Abstract

Monte Carlo studies of the field-induced complex refractive index changes in nano-dispersed nematic liquid crystals (NLCs) exhibiting negative–positive refractive indices have been performed for various cases of applied field strengths and anchoring conditions over a broad spectral regime. The resultant field-induced spatially inhomogeneous molecular order and the corresponding metamaterial properties are obtained for various wavelengths and applied field strengths below and above the Freedericksz transition. In general, the director axis reorientation and the resultant refractive index distribution are spatially inhomogeneous, even under a uniform applied field. The detailed computations have identified parameter sets for obtaining the negative index of refraction and maximal index modulations that can be more than an order of magnitude larger than those obtainable from pure NLC systems.

© 2010 Optical Society of America

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  1. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  2. N. Engheta and R. W. Ziolkowski, Metamaterials: Physics and Engineering Explorations, (Wiley, 2006).
  3. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534-537 (2005).
    [CrossRef] [PubMed]
  4. V. M. Shalaev, W. S. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildeshev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30, 3356-3358 (2005).
    [CrossRef]
  5. E. Graugnard, J. S. King, S. Jain, C. J. Summers, Y. Zhang-Williams, and I. C. Khoo, “Electric field tuning of the Bragg peak in large-pore TiO2 inverse shell opals,” Phys. Rev. B 72, 233105 (2005).
    [CrossRef]
  6. S. Xiao, U. K. Chettiar, A. V. Kildishev, V. Drachev, I. C. Khoo, and V. M. Shalaev, “Tunable magnetic response of metamaterials,” Appl. Phys. Lett. 95033115 (2009).
    [CrossRef]
  7. J. A. Bossard, X. Liang, L. Li, D. H. Werner, B. Weiner, P. F. Cristman, A. Diaz, and I. C. Khoo “Tunable frequency selective surfaces and negative-zero-positive index metamaterials based on liquid crystals,” IEEE Trans. Antennas Propag. 56, 1308-1320 (2008).
    [CrossRef]
  8. X. Wang, D. H. Kwon, D. H. Werner, I. C. Khoo, A. Kildishev, and V. M. Shalaev, “Tunable optical negative-index metamaterials employing anisotropic liquid crystals,” Appl. Phys. Lett. 91, 143122 (2007).
    [CrossRef]
  9. M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coated nonmagnetic spheres with a negative index of refraction at infrared frequencies,” Phys. Rev. B 73, 045105 (2006).
    [CrossRef]
  10. Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Z. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90, 011112 (2007).
    [CrossRef]
  11. I. C. Khoo, A. Diaz, S. Kubo, J. Liou, M. Stinger, T. Mallouk, and J. H. Park, “Nano-dispersed organic liquid and liquid crystals for all-time-scales optical switching and tunable negative- and zero-index materials,” Mol. Cryst. Liq. Cryst. 485, 934-944 (2008).
    [CrossRef]
  12. I. C. Khoo, D. H. Werner, X. Liang, and A. Diaz, “Nanosphere dispersed liquid crystals for tunable negative-zero-positive index of refraction in the optical and terahertz regimes,” Opt. Lett. 31, 2592-2594 (2006).
    [CrossRef] [PubMed]
  13. I. C. Khoo, Liquid Crystals, 2nd ed. (Wiley, 2007).
    [CrossRef]
  14. I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471, 221-267 (2009).
    [CrossRef]
  15. G. Pawlik, A. C. Mitus, and A. Miniewicz, “Monte-Carlo simulations of refractive index changes in nematic liquid crystal upon spatially nonuniform illumination,” Opt. Commun. 182, 249-254 (2000).
    [CrossRef]
  16. K. Komorowska, G. Pawlik, A. C. Mitus, and A. Miniewicz, “Electro-optic phenomena in nematic liquid crystals studied experimentally and by Monte-Carlo simulations,” J. Appl. Phys. 90, 1836-1842 (2001).
    [CrossRef]
  17. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
    [CrossRef]
  18. J. C. Maxwell Garnett, “Colors in metal glasses and in metallic films,” Philos. Trans. R. Soc. London, Ser. A 203, 385-420 (1904).
    [CrossRef]
  19. C. A. Guérin, P. Mallet, and A. Sentenac, “Effective-medium theory for finite-size aggregates,” J. Opt. Soc. Am. A 23, 349-358 (2006).
    [CrossRef]
  20. P. A. Lebwohl and G. Lasher, “Nematic-liquid-crystal order--a Monte Carlo calculation,” Phys. Rev. A 6, 426-429 (1972).
    [CrossRef]
  21. A. Rapini and M. Papoular, “Distorsion d'une lamelle nematique sous champ magnetique conditions dancrage aux parois,” J. Phys. (France) 30, 54-56 (1969).
  22. M. Kaczmarek, A. Dyaduysha, S. Slussarenko, and I. C. Khoo, “The role of surface charge field in two-beam coupling in liquid crystal cells with photoconducting polymer layers,” J. Appl. Phys. 96, 2616-2623 (2004).
    [CrossRef]
  23. N. V. Tabiryan and C. Umeton, “Surface-activated photorefractive and electro-optics phenomena in liquid crystals,” J. Opt. Soc. Am. B 15, 1912-1917 (1998).
    [CrossRef]
  24. P. Allen and D. Tildesley, Computer Simulation of Liquids, (Clarendon Press, 1987).
  25. D. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, (Cambridge Univ. Press, 2000).
  26. W. Walasik, M. Jarema, G. Pawlik, A. C. Mitus and F. Kajzar, “Monte Carlo study of tunable negative-zero-positive index of refraction in nanosphere dispersed liquid crystals,” Proc. SPIE Vol. 7213, 72130A (2009).
    [CrossRef]

2009 (3)

S. Xiao, U. K. Chettiar, A. V. Kildishev, V. Drachev, I. C. Khoo, and V. M. Shalaev, “Tunable magnetic response of metamaterials,” Appl. Phys. Lett. 95033115 (2009).
[CrossRef]

I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471, 221-267 (2009).
[CrossRef]

W. Walasik, M. Jarema, G. Pawlik, A. C. Mitus and F. Kajzar, “Monte Carlo study of tunable negative-zero-positive index of refraction in nanosphere dispersed liquid crystals,” Proc. SPIE Vol. 7213, 72130A (2009).
[CrossRef]

2008 (2)

I. C. Khoo, A. Diaz, S. Kubo, J. Liou, M. Stinger, T. Mallouk, and J. H. Park, “Nano-dispersed organic liquid and liquid crystals for all-time-scales optical switching and tunable negative- and zero-index materials,” Mol. Cryst. Liq. Cryst. 485, 934-944 (2008).
[CrossRef]

J. A. Bossard, X. Liang, L. Li, D. H. Werner, B. Weiner, P. F. Cristman, A. Diaz, and I. C. Khoo “Tunable frequency selective surfaces and negative-zero-positive index metamaterials based on liquid crystals,” IEEE Trans. Antennas Propag. 56, 1308-1320 (2008).
[CrossRef]

2007 (2)

X. Wang, D. H. Kwon, D. H. Werner, I. C. Khoo, A. Kildishev, and V. M. Shalaev, “Tunable optical negative-index metamaterials employing anisotropic liquid crystals,” Appl. Phys. Lett. 91, 143122 (2007).
[CrossRef]

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Z. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

2006 (3)

2005 (3)

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534-537 (2005).
[CrossRef] [PubMed]

V. M. Shalaev, W. S. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildeshev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

E. Graugnard, J. S. King, S. Jain, C. J. Summers, Y. Zhang-Williams, and I. C. Khoo, “Electric field tuning of the Bragg peak in large-pore TiO2 inverse shell opals,” Phys. Rev. B 72, 233105 (2005).
[CrossRef]

2004 (1)

M. Kaczmarek, A. Dyaduysha, S. Slussarenko, and I. C. Khoo, “The role of surface charge field in two-beam coupling in liquid crystal cells with photoconducting polymer layers,” J. Appl. Phys. 96, 2616-2623 (2004).
[CrossRef]

2001 (1)

K. Komorowska, G. Pawlik, A. C. Mitus, and A. Miniewicz, “Electro-optic phenomena in nematic liquid crystals studied experimentally and by Monte-Carlo simulations,” J. Appl. Phys. 90, 1836-1842 (2001).
[CrossRef]

2000 (1)

G. Pawlik, A. C. Mitus, and A. Miniewicz, “Monte-Carlo simulations of refractive index changes in nematic liquid crystal upon spatially nonuniform illumination,” Opt. Commun. 182, 249-254 (2000).
[CrossRef]

1998 (1)

1972 (1)

P. A. Lebwohl and G. Lasher, “Nematic-liquid-crystal order--a Monte Carlo calculation,” Phys. Rev. A 6, 426-429 (1972).
[CrossRef]

1969 (1)

A. Rapini and M. Papoular, “Distorsion d'une lamelle nematique sous champ magnetique conditions dancrage aux parois,” J. Phys. (France) 30, 54-56 (1969).

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

1904 (1)

J. C. Maxwell Garnett, “Colors in metal glasses and in metallic films,” Philos. Trans. R. Soc. London, Ser. A 203, 385-420 (1904).
[CrossRef]

Aitchison, J. S.

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coated nonmagnetic spheres with a negative index of refraction at infrared frequencies,” Phys. Rev. B 73, 045105 (2006).
[CrossRef]

Allen, P.

P. Allen and D. Tildesley, Computer Simulation of Liquids, (Clarendon Press, 1987).

Binder, K.

D. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, (Cambridge Univ. Press, 2000).

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
[CrossRef]

Bossard, J. A.

J. A. Bossard, X. Liang, L. Li, D. H. Werner, B. Weiner, P. F. Cristman, A. Diaz, and I. C. Khoo “Tunable frequency selective surfaces and negative-zero-positive index metamaterials based on liquid crystals,” IEEE Trans. Antennas Propag. 56, 1308-1320 (2008).
[CrossRef]

Cai, W. S.

Chettiar, U. K.

S. Xiao, U. K. Chettiar, A. V. Kildishev, V. Drachev, I. C. Khoo, and V. M. Shalaev, “Tunable magnetic response of metamaterials,” Appl. Phys. Lett. 95033115 (2009).
[CrossRef]

V. M. Shalaev, W. S. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildeshev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

Cristman, P. F.

J. A. Bossard, X. Liang, L. Li, D. H. Werner, B. Weiner, P. F. Cristman, A. Diaz, and I. C. Khoo “Tunable frequency selective surfaces and negative-zero-positive index metamaterials based on liquid crystals,” IEEE Trans. Antennas Propag. 56, 1308-1320 (2008).
[CrossRef]

Diaz, A.

J. A. Bossard, X. Liang, L. Li, D. H. Werner, B. Weiner, P. F. Cristman, A. Diaz, and I. C. Khoo “Tunable frequency selective surfaces and negative-zero-positive index metamaterials based on liquid crystals,” IEEE Trans. Antennas Propag. 56, 1308-1320 (2008).
[CrossRef]

I. C. Khoo, A. Diaz, S. Kubo, J. Liou, M. Stinger, T. Mallouk, and J. H. Park, “Nano-dispersed organic liquid and liquid crystals for all-time-scales optical switching and tunable negative- and zero-index materials,” Mol. Cryst. Liq. Cryst. 485, 934-944 (2008).
[CrossRef]

I. C. Khoo, D. H. Werner, X. Liang, and A. Diaz, “Nanosphere dispersed liquid crystals for tunable negative-zero-positive index of refraction in the optical and terahertz regimes,” Opt. Lett. 31, 2592-2594 (2006).
[CrossRef] [PubMed]

Drachev, V.

S. Xiao, U. K. Chettiar, A. V. Kildishev, V. Drachev, I. C. Khoo, and V. M. Shalaev, “Tunable magnetic response of metamaterials,” Appl. Phys. Lett. 95033115 (2009).
[CrossRef]

Drachev, V. P.

Du, B.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Z. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

Dyaduysha, A.

M. Kaczmarek, A. Dyaduysha, S. Slussarenko, and I. C. Khoo, “The role of surface charge field in two-beam coupling in liquid crystal cells with photoconducting polymer layers,” J. Appl. Phys. 96, 2616-2623 (2004).
[CrossRef]

Engheta, N.

N. Engheta and R. W. Ziolkowski, Metamaterials: Physics and Engineering Explorations, (Wiley, 2006).

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534-537 (2005).
[CrossRef] [PubMed]

Graugnard, E.

E. Graugnard, J. S. King, S. Jain, C. J. Summers, Y. Zhang-Williams, and I. C. Khoo, “Electric field tuning of the Bragg peak in large-pore TiO2 inverse shell opals,” Phys. Rev. B 72, 233105 (2005).
[CrossRef]

Guérin, C. A.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
[CrossRef]

Jain, S.

E. Graugnard, J. S. King, S. Jain, C. J. Summers, Y. Zhang-Williams, and I. C. Khoo, “Electric field tuning of the Bragg peak in large-pore TiO2 inverse shell opals,” Phys. Rev. B 72, 233105 (2005).
[CrossRef]

Jarema, M.

W. Walasik, M. Jarema, G. Pawlik, A. C. Mitus and F. Kajzar, “Monte Carlo study of tunable negative-zero-positive index of refraction in nanosphere dispersed liquid crystals,” Proc. SPIE Vol. 7213, 72130A (2009).
[CrossRef]

Kaczmarek, M.

M. Kaczmarek, A. Dyaduysha, S. Slussarenko, and I. C. Khoo, “The role of surface charge field in two-beam coupling in liquid crystal cells with photoconducting polymer layers,” J. Appl. Phys. 96, 2616-2623 (2004).
[CrossRef]

Kajzar, F.

W. Walasik, M. Jarema, G. Pawlik, A. C. Mitus and F. Kajzar, “Monte Carlo study of tunable negative-zero-positive index of refraction in nanosphere dispersed liquid crystals,” Proc. SPIE Vol. 7213, 72130A (2009).
[CrossRef]

Kang, L.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Z. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

Khoo, I. C.

I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471, 221-267 (2009).
[CrossRef]

S. Xiao, U. K. Chettiar, A. V. Kildishev, V. Drachev, I. C. Khoo, and V. M. Shalaev, “Tunable magnetic response of metamaterials,” Appl. Phys. Lett. 95033115 (2009).
[CrossRef]

J. A. Bossard, X. Liang, L. Li, D. H. Werner, B. Weiner, P. F. Cristman, A. Diaz, and I. C. Khoo “Tunable frequency selective surfaces and negative-zero-positive index metamaterials based on liquid crystals,” IEEE Trans. Antennas Propag. 56, 1308-1320 (2008).
[CrossRef]

I. C. Khoo, A. Diaz, S. Kubo, J. Liou, M. Stinger, T. Mallouk, and J. H. Park, “Nano-dispersed organic liquid and liquid crystals for all-time-scales optical switching and tunable negative- and zero-index materials,” Mol. Cryst. Liq. Cryst. 485, 934-944 (2008).
[CrossRef]

X. Wang, D. H. Kwon, D. H. Werner, I. C. Khoo, A. Kildishev, and V. M. Shalaev, “Tunable optical negative-index metamaterials employing anisotropic liquid crystals,” Appl. Phys. Lett. 91, 143122 (2007).
[CrossRef]

I. C. Khoo, D. H. Werner, X. Liang, and A. Diaz, “Nanosphere dispersed liquid crystals for tunable negative-zero-positive index of refraction in the optical and terahertz regimes,” Opt. Lett. 31, 2592-2594 (2006).
[CrossRef] [PubMed]

E. Graugnard, J. S. King, S. Jain, C. J. Summers, Y. Zhang-Williams, and I. C. Khoo, “Electric field tuning of the Bragg peak in large-pore TiO2 inverse shell opals,” Phys. Rev. B 72, 233105 (2005).
[CrossRef]

M. Kaczmarek, A. Dyaduysha, S. Slussarenko, and I. C. Khoo, “The role of surface charge field in two-beam coupling in liquid crystal cells with photoconducting polymer layers,” J. Appl. Phys. 96, 2616-2623 (2004).
[CrossRef]

I. C. Khoo, Liquid Crystals, 2nd ed. (Wiley, 2007).
[CrossRef]

Kildeshev, A. V.

Kildishev, A.

X. Wang, D. H. Kwon, D. H. Werner, I. C. Khoo, A. Kildishev, and V. M. Shalaev, “Tunable optical negative-index metamaterials employing anisotropic liquid crystals,” Appl. Phys. Lett. 91, 143122 (2007).
[CrossRef]

Kildishev, A. V.

S. Xiao, U. K. Chettiar, A. V. Kildishev, V. Drachev, I. C. Khoo, and V. M. Shalaev, “Tunable magnetic response of metamaterials,” Appl. Phys. Lett. 95033115 (2009).
[CrossRef]

King, J. S.

E. Graugnard, J. S. King, S. Jain, C. J. Summers, Y. Zhang-Williams, and I. C. Khoo, “Electric field tuning of the Bragg peak in large-pore TiO2 inverse shell opals,” Phys. Rev. B 72, 233105 (2005).
[CrossRef]

Komorowska, K.

K. Komorowska, G. Pawlik, A. C. Mitus, and A. Miniewicz, “Electro-optic phenomena in nematic liquid crystals studied experimentally and by Monte-Carlo simulations,” J. Appl. Phys. 90, 1836-1842 (2001).
[CrossRef]

Kubo, S.

I. C. Khoo, A. Diaz, S. Kubo, J. Liou, M. Stinger, T. Mallouk, and J. H. Park, “Nano-dispersed organic liquid and liquid crystals for all-time-scales optical switching and tunable negative- and zero-index materials,” Mol. Cryst. Liq. Cryst. 485, 934-944 (2008).
[CrossRef]

Kwon, D. H.

X. Wang, D. H. Kwon, D. H. Werner, I. C. Khoo, A. Kildishev, and V. M. Shalaev, “Tunable optical negative-index metamaterials employing anisotropic liquid crystals,” Appl. Phys. Lett. 91, 143122 (2007).
[CrossRef]

Landau, D.

D. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, (Cambridge Univ. Press, 2000).

Lasher, G.

P. A. Lebwohl and G. Lasher, “Nematic-liquid-crystal order--a Monte Carlo calculation,” Phys. Rev. A 6, 426-429 (1972).
[CrossRef]

Lebwohl, P. A.

P. A. Lebwohl and G. Lasher, “Nematic-liquid-crystal order--a Monte Carlo calculation,” Phys. Rev. A 6, 426-429 (1972).
[CrossRef]

Lee, H.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534-537 (2005).
[CrossRef] [PubMed]

Li, B.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Z. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

Li, L.

J. A. Bossard, X. Liang, L. Li, D. H. Werner, B. Weiner, P. F. Cristman, A. Diaz, and I. C. Khoo “Tunable frequency selective surfaces and negative-zero-positive index metamaterials based on liquid crystals,” IEEE Trans. Antennas Propag. 56, 1308-1320 (2008).
[CrossRef]

Liang, X.

J. A. Bossard, X. Liang, L. Li, D. H. Werner, B. Weiner, P. F. Cristman, A. Diaz, and I. C. Khoo “Tunable frequency selective surfaces and negative-zero-positive index metamaterials based on liquid crystals,” IEEE Trans. Antennas Propag. 56, 1308-1320 (2008).
[CrossRef]

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Z. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

I. C. Khoo, D. H. Werner, X. Liang, and A. Diaz, “Nanosphere dispersed liquid crystals for tunable negative-zero-positive index of refraction in the optical and terahertz regimes,” Opt. Lett. 31, 2592-2594 (2006).
[CrossRef] [PubMed]

Liou, J.

I. C. Khoo, A. Diaz, S. Kubo, J. Liou, M. Stinger, T. Mallouk, and J. H. Park, “Nano-dispersed organic liquid and liquid crystals for all-time-scales optical switching and tunable negative- and zero-index materials,” Mol. Cryst. Liq. Cryst. 485, 934-944 (2008).
[CrossRef]

Mallet, P.

Mallouk, T.

I. C. Khoo, A. Diaz, S. Kubo, J. Liou, M. Stinger, T. Mallouk, and J. H. Park, “Nano-dispersed organic liquid and liquid crystals for all-time-scales optical switching and tunable negative- and zero-index materials,” Mol. Cryst. Liq. Cryst. 485, 934-944 (2008).
[CrossRef]

Maxwell Garnett, J. C.

J. C. Maxwell Garnett, “Colors in metal glasses and in metallic films,” Philos. Trans. R. Soc. London, Ser. A 203, 385-420 (1904).
[CrossRef]

Miniewicz, A.

K. Komorowska, G. Pawlik, A. C. Mitus, and A. Miniewicz, “Electro-optic phenomena in nematic liquid crystals studied experimentally and by Monte-Carlo simulations,” J. Appl. Phys. 90, 1836-1842 (2001).
[CrossRef]

G. Pawlik, A. C. Mitus, and A. Miniewicz, “Monte-Carlo simulations of refractive index changes in nematic liquid crystal upon spatially nonuniform illumination,” Opt. Commun. 182, 249-254 (2000).
[CrossRef]

Mitus, A. C.

W. Walasik, M. Jarema, G. Pawlik, A. C. Mitus and F. Kajzar, “Monte Carlo study of tunable negative-zero-positive index of refraction in nanosphere dispersed liquid crystals,” Proc. SPIE Vol. 7213, 72130A (2009).
[CrossRef]

K. Komorowska, G. Pawlik, A. C. Mitus, and A. Miniewicz, “Electro-optic phenomena in nematic liquid crystals studied experimentally and by Monte-Carlo simulations,” J. Appl. Phys. 90, 1836-1842 (2001).
[CrossRef]

G. Pawlik, A. C. Mitus, and A. Miniewicz, “Monte-Carlo simulations of refractive index changes in nematic liquid crystal upon spatially nonuniform illumination,” Opt. Commun. 182, 249-254 (2000).
[CrossRef]

Mojahedi, M.

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coated nonmagnetic spheres with a negative index of refraction at infrared frequencies,” Phys. Rev. B 73, 045105 (2006).
[CrossRef]

Papoular, M.

A. Rapini and M. Papoular, “Distorsion d'une lamelle nematique sous champ magnetique conditions dancrage aux parois,” J. Phys. (France) 30, 54-56 (1969).

Park, J. H.

I. C. Khoo, A. Diaz, S. Kubo, J. Liou, M. Stinger, T. Mallouk, and J. H. Park, “Nano-dispersed organic liquid and liquid crystals for all-time-scales optical switching and tunable negative- and zero-index materials,” Mol. Cryst. Liq. Cryst. 485, 934-944 (2008).
[CrossRef]

Pawlik, G.

W. Walasik, M. Jarema, G. Pawlik, A. C. Mitus and F. Kajzar, “Monte Carlo study of tunable negative-zero-positive index of refraction in nanosphere dispersed liquid crystals,” Proc. SPIE Vol. 7213, 72130A (2009).
[CrossRef]

K. Komorowska, G. Pawlik, A. C. Mitus, and A. Miniewicz, “Electro-optic phenomena in nematic liquid crystals studied experimentally and by Monte-Carlo simulations,” J. Appl. Phys. 90, 1836-1842 (2001).
[CrossRef]

G. Pawlik, A. C. Mitus, and A. Miniewicz, “Monte-Carlo simulations of refractive index changes in nematic liquid crystal upon spatially nonuniform illumination,” Opt. Commun. 182, 249-254 (2000).
[CrossRef]

Rapini, A.

A. Rapini and M. Papoular, “Distorsion d'une lamelle nematique sous champ magnetique conditions dancrage aux parois,” J. Phys. (France) 30, 54-56 (1969).

Sarychev, A. K.

Sentenac, A.

Shalaev, V. M.

S. Xiao, U. K. Chettiar, A. V. Kildishev, V. Drachev, I. C. Khoo, and V. M. Shalaev, “Tunable magnetic response of metamaterials,” Appl. Phys. Lett. 95033115 (2009).
[CrossRef]

X. Wang, D. H. Kwon, D. H. Werner, I. C. Khoo, A. Kildishev, and V. M. Shalaev, “Tunable optical negative-index metamaterials employing anisotropic liquid crystals,” Appl. Phys. Lett. 91, 143122 (2007).
[CrossRef]

V. M. Shalaev, W. S. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildeshev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

Slussarenko, S.

M. Kaczmarek, A. Dyaduysha, S. Slussarenko, and I. C. Khoo, “The role of surface charge field in two-beam coupling in liquid crystal cells with photoconducting polymer layers,” J. Appl. Phys. 96, 2616-2623 (2004).
[CrossRef]

Stinger, M.

I. C. Khoo, A. Diaz, S. Kubo, J. Liou, M. Stinger, T. Mallouk, and J. H. Park, “Nano-dispersed organic liquid and liquid crystals for all-time-scales optical switching and tunable negative- and zero-index materials,” Mol. Cryst. Liq. Cryst. 485, 934-944 (2008).
[CrossRef]

Summers, C. J.

E. Graugnard, J. S. King, S. Jain, C. J. Summers, Y. Zhang-Williams, and I. C. Khoo, “Electric field tuning of the Bragg peak in large-pore TiO2 inverse shell opals,” Phys. Rev. B 72, 233105 (2005).
[CrossRef]

Sun, C.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534-537 (2005).
[CrossRef] [PubMed]

Tabiryan, N. V.

Tang, H.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Z. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

Tildesley, D.

P. Allen and D. Tildesley, Computer Simulation of Liquids, (Clarendon Press, 1987).

Umeton, C.

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Walasik, W.

W. Walasik, M. Jarema, G. Pawlik, A. C. Mitus and F. Kajzar, “Monte Carlo study of tunable negative-zero-positive index of refraction in nanosphere dispersed liquid crystals,” Proc. SPIE Vol. 7213, 72130A (2009).
[CrossRef]

Wang, X.

X. Wang, D. H. Kwon, D. H. Werner, I. C. Khoo, A. Kildishev, and V. M. Shalaev, “Tunable optical negative-index metamaterials employing anisotropic liquid crystals,” Appl. Phys. Lett. 91, 143122 (2007).
[CrossRef]

Weiner, B.

J. A. Bossard, X. Liang, L. Li, D. H. Werner, B. Weiner, P. F. Cristman, A. Diaz, and I. C. Khoo “Tunable frequency selective surfaces and negative-zero-positive index metamaterials based on liquid crystals,” IEEE Trans. Antennas Propag. 56, 1308-1320 (2008).
[CrossRef]

Werner, D. H.

J. A. Bossard, X. Liang, L. Li, D. H. Werner, B. Weiner, P. F. Cristman, A. Diaz, and I. C. Khoo “Tunable frequency selective surfaces and negative-zero-positive index metamaterials based on liquid crystals,” IEEE Trans. Antennas Propag. 56, 1308-1320 (2008).
[CrossRef]

X. Wang, D. H. Kwon, D. H. Werner, I. C. Khoo, A. Kildishev, and V. M. Shalaev, “Tunable optical negative-index metamaterials employing anisotropic liquid crystals,” Appl. Phys. Lett. 91, 143122 (2007).
[CrossRef]

I. C. Khoo, D. H. Werner, X. Liang, and A. Diaz, “Nanosphere dispersed liquid crystals for tunable negative-zero-positive index of refraction in the optical and terahertz regimes,” Opt. Lett. 31, 2592-2594 (2006).
[CrossRef] [PubMed]

Wheeler, M. S.

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coated nonmagnetic spheres with a negative index of refraction at infrared frequencies,” Phys. Rev. B 73, 045105 (2006).
[CrossRef]

Xiao, S.

S. Xiao, U. K. Chettiar, A. V. Kildishev, V. Drachev, I. C. Khoo, and V. M. Shalaev, “Tunable magnetic response of metamaterials,” Appl. Phys. Lett. 95033115 (2009).
[CrossRef]

Yuan, H. K.

Zhang, B. Z.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Z. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

Zhang, X.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534-537 (2005).
[CrossRef] [PubMed]

Zhang-Williams, Y.

E. Graugnard, J. S. King, S. Jain, C. J. Summers, Y. Zhang-Williams, and I. C. Khoo, “Electric field tuning of the Bragg peak in large-pore TiO2 inverse shell opals,” Phys. Rev. B 72, 233105 (2005).
[CrossRef]

Zhao, Q.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Z. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

Zhou, J.

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Z. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

Ziolkowski, R. W.

N. Engheta and R. W. Ziolkowski, Metamaterials: Physics and Engineering Explorations, (Wiley, 2006).

Appl. Phys. Lett. (3)

S. Xiao, U. K. Chettiar, A. V. Kildishev, V. Drachev, I. C. Khoo, and V. M. Shalaev, “Tunable magnetic response of metamaterials,” Appl. Phys. Lett. 95033115 (2009).
[CrossRef]

X. Wang, D. H. Kwon, D. H. Werner, I. C. Khoo, A. Kildishev, and V. M. Shalaev, “Tunable optical negative-index metamaterials employing anisotropic liquid crystals,” Appl. Phys. Lett. 91, 143122 (2007).
[CrossRef]

Q. Zhao, L. Kang, B. Du, B. Li, J. Zhou, H. Tang, X. Liang, and B. Z. Zhang, “Electrically tunable negative permeability metamaterials based on nematic liquid crystals,” Appl. Phys. Lett. 90, 011112 (2007).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

J. A. Bossard, X. Liang, L. Li, D. H. Werner, B. Weiner, P. F. Cristman, A. Diaz, and I. C. Khoo “Tunable frequency selective surfaces and negative-zero-positive index metamaterials based on liquid crystals,” IEEE Trans. Antennas Propag. 56, 1308-1320 (2008).
[CrossRef]

J. Appl. Phys. (2)

K. Komorowska, G. Pawlik, A. C. Mitus, and A. Miniewicz, “Electro-optic phenomena in nematic liquid crystals studied experimentally and by Monte-Carlo simulations,” J. Appl. Phys. 90, 1836-1842 (2001).
[CrossRef]

M. Kaczmarek, A. Dyaduysha, S. Slussarenko, and I. C. Khoo, “The role of surface charge field in two-beam coupling in liquid crystal cells with photoconducting polymer layers,” J. Appl. Phys. 96, 2616-2623 (2004).
[CrossRef]

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

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

J. Phys. (France) (1)

A. Rapini and M. Papoular, “Distorsion d'une lamelle nematique sous champ magnetique conditions dancrage aux parois,” J. Phys. (France) 30, 54-56 (1969).

Mol. Cryst. Liq. Cryst. (1)

I. C. Khoo, A. Diaz, S. Kubo, J. Liou, M. Stinger, T. Mallouk, and J. H. Park, “Nano-dispersed organic liquid and liquid crystals for all-time-scales optical switching and tunable negative- and zero-index materials,” Mol. Cryst. Liq. Cryst. 485, 934-944 (2008).
[CrossRef]

Opt. Commun. (1)

G. Pawlik, A. C. Mitus, and A. Miniewicz, “Monte-Carlo simulations of refractive index changes in nematic liquid crystal upon spatially nonuniform illumination,” Opt. Commun. 182, 249-254 (2000).
[CrossRef]

Opt. Lett. (2)

Philos. Trans. R. Soc. London, Ser. A (1)

J. C. Maxwell Garnett, “Colors in metal glasses and in metallic films,” Philos. Trans. R. Soc. London, Ser. A 203, 385-420 (1904).
[CrossRef]

Phys. Rep. (1)

I. C. Khoo, “Nonlinear optics of liquid crystalline materials,” Phys. Rep. 471, 221-267 (2009).
[CrossRef]

Phys. Rev. A (1)

P. A. Lebwohl and G. Lasher, “Nematic-liquid-crystal order--a Monte Carlo calculation,” Phys. Rev. A 6, 426-429 (1972).
[CrossRef]

Phys. Rev. B (2)

E. Graugnard, J. S. King, S. Jain, C. J. Summers, Y. Zhang-Williams, and I. C. Khoo, “Electric field tuning of the Bragg peak in large-pore TiO2 inverse shell opals,” Phys. Rev. B 72, 233105 (2005).
[CrossRef]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Coated nonmagnetic spheres with a negative index of refraction at infrared frequencies,” Phys. Rev. B 73, 045105 (2006).
[CrossRef]

Proc. SPIE (1)

W. Walasik, M. Jarema, G. Pawlik, A. C. Mitus and F. Kajzar, “Monte Carlo study of tunable negative-zero-positive index of refraction in nanosphere dispersed liquid crystals,” Proc. SPIE Vol. 7213, 72130A (2009).
[CrossRef]

Science (1)

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308, 534-537 (2005).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Other (5)

N. Engheta and R. W. Ziolkowski, Metamaterials: Physics and Engineering Explorations, (Wiley, 2006).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
[CrossRef]

I. C. Khoo, Liquid Crystals, 2nd ed. (Wiley, 2007).
[CrossRef]

P. Allen and D. Tildesley, Computer Simulation of Liquids, (Clarendon Press, 1987).

D. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, (Cambridge Univ. Press, 2000).

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Figures (16)

Fig. 1
Fig. 1

Cross section of a coated nanosphere inside the liquid crystal host.

Fig. 2
Fig. 2

Plots of real and imaginary parts of an effective refractive index: n eff ( λ , θ ) (top) and n eff ( λ , θ ) (bottom).

Fig. 3
Fig. 3

Real part n eff ( θ ) of the local refractive index versus θ for wavelengths λ = 2820 , 2830, 2850 nm (upper left), and 2900 nm (upper right). Contour plot of n eff ( θ , λ ) with lines corresponding to λ = 2820 , 2830, 2850, and 2900 nm (bottom).

Fig. 4
Fig. 4

n eff against λ in case of homogeneous order ( θ = const ) .

Fig. 5
Fig. 5

Geometry of the simulated system. Electric field is along the z axis.

Fig. 6
Fig. 6

2D maps of n eff ( x , z ) . Regions marked with striped pattern have negative values of refractive index: λ = 2.820 μ m (top), λ = 2.850 μ m (bottom). Profiles n eff ( z ) : λ = 2.820 μ m (lower left), λ = 2.850 μ m (lower right). E 0 = 1.2 , α = 50 (after [26]).

Fig. 7
Fig. 7

Profiles n eff ( z ) in function of wavelength λ in strong anchoring regime α = 50 , E 0 = 0.6 (upper left), E 0 = 1.2 (upper right and bottom).

Fig. 8
Fig. 8

Cross section in the x– z plane of a typical spatially modulated 3D configuration of NLC particles ( E 0 = 1.2 , α = 50 ).

Fig. 9
Fig. 9

2D maps of n eff ( x , z ) for λ = 2900 nm , in strong ( α = 50 , left) and weak ( α = 10 , right) anchoring regimes for a few values of E 0 shown in the figures.

Fig. 10
Fig. 10

Plots of n eff ( x , z ) for λ = 2900 nm , in strong ( α = 50 , top) and weak ( α = 10 , bottom) anchoring regimes for a few values of E 0 shown in the figures.

Fig. 11
Fig. 11

Averaged profiles n ( x ) for λ = 2900 nm in strong ( α = 50 , left) and weak ( α = 10 , right) anchoring regimes for a few values of E 0 shown in the legends.

Fig. 12
Fig. 12

Modulation of refractive index for λ = 2900 nm for NDLQ (upper) and NLC cell (lower) for weak anchoring case ( α = 10 ) , E 0 = 0.85 .  

Fig. 13
Fig. 13

2D maps of n eff ( x , z ) for λ = 2830 nm in strong ( α = 50 , left) and weak ( α = 10 , right) anchoring regimes for a few values of E 0 shown in the figures.

Fig. 14
Fig. 14

Plots of n eff ( x , z ) for λ = 2830 nm in strong ( α = 50 , top) and weak ( α = 10 , bottom) anchoring regimes for a few values of E 0 shown in the figures.

Fig. 15
Fig. 15

Averaged profiles n ( x ) for λ = 2830 nm in strong ( α = 50 , left) and weak ( α = 10 , right) anchoring regimes for a few values of E 0 shown in the legends.

Fig. 16
Fig. 16

2D maps of n eff ( x , z ) for λ = 2830 nm and E 0 = 0.8 in three anchoring regimes: strong ( α = 50 , top), medium ( α = 30 , middle), and weak ( α = 10 , bottom).

Equations (8)

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ε 1 = ε ( ) ( 1 + ω L 2 ω T 2 ω T 2 ω 2 i ω γ 1 ) .
ε 2 ( ω ) = 1 ω p 2 ω 2 + i ω γ 2 ,
ε 3 ( θ ) = ε ε ε cos 2 θ + ε sin 2 θ ,
ε eff = ε 3 ( k 3 3 + 4 π i N a 1 k 3 3 2 π i N a 1 ) , μ eff = k 3 3 + 4 π i N b 1 k 3 3 2 π i N b 1 .
n eff = n eff + i n eff = ± ε eff μ eff ,
H = ξ r , r P 2 ( cos β ( r , r ) ) r E 2 ( r ) P 2 ( cos β ( r ) ) + r w α ( r w ) sin 2 γ ( r w ) .
E ( x ) = E 0 + A sin ( q x ) .
n ( x ) = 1 L 0 L n eff ( x , z ) d z .

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