la Tocnaye, B. Caillaud, A. Le Corre, O. Dehaese, H. Folliot, and S. Loualiche, “1.55-μm optically pumped tunable VCSEL based on a nano-polymer dispersive liquid crystal phase modulator,” Proc. SPIE 6185, 61850W (2006).
[CrossRef]

Erdman, J. H.

B.-G. Wu, J. H. Erdman, and J. W. Doane, “Response times and voltages for PDLC shutters,” Liq. Cryst. 5, 1453-1465 (1989).
[CrossRef]

Fan, Y.-H.

H. Ren, Y.-H. Fan, Y.-H. Lin, and S.-T. Wu, “Tunable-focus microlens arrays using nanosized polymer-dispersed liquid crystal droplets,” Opt. Commun. 247, 101-106 (2005).
[CrossRef]

H. Ren, Y.-H. Fan, and S.-T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83, 1515-1517 (2003).
[CrossRef]

Folliot, H.

C. Levallois, V. Verbrugge, L. Dupont, J.-L. de Bougrenet de la Tocnaye, B. Caillaud, A. Le Corre, O. Dehaese, H. Folliot, and S. Loualiche, “1.55-μm optically pumped tunable VCSEL based on a nano-polymer dispersive liquid crystal phase modulator,” Proc. SPIE 6185, 61850W (2006).
[CrossRef]

Golemme, A.

Gonzales, A. M.

P. S. Drzaic and A. M. Gonzales, “Refractive index gradients and light scattering in polymer-dispersed liquid crystal films,” Appl. Phys. Lett. 62, 1332-1334 (1993).
[CrossRef]

Gottardo, S.

S. Gottardo, S. Cavalieri, O. V. Yaroshchuk, and D. S. Wiersma, “Quasi-two-dimensional diffusive random laser action,” Phys. Rev. Lett. 93, 263901 (2004).
[CrossRef]

Hands, P. J. W.

P. J. W. Hands, A. K. Kirby, and G. D. Love, “Phase modulation with polymer-dispersed liquid crystals,” Proc. SPIE 5894, 193-200 (2005).
[CrossRef]

Hayashi, T.

S. Matsumoto, M. Houlbert, T. Hayashi, and K.-i. Kubodera, “Fine droplets of liquid crystals in a transparent polymer and their response to an electric field,” Appl. Phys. Lett. 69, 1044-1046 (1996).
[CrossRef]

Houlbert, M.

S. Matsumoto, M. Houlbert, T. Hayashi, and K.-i. Kubodera, “Fine droplets of liquid crystals in a transparent polymer and their response to an electric field,” Appl. Phys. Lett. 69, 1044-1046 (1996).
[CrossRef]

Isimaru, A.

A. Isimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

Ivanov, A. P.

A. P. Ivanov, V. A. Loiko, and V. P. Dick, Light Propagation in Densely Packed Disperse Media (Science & Technics, 1988).

Kelly, J. R.

J. R. Kelly and P. Palffy-Muhoray, “The optical response of polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. 243, 11-29 (1994).
[CrossRef]

Kirby, A. K.

P. J. W. Hands, A. K. Kirby, and G. D. Love, “Phase modulation with polymer-dispersed liquid crystals,” Proc. SPIE 5894, 193-200 (2005).
[CrossRef]

Kiselev, A. D.

A. D. Kiselev, O. V. Yaroshchuk, and L. O. Dolgov, “Ordering of droplets and light scattering in polymer dispersed liquid crystal films,” J. Phys. Condens. Matter 16, 7183-7197 (2004).
[CrossRef]

Konkolovich, A. V.

V. A. Loiko, P. G. Maksimenko, and A. V. Konkolovich, “A method for calculating the light extinction coefficients of a polymer layer with small nematic liquid-crystal droplets,” Opt. Spectrosc. 105, 791-797 (2008).
[CrossRef]

V. A. Loiko and A. V. Konkolovich, “Focusing of light by polymer-dispersed liquid-crystal films with nanosized droplets,” JETP 103, 935-943 (2006).
[CrossRef]

V. A. Loiko, A. V. Konkolovich, and P. G. Maksimenko, “Polarization and phase of light transmitted through polymer-dispersed liquid crystal film,” J. Soc. Inf. Disp. 14, 595-601(2006).
[CrossRef]

V. A. Loiko, A. V. Konkolovich, A. A. Miskevich, and P. G. Maksimenko, “Propagation of light in the polymer dispersed liquid-crystal film with nanosized nematic droplets,” Proc. SPIE 6023, 49-58 (2005).
[CrossRef]

V. A. Loiko and A. V. Konkolovich, “Phase change of a plane wave propagating through a polymer film with encapsulated nanodimensional nematic liquid crystal particles,” JETP 96, 489-495 (2003).
[CrossRef]

Kubodera, K.-i.

S. Matsumoto, M. Houlbert, T. Hayashi, and K.-i. Kubodera, “Fine droplets of liquid crystals in a transparent polymer and their response to an electric field,” Appl. Phys. Lett. 69, 1044-1046 (1996).
[CrossRef]

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge U. Press, 2006).

Le Corre, A.

C. Levallois, V. Verbrugge, L. Dupont, J.-L. de Bougrenet de la Tocnaye, B. Caillaud, A. Le Corre, O. Dehaese, H. Folliot, and S. Loualiche, “1.55-μm optically pumped tunable VCSEL based on a nano-polymer dispersive liquid crystal phase modulator,” Proc. SPIE 6185, 61850W (2006).
[CrossRef]

Levallois, C.

C. Levallois, V. Verbrugge, L. Dupont, J.-L. de Bougrenet de la Tocnaye, B. Caillaud, A. Le Corre, O. Dehaese, H. Folliot, and S. Loualiche, “1.55-μm optically pumped tunable VCSEL based on a nano-polymer dispersive liquid crystal phase modulator,” Proc. SPIE 6185, 61850W (2006).
[CrossRef]

Lin, Y.-H.

H. Ren, Y.-H. Fan, Y.-H. Lin, and S.-T. Wu, “Tunable-focus microlens arrays using nanosized polymer-dispersed liquid crystal droplets,” Opt. Commun. 247, 101-106 (2005).
[CrossRef]

Loiko, V. A.

V. A. Loiko, P. G. Maksimenko, and A. V. Konkolovich, “A method for calculating the light extinction coefficients of a polymer layer with small nematic liquid-crystal droplets,” Opt. Spectrosc. 105, 791-797 (2008).
[CrossRef]

V. A. Loiko and A. V. Konkolovich, “Focusing of light by polymer-dispersed liquid-crystal films with nanosized droplets,” JETP 103, 935-943 (2006).
[CrossRef]

V. A. Loiko, A. V. Konkolovich, and P. G. Maksimenko, “Polarization and phase of light transmitted through polymer-dispersed liquid crystal film,” J. Soc. Inf. Disp. 14, 595-601(2006).
[CrossRef]

V. A. Loiko, A. V. Konkolovich, A. A. Miskevich, and P. G. Maksimenko, “Propagation of light in the polymer dispersed liquid-crystal film with nanosized nematic droplets,” Proc. SPIE 6023, 49-58 (2005).
[CrossRef]

V. A. Loiko and A. V. Konkolovich, “Phase change of a plane wave propagating through a polymer film with encapsulated nanodimensional nematic liquid crystal particles,” JETP 96, 489-495 (2003).
[CrossRef]

A. P. Ivanov, V. A. Loiko, and V. P. Dick, Light Propagation in Densely Packed Disperse Media (Science & Technics, 1988).

Loualiche, S.

C. Levallois, V. Verbrugge, L. Dupont, J.-L. de Bougrenet de la Tocnaye, B. Caillaud, A. Le Corre, O. Dehaese, H. Folliot, and S. Loualiche, “1.55-μm optically pumped tunable VCSEL based on a nano-polymer dispersive liquid crystal phase modulator,” Proc. SPIE 6185, 61850W (2006).
[CrossRef]

Love, G. D.

P. J. W. Hands, A. K. Kirby, and G. D. Love, “Phase modulation with polymer-dispersed liquid crystals,” Proc. SPIE 5894, 193-200 (2005).
[CrossRef]

Maksimenko, P. G.

V. A. Loiko, P. G. Maksimenko, and A. V. Konkolovich, “A method for calculating the light extinction coefficients of a polymer layer with small nematic liquid-crystal droplets,” Opt. Spectrosc. 105, 791-797 (2008).
[CrossRef]

V. A. Loiko, A. V. Konkolovich, and P. G. Maksimenko, “Polarization and phase of light transmitted through polymer-dispersed liquid crystal film,” J. Soc. Inf. Disp. 14, 595-601(2006).
[CrossRef]

V. A. Loiko, A. V. Konkolovich, A. A. Miskevich, and P. G. Maksimenko, “Propagation of light in the polymer dispersed liquid-crystal film with nanosized nematic droplets,” Proc. SPIE 6023, 49-58 (2005).
[CrossRef]

Matsumoto, S.

S. Matsumoto, M. Houlbert, T. Hayashi, and K.-i. Kubodera, “Fine droplets of liquid crystals in a transparent polymer and their response to an electric field,” Appl. Phys. Lett. 69, 1044-1046 (1996).
[CrossRef]

McKenna, L.

L. McKenna, L. S. Miller, and I. R. Peterson, “Polymer dispersed liquid crystal films for modulating infra-red radiation,” Polymer 45, 6977-6984 (2004).
[CrossRef]

Mertelj, A.

A. Mertelj and M. Copic, “Anisotropic diffusion of light in polymer dispersed liquid crystals,” Phys. Rev. E 75, 011705 (2007).
[CrossRef]

Miller, L. S.

L. McKenna, L. S. Miller, and I. R. Peterson, “Polymer dispersed liquid crystal films for modulating infra-red radiation,” Polymer 45, 6977-6984 (2004).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge U. Press, 2006).

Miskevich, A. A.

V. A. Loiko, A. V. Konkolovich, A. A. Miskevich, and P. G. Maksimenko, “Propagation of light in the polymer dispersed liquid-crystal film with nanosized nematic droplets,” Proc. SPIE 6023, 49-58 (2005).
[CrossRef]

Palffy-Muhoray, P.

J. R. Kelly and P. Palffy-Muhoray, “The optical response of polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. 243, 11-29 (1994).
[CrossRef]

Pelcovits, R. A.

I. Amimori, N. V. Priezjev, R. A. Pelcovits, and G. P. Crawford, “Optomechanical properties of stretched polymer dispersed liquid crystal films for scattering polarizer applications,” J. Appl. Phys. 93, 3248-3252 (2003).
[CrossRef]

Peterson, I. R.

L. McKenna, L. S. Miller, and I. R. Peterson, “Polymer dispersed liquid crystal films for modulating infra-red radiation,” Polymer 45, 6977-6984 (2004).
[CrossRef]

Priezjev, N. V.

I. Amimori, N. V. Priezjev, R. A. Pelcovits, and G. P. Crawford, “Optomechanical properties of stretched polymer dispersed liquid crystal films for scattering polarizer applications,” J. Appl. Phys. 93, 3248-3252 (2003).
[CrossRef]

Ren, H.

H. Ren, Y.-H. Fan, Y.-H. Lin, and S.-T. Wu, “Tunable-focus microlens arrays using nanosized polymer-dispersed liquid crystal droplets,” Opt. Commun. 247, 101-106 (2005).
[CrossRef]

H. Ren, Y.-H. Fan, and S.-T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83, 1515-1517 (2003).
[CrossRef]

Ruocchio, C.

F. Bloisi, C. Ruocchio, P. Terrecuso, and L. Vicari, “Optoelectronic polarizer by PDLC,” Liq. Cryst. 20, 377-379 (1996).
[CrossRef]

Simoni, F.

F. Basile, F. Bloisi, L. Vicari, and F. Simoni, “Optical phase shift of polymer-dispersed liquid crystals,” Phys. Rev. E 48, 432-438 (1993).
[CrossRef]

F. Simoni, Nonlinear Optical Properties of Liquid Crystals (World Scientific, 1997).

Terrecuso, P.

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[CrossRef]

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge U. Press, 2006).

van de Hulst, G.

G. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).

Verbrugge, V.

C. Levallois, V. Verbrugge, L. Dupont, J.-L. de Bougrenet de la Tocnaye, B. Caillaud, A. Le Corre, O. Dehaese, H. Folliot, and S. Loualiche, “1.55-μm optically pumped tunable VCSEL based on a nano-polymer dispersive liquid crystal phase modulator,” Proc. SPIE 6185, 61850W (2006).
[CrossRef]

Vicari, L.

F. Bloisi, C. Ruocchio, P. Terrecuso, and L. Vicari, “Optoelectronic polarizer by PDLC,” Liq. Cryst. 20, 377-379 (1996).
[CrossRef]

F. Basile, F. Bloisi, L. Vicari, and F. Simoni, “Optical phase shift of polymer-dispersed liquid crystals,” Phys. Rev. E 48, 432-438 (1993).
[CrossRef]

Wiersma, D. S.

S. Gottardo, S. Cavalieri, O. V. Yaroshchuk, and D. S. Wiersma, “Quasi-two-dimensional diffusive random laser action,” Phys. Rev. Lett. 93, 263901 (2004).
[CrossRef]

Wu, B.-G.

B.-G. Wu, J. H. Erdman, and J. W. Doane, “Response times and voltages for PDLC shutters,” Liq. Cryst. 5, 1453-1465 (1989).
[CrossRef]

Wu, S.-T.

H. Ren, Y.-H. Fan, Y.-H. Lin, and S.-T. Wu, “Tunable-focus microlens arrays using nanosized polymer-dispersed liquid crystal droplets,” Opt. Commun. 247, 101-106 (2005).
[CrossRef]

H. Ren, Y.-H. Fan, and S.-T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83, 1515-1517 (2003).
[CrossRef]

Yaroshchuk, O. V.

S. Gottardo, S. Cavalieri, O. V. Yaroshchuk, and D. S. Wiersma, “Quasi-two-dimensional diffusive random laser action,” Phys. Rev. Lett. 93, 263901 (2004).
[CrossRef]

A. D. Kiselev, O. V. Yaroshchuk, and L. O. Dolgov, “Ordering of droplets and light scattering in polymer dispersed liquid crystal films,” J. Phys. Condens. Matter 16, 7183-7197 (2004).
[CrossRef]

Zumer, S.

Appl. Phys. Lett.

H. Ren, Y.-H. Fan, and S.-T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83, 1515-1517 (2003).
[CrossRef]

S. Matsumoto, M. Houlbert, T. Hayashi, and K.-i. Kubodera, “Fine droplets of liquid crystals in a transparent polymer and their response to an electric field,” Appl. Phys. Lett. 69, 1044-1046 (1996).
[CrossRef]

P. S. Drzaic and A. M. Gonzales, “Refractive index gradients and light scattering in polymer-dispersed liquid crystal films,” Appl. Phys. Lett. 62, 1332-1334 (1993).
[CrossRef]

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I. Amimori, N. V. Priezjev, R. A. Pelcovits, and G. P. Crawford, “Optomechanical properties of stretched polymer dispersed liquid crystal films for scattering polarizer applications,” J. Appl. Phys. 93, 3248-3252 (2003).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. Condens. Matter

A. D. Kiselev, O. V. Yaroshchuk, and L. O. Dolgov, “Ordering of droplets and light scattering in polymer dispersed liquid crystal films,” J. Phys. Condens. Matter 16, 7183-7197 (2004).
[CrossRef]

J. Soc. Inf. Disp.

V. A. Loiko, A. V. Konkolovich, and P. G. Maksimenko, “Polarization and phase of light transmitted through polymer-dispersed liquid crystal film,” J. Soc. Inf. Disp. 14, 595-601(2006).
[CrossRef]

JETP

V. A. Loiko and A. V. Konkolovich, “Focusing of light by polymer-dispersed liquid-crystal films with nanosized droplets,” JETP 103, 935-943 (2006).
[CrossRef]

V. A. Loiko and A. V. Konkolovich, “Phase change of a plane wave propagating through a polymer film with encapsulated nanodimensional nematic liquid crystal particles,” JETP 96, 489-495 (2003).
[CrossRef]

Liq. Cryst.

F. Bloisi, C. Ruocchio, P. Terrecuso, and L. Vicari, “Optoelectronic polarizer by PDLC,” Liq. Cryst. 20, 377-379 (1996).
[CrossRef]

B.-G. Wu, J. H. Erdman, and J. W. Doane, “Response times and voltages for PDLC shutters,” Liq. Cryst. 5, 1453-1465 (1989).
[CrossRef]

Mol. Cryst. Liq. Cryst.

J. R. Kelly and P. Palffy-Muhoray, “The optical response of polymer dispersed liquid crystals,” Mol. Cryst. Liq. Cryst. 243, 11-29 (1994).
[CrossRef]

Opt. Commun.

H. Ren, Y.-H. Fan, Y.-H. Lin, and S.-T. Wu, “Tunable-focus microlens arrays using nanosized polymer-dispersed liquid crystal droplets,” Opt. Commun. 247, 101-106 (2005).
[CrossRef]

Opt. Spectrosc.

V. A. Loiko, P. G. Maksimenko, and A. V. Konkolovich, “A method for calculating the light extinction coefficients of a polymer layer with small nematic liquid-crystal droplets,” Opt. Spectrosc. 105, 791-797 (2008).
[CrossRef]

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[CrossRef] [PubMed]

Phys. Rev. E

F. Basile, F. Bloisi, L. Vicari, and F. Simoni, “Optical phase shift of polymer-dispersed liquid crystals,” Phys. Rev. E 48, 432-438 (1993).
[CrossRef]

A. Mertelj and M. Copic, “Anisotropic diffusion of light in polymer dispersed liquid crystals,” Phys. Rev. E 75, 011705 (2007).
[CrossRef]

Phys. Rev. Lett.

S. Gottardo, S. Cavalieri, O. V. Yaroshchuk, and D. S. Wiersma, “Quasi-two-dimensional diffusive random laser action,” Phys. Rev. Lett. 93, 263901 (2004).
[CrossRef]

Polymer

L. McKenna, L. S. Miller, and I. R. Peterson, “Polymer dispersed liquid crystal films for modulating infra-red radiation,” Polymer 45, 6977-6984 (2004).
[CrossRef]

Proc. SPIE

C. Levallois, V. Verbrugge, L. Dupont, J.-L. de Bougrenet de la Tocnaye, B. Caillaud, A. Le Corre, O. Dehaese, H. Folliot, and S. Loualiche, “1.55-μm optically pumped tunable VCSEL based on a nano-polymer dispersive liquid crystal phase modulator,” Proc. SPIE 6185, 61850W (2006).
[CrossRef]

P. J. W. Hands, A. K. Kirby, and G. D. Love, “Phase modulation with polymer-dispersed liquid crystals,” Proc. SPIE 5894, 193-200 (2005).
[CrossRef]

V. A. Loiko, A. V. Konkolovich, A. A. Miskevich, and P. G. Maksimenko, “Propagation of light in the polymer dispersed liquid-crystal film with nanosized nematic droplets,” Proc. SPIE 6023, 49-58 (2005).
[CrossRef]

Other

G. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).

A. Isimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge U. Press, 2006).

A. P. Ivanov, V. A. Loiko, and V. P. Dick, Light Propagation in Densely Packed Disperse Media (Science & Technics, 1988).

F. Simoni, Nonlinear Optical Properties of Liquid Crystals (World Scientific, 1997).

P. S. Drzaic, Liquid Crystal Dispersions (World Scientific, 1995).

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Figures (8)

Fig. 1
Fig. 1

Schematic representation of the laboratory frame, the scattering plane, and the eigenvectors relevant to the problem under consideration.

Fig. 2
Fig. 2

Phase shift Δ Φ n between extraordinary and ordinary waves versus the applied electric field strength at 1, θ d max = φ d max = 5 ° ; 2, θ d max = 45 ° and φ d max = 5 ° ; 3, θ d max = 5 ° and φ d max = 45 ° ; 4, θ d max = φ d max = 45 ° .

Fig. 3
Fig. 3

Schematic representation of the experimental setup in [7].

Fig. 4
Fig. 4

Output power versus applied electric field strength. Theoretical results obtained by our model (curves) in comparison with the experimental data of [7] (symbols).

Fig. 5
Fig. 5

Phase shift Δ Φ n between extraordinary and ordinary waves (dashed curve); ellipticity η (thin solid curve); and azimuth ξ (bold solid curve) of transmitted light versus applied electric field strength.

Fig. 6
Fig. 6

Polarization angle ξ lin of the transmitted linearly polarized light versus the average LC droplet radius R at different polarization angles of incident light.

Fig. 7
Fig. 7

(a) Ellipticity η versus polarization angle α of the incident light and the applied electric field strength. (b) Plane ( η , α ) projection of (a).

Fig. 8
Fig. 8

Polarization angle of incident light α circ at which the transmitted light is circularly polarized versus the average LC droplet radius R .

Equations (53)

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( E s · e s E s · e ) = exp ( i k r ) i k r ( S 2 S 3 S 4 S 1 ) ( E i · e i E i · e ) .
S 1 = i k 3 4 π f [ ε d o ε p 1 + Δ ε d ε p ( e · e d ) 2 ] ,
S 2 = i k 3 4 π f [ ( ε d o ε p 1 ) e i · e s + Δ ε d ε p ( e s · e d ) ( e i · e d ) ] ,
S 3 = i k 3 4 π f Δ ε d ε p ( e s · e d ) ( e · e d ) ,
S 4 = i k 3 4 π f Δ ε d ε p ( e i · e d ) ( e · e d ) ,
ε d o = 1 3 ( 2 ε o + ε e Δ ε d ) ,
Δ ε d = ( ε e ε o ) S S d ,
f = 4 π a 3 ( sin a R a R cos a R ) .
( E s · e s E s · e ) = ( Ψ 2 Ψ 3 Ψ 4 Ψ 1 ) ( E i · e i E i · e ) ,
Ψ 1 , 2 = exp [ i k l ( 1 + i 2 π N k 3 S 1 , 2 ( 0 ) ) ] ,
Ψ 3 , 4 = 0 .
E s e = Re ( E s · e e E i exp ( i k l ) ) = 1 E i exp ( 1 2 γ e l ) cos Φ e ( E i · e e ) ,
E s o = Re ( E s · e o E i exp ( i k l ) ) = 1 E i exp ( 1 2 γ o l ) cos Φ o ( E i · e o ) .
γ e , o = 4 π N k 2 Re S 2 , 1 ( 0 ) ,
Φ e , o = 2 π N l k 2 Im S 2 , 1 ( 0 ) .
Δ Φ = Φ o Φ e = L k c v 2 cos θ i Δ ε d ε p [ ( e e · e d ) 2 ( e o · e d ) 2 ] .
Δ Φ n = L k c v 2 Δ ε d ε p [ sin 2 θ d cos 2 φ d sin 2 θ d sin 2 φ d ] ,
S i j = 1 2 3 ( e d ) i ( e d ) j δ i j ,
S ^ = 1 2 [ 3 sin 2 θ d cos 2 φ d 1 0 0 0 3 sin 2 θ d sin 2 φ d 1 0 0 0 3 cos 2 θ d 1 ] .
S x = 1 2 ( ( 1 S z ) sin 2 φ d max 2 φ d max S z ) ,
S y = 1 2 ( ( S z 1 ) sin 2 φ d max 2 φ d max S z ) .
S z = 1 4 + 3 4 ( u 4 E 2 + 3 E 4 2 E 2 1 16 E 3 sin θ d max ln | u + 2 E sin θ d max u 2 E sin θ d max | ) ,
u = ( E 2 1 ) 2 + 4 E 2 sin 2 θ d max .
Δ Φ n = L k c v 3 Δ ε d ε p sin 2 φ d max 2 φ d max [ 1 S z ] .
γ e , o = N 4 π d σ d Ω ( e = e e , o ) sin θ s d θ s d φ s .
d σ d Ω = 1 k 2 ( | S 2 e · e i + S 3 e · e | 2 + | S 4 e · e i + S 1 e · e | 2 ) .
( d σ d Ω ) e ( 1 ) = ( d σ d Ω ( e = e e ) ) ( 1 ) = 1 k 2 ( | S 2 ( 1 ) | 2 + | S 4 ( 1 ) | 2 ) ,
( d σ d Ω ) o ( 1 ) = ( d σ d Ω ( e = e o ) ) ( 1 ) = 1 k 2 ( | S 3 ( 1 ) | 2 + | S 1 ( 1 ) | 2 ) .
( d σ d Ω ) e ( 2 ) = ( d σ d Ω ( e = e e ) ) ( 2 ) = 1 k 2 ( | S 3 ( 2 ) | 2 + | S 1 ( 2 ) | 2 ) ,
( d σ d Ω ) o ( 2 ) = ( d σ d Ω ( e = e o ) ) ( 2 ) = 1 k 2 ( | S 2 ( 2 ) | 2 + | S 4 ( 2 ) | 2 ) .
γ e , o eff = π N 0 π [ ( d σ d Ω ) e , o ( 1 ) + ( d σ d Ω ) e , o ( 2 ) ] sin θ s d θ s .
γ e , o eff = N k 4 g 16 π ( ε d o ε p 1 + Δ ε d 3 ε p ( 1 + 2 S x , y ) ) 2 ,
g = 0 π f 2 ( cos 2 θ s + 1 ) sin θ s d θ s .
ρ μ ( R ) = μ μ R μ 1 R μ Γ ( μ ) exp ( μ R R ) ,
f = 4 π a 3 ( t 2 + 1 ) μ + 1 2 ( sin ( ( μ + 1 ) arctan t ) t ( μ + 1 ) t 2 + 1 cos ( ( μ + 2 ) arctan t ) ) ,
t = a R μ + 1 .
Δ Φ = l k c v 2 Δ ε d ε p [ cos 2 θ d sin 2 θ d cos 2 φ d ] .
Δ Φ = l k c v 2 Δ ε d ε p S z .
γ e eff = N k 4 32 π 2 ( ε d o ε p 1 + Δ ε d 3 ε p ( 1 + 2 S z ) ) 2 4 π ( f 1 2 sin 2 θ s + f 2 2 ) d Ω ,
γ o eff = N k 4 32 π 2 ( ε d o ε p 1 + Δ ε d 3 ε p ( 1 + 2 S x ) ) 2 4 π ( f 1 2 + f 2 2 sin 2 φ s ) d Ω .
a 1 = k 2 ( 1 sin θ s ) ,
a 2 = k 2 ( 1 sin φ s ) .
T = exp ( γ e eff l ) cos 4 α + exp ( γ o eff l ) sin 4 α + 1 2 exp ( 1 2 ( γ e eff + γ o eff ) l ) sin 2 2 α cos Δ Φ ,
T = sin 2 α cos 2 α ( exp ( γ e eff l ) + exp ( γ o eff l ) ) 1 2 exp ( 1 2 ( γ e eff + γ o eff ) l ) sin 2 2 α cos Δ Φ .
a e , o = t e , o ( cos α sin α ) .
t e , o = exp ( 1 2 γ e , o L ) .
( E x a e ) 2 + ( E y a o ) 2 2 E x E y a e a o cos Δ Φ n = sin 2 Δ Φ n .
A 2 = ( a e cos β ) 2 + ( a o sin β ) 2 + a e a o sin 2 β cos Δ Φ n ,
B 2 = ( a e sin β ) 2 + ( a o cos β ) 2 a e a o sin 2 β cos Δ Φ n ,
tan 2 β = 2 a e a o a e 2 a o 2 cos Δ Φ n .
η = ( a e sin ξ ) 2 + ( a o cos ξ ) 2 a e a o sin 2 ξ cos Δ Φ n ( a e cos ξ ) 2 + ( a o sin ξ ) 2 + a e a o sin 2 ξ cos Δ Φ n .
tan ξ lin = ( 1 ) n { exp [ k 3 g n 8 V ( ε d o ε p 1 + 2 n π φ d max L k c v sin ( 2 φ d max ) ) ] tan α } .
α circ = arctan { exp [ k 3 g ( n + 1 / 2 ) 8 V ( ε d o ε p 1 + π ( n + 1 / 2 ) φ d max l k c v sin ( 2 φ d max ) ) ] }

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