Abstract

The expected permittivity and third-order nonlinear susceptibility of a composite consisting of semiconductor nanorods (NRs) dispersed in a polymer host are derived using a generalized Maxwell Garnett model under various NR axis orientation statistics, achieved by an aligning electric field. The semiconductor NRs are analyzed as prolate spheroids and modeled as more realistic capsule shapes. From the angular distribution function of the NRs, the composite macroscopic characteristics are found for low filling fractions. As the alignment field strength increases, the composite optical properties asymptotically converge toward the nematic case. Aligning fields of order 107V/m are required for the optical properties to increase to half the value between random orientation and nematic array composites.

© 2013 Optical Society of America

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  1. F. Trani, “Polarization anisotropy in the optical properties of silicon ellipsoids,” Surf. Sci. 601, 2702–2706 (2007).
    [CrossRef]
  2. J. Valenta, B. Bruhn, and J. Linnros, “Polarization of photoluminescence excitation and emission spectra of silicon nanorods within single Si/SiO2 nanowires,” Phys. Status Solidi C 8, 1017–1020 (2011).
    [CrossRef]
  3. Y. K. Olsson, G. Chen, R. Rapaport, D. T. Fuchs, V. C. Sundara, J. S. Steckel, M. G. Bawendi, A. Aharoni, and U. Banin, “Fabrication and optical properties of polymeric waveguides containing nanocrystalline quantum dots,” Appl. Phys. Lett. 85, 4469–4471 (2004).
    [CrossRef]
  4. G. Chen, R. Rapaport, D. T. Fuchs, L. Lucas, A. J. Lovinger, S. Vilan, A. Aharoni, and U. Banin, “Optical gain from InAs nanocrystal quantum dots in a polymer matrix,” Appl. Phys. Lett. 87, 251108 (2005).
    [CrossRef]
  5. C. Sciancalepore, T. Cassano, M. L. Curri, D. Mecerreyes, A. Valentini, A. Agostiano, R. Tommasi, and M. Striccoli, “TiO2 nanorods/PMMA copolymer-based nanocomposites: highly homogeneous linear and nonlinear optical material,” Nanotechnology 19, 205705 (2008).
    [CrossRef]
  6. J. M. Lamarre, F. Billard, and L. Martinu, “Local field calculations of the anisotropic nonlinear absorption coefficient of aligned gold nanorods embedded in silica,” J. Opt. Soc. Am. B 25, 961–971 (2008).
    [CrossRef]
  7. H. Sihvola, Electromagnetic Mixing Formulas and Applications (Institution of Engineering and Technology, 2008).
  8. S. Giordano, “Effective medium theory for dispersions of dielectric ellipsoids,” J. Electrost. 58, 59–76 (2003).
    [CrossRef]
  9. H. Sihvola and J. A. Kong, “Effective permittivity of dielectric mixtures,” IEEE Trans. Geosci. Remote Sens. 26, 420–429 (1988).
    [CrossRef]
  10. B. Weintraub, Y. Deng, and Z. L. Wang, “Position-controlled seedless growth of ZnO nanorod arrays on a polymer substrate via wet chemical synthesis,” J. Phys. Chem. C 111, 10162–10165 (2007).
    [CrossRef]
  11. C. Lai, Y. J. Lee, P. H. Yeh, and S. W. Lee, “Formation mechanism of SiGe nanorod arrays by combining nanosphere lithography and Au-assisted chemical etching,” Nanoscale Res. Lett. 7140 (2012).
  12. J. L. Baker, A. Widmer-Cooper, M. F. Toney, P. L. Geissler, and A. P. Alivisatos, “Device-scale perpendicular alignment of colloidal nanorods,” Nano Lett. 10, 195–201 (2010).
    [CrossRef]
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    [CrossRef]
  14. H. E. Ruda and A. Shik, “Nanorod dynamics in ac electric fields” Nanotechnology 21, 235502 (2010).
    [CrossRef]
  15. M. Shim and P. Guyot-Sionnest, “Permanent dipole moment and charges in colloidal semiconductor quantum dots,” J. Chem. Phys. 111, 6955–6964 (1999).
    [CrossRef]
  16. N. Venkatram, R. Sathyavathi, and D. Narayana Rao, “Size dependent multiphoton absorption and refraction of CdSe nanoparticles,” Opt. Express 15, 12258–12263 (2007).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  23. T. Nann and J. Schneider, “Origin of permanent electric dipole moments in wurtzite nanocrystals,” Chem. Phys. Lett. 384, 150–152 (2004).
    [CrossRef]
  24. Ruda and Shik calculated the ADF with the integration in the denominator over the interval [0,2π]. When examining the whole three-dimensional characteristics of the composite, θ is defined over the interval [0,π].
  25. The integration for θ is over d(cos θ)=sin θ·dθ. See, for example, the denominator of Eq. (7).
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    [CrossRef]
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  28. The variance is the integration of the square of the relevant function (permittivity or susceptibility) minus its mean value. The STD is the square root of the variance.

2012

C. Lai, Y. J. Lee, P. H. Yeh, and S. W. Lee, “Formation mechanism of SiGe nanorod arrays by combining nanosphere lithography and Au-assisted chemical etching,” Nanoscale Res. Lett. 7140 (2012).

2011

J. Valenta, B. Bruhn, and J. Linnros, “Polarization of photoluminescence excitation and emission spectra of silicon nanorods within single Si/SiO2 nanowires,” Phys. Status Solidi C 8, 1017–1020 (2011).
[CrossRef]

2010

J. L. Baker, A. Widmer-Cooper, M. F. Toney, P. L. Geissler, and A. P. Alivisatos, “Device-scale perpendicular alignment of colloidal nanorods,” Nano Lett. 10, 195–201 (2010).
[CrossRef]

H. E. Ruda and A. Shik, “Nanorod dynamics in ac electric fields” Nanotechnology 21, 235502 (2010).
[CrossRef]

2008

C. Sciancalepore, T. Cassano, M. L. Curri, D. Mecerreyes, A. Valentini, A. Agostiano, R. Tommasi, and M. Striccoli, “TiO2 nanorods/PMMA copolymer-based nanocomposites: highly homogeneous linear and nonlinear optical material,” Nanotechnology 19, 205705 (2008).
[CrossRef]

J. M. Lamarre, F. Billard, and L. Martinu, “Local field calculations of the anisotropic nonlinear absorption coefficient of aligned gold nanorods embedded in silica,” J. Opt. Soc. Am. B 25, 961–971 (2008).
[CrossRef]

C. Pecharromán, J. Pérez-Juste, G. Mata-Osoro, L. M. Liz-Marzán, and P. Mulvaney, “Redshift of surface plasmon modes of small gold rods due to their atomic roughness and end-cap geometry,” Phys. Rev. B 77, 035418 (2008).
[CrossRef]

2007

F. Trani, “Polarization anisotropy in the optical properties of silicon ellipsoids,” Surf. Sci. 601, 2702–2706 (2007).
[CrossRef]

N. Venkatram, R. Sathyavathi, and D. Narayana Rao, “Size dependent multiphoton absorption and refraction of CdSe nanoparticles,” Opt. Express 15, 12258–12263 (2007).
[CrossRef]

B. Weintraub, Y. Deng, and Z. L. Wang, “Position-controlled seedless growth of ZnO nanorod arrays on a polymer substrate via wet chemical synthesis,” J. Phys. Chem. C 111, 10162–10165 (2007).
[CrossRef]

2005

G. Chen, R. Rapaport, D. T. Fuchs, L. Lucas, A. J. Lovinger, S. Vilan, A. Aharoni, and U. Banin, “Optical gain from InAs nanocrystal quantum dots in a polymer matrix,” Appl. Phys. Lett. 87, 251108 (2005).
[CrossRef]

C. Sönnichsen and A. P. Alivisatos, “Gold nanorods as novel nonbleaching plasmon-based orientation sensors for polarized single-particle microscopy,” Nano Lett. 5, 301–304 (2005).
[CrossRef]

2004

T. Nann and J. Schneider, “Origin of permanent electric dipole moments in wurtzite nanocrystals,” Chem. Phys. Lett. 384, 150–152 (2004).
[CrossRef]

Y. K. Olsson, G. Chen, R. Rapaport, D. T. Fuchs, V. C. Sundara, J. S. Steckel, M. G. Bawendi, A. Aharoni, and U. Banin, “Fabrication and optical properties of polymeric waveguides containing nanocrystalline quantum dots,” Appl. Phys. Lett. 85, 4469–4471 (2004).
[CrossRef]

2003

S. Giordano, “Effective medium theory for dispersions of dielectric ellipsoids,” J. Electrost. 58, 59–76 (2003).
[CrossRef]

L. S. Li and A. P. Alivisatos, “Semiconductor nanorod liquid crystals and their assembly on a substrate,” Adv. Mater. 15, 408–411 (2003).
[CrossRef]

L. S. Li and A. P. Alivisatos, “Origin and scaling of the permanent dipole moment in CdSe nanorods,” Phys. Rev. Lett. 90, 097402 (2003).
[CrossRef]

1999

M. Shim and P. Guyot-Sionnest, “Permanent dipole moment and charges in colloidal semiconductor quantum dots,” J. Chem. Phys. 111, 6955–6964 (1999).
[CrossRef]

1995

1992

J. E. Sipe and R. W. Boyd, “Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model,” Phys. Rev. A 46, 1614–1629 (1992).
[CrossRef]

1988

H. Sihvola and J. A. Kong, “Effective permittivity of dielectric mixtures,” IEEE Trans. Geosci. Remote Sens. 26, 420–429 (1988).
[CrossRef]

1904

J. C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London Ser. A 203, 385–420 (1904).

Agostiano, A.

C. Sciancalepore, T. Cassano, M. L. Curri, D. Mecerreyes, A. Valentini, A. Agostiano, R. Tommasi, and M. Striccoli, “TiO2 nanorods/PMMA copolymer-based nanocomposites: highly homogeneous linear and nonlinear optical material,” Nanotechnology 19, 205705 (2008).
[CrossRef]

Aharoni, A.

G. Chen, R. Rapaport, D. T. Fuchs, L. Lucas, A. J. Lovinger, S. Vilan, A. Aharoni, and U. Banin, “Optical gain from InAs nanocrystal quantum dots in a polymer matrix,” Appl. Phys. Lett. 87, 251108 (2005).
[CrossRef]

Y. K. Olsson, G. Chen, R. Rapaport, D. T. Fuchs, V. C. Sundara, J. S. Steckel, M. G. Bawendi, A. Aharoni, and U. Banin, “Fabrication and optical properties of polymeric waveguides containing nanocrystalline quantum dots,” Appl. Phys. Lett. 85, 4469–4471 (2004).
[CrossRef]

Alivisatos, A. P.

J. L. Baker, A. Widmer-Cooper, M. F. Toney, P. L. Geissler, and A. P. Alivisatos, “Device-scale perpendicular alignment of colloidal nanorods,” Nano Lett. 10, 195–201 (2010).
[CrossRef]

C. Sönnichsen and A. P. Alivisatos, “Gold nanorods as novel nonbleaching plasmon-based orientation sensors for polarized single-particle microscopy,” Nano Lett. 5, 301–304 (2005).
[CrossRef]

L. S. Li and A. P. Alivisatos, “Semiconductor nanorod liquid crystals and their assembly on a substrate,” Adv. Mater. 15, 408–411 (2003).
[CrossRef]

L. S. Li and A. P. Alivisatos, “Origin and scaling of the permanent dipole moment in CdSe nanorods,” Phys. Rev. Lett. 90, 097402 (2003).
[CrossRef]

Baker, J. L.

J. L. Baker, A. Widmer-Cooper, M. F. Toney, P. L. Geissler, and A. P. Alivisatos, “Device-scale perpendicular alignment of colloidal nanorods,” Nano Lett. 10, 195–201 (2010).
[CrossRef]

Banin, U.

G. Chen, R. Rapaport, D. T. Fuchs, L. Lucas, A. J. Lovinger, S. Vilan, A. Aharoni, and U. Banin, “Optical gain from InAs nanocrystal quantum dots in a polymer matrix,” Appl. Phys. Lett. 87, 251108 (2005).
[CrossRef]

Y. K. Olsson, G. Chen, R. Rapaport, D. T. Fuchs, V. C. Sundara, J. S. Steckel, M. G. Bawendi, A. Aharoni, and U. Banin, “Fabrication and optical properties of polymeric waveguides containing nanocrystalline quantum dots,” Appl. Phys. Lett. 85, 4469–4471 (2004).
[CrossRef]

Bawendi, M. G.

Y. K. Olsson, G. Chen, R. Rapaport, D. T. Fuchs, V. C. Sundara, J. S. Steckel, M. G. Bawendi, A. Aharoni, and U. Banin, “Fabrication and optical properties of polymeric waveguides containing nanocrystalline quantum dots,” Appl. Phys. Lett. 85, 4469–4471 (2004).
[CrossRef]

Billard, F.

Boyd, R. W.

J. E. Sipe and R. W. Boyd, “Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model,” Phys. Rev. A 46, 1614–1629 (1992).
[CrossRef]

R. W. Boyd, “The intensity-dependent refractive index,” in Nonlinear Optics, 2nd ed. (Academic, 2003), pp. 189–236.

Bruhn, B.

J. Valenta, B. Bruhn, and J. Linnros, “Polarization of photoluminescence excitation and emission spectra of silicon nanorods within single Si/SiO2 nanowires,” Phys. Status Solidi C 8, 1017–1020 (2011).
[CrossRef]

Cassano, T.

C. Sciancalepore, T. Cassano, M. L. Curri, D. Mecerreyes, A. Valentini, A. Agostiano, R. Tommasi, and M. Striccoli, “TiO2 nanorods/PMMA copolymer-based nanocomposites: highly homogeneous linear and nonlinear optical material,” Nanotechnology 19, 205705 (2008).
[CrossRef]

Chen, G.

G. Chen, R. Rapaport, D. T. Fuchs, L. Lucas, A. J. Lovinger, S. Vilan, A. Aharoni, and U. Banin, “Optical gain from InAs nanocrystal quantum dots in a polymer matrix,” Appl. Phys. Lett. 87, 251108 (2005).
[CrossRef]

Y. K. Olsson, G. Chen, R. Rapaport, D. T. Fuchs, V. C. Sundara, J. S. Steckel, M. G. Bawendi, A. Aharoni, and U. Banin, “Fabrication and optical properties of polymeric waveguides containing nanocrystalline quantum dots,” Appl. Phys. Lett. 85, 4469–4471 (2004).
[CrossRef]

Curri, M. L.

C. Sciancalepore, T. Cassano, M. L. Curri, D. Mecerreyes, A. Valentini, A. Agostiano, R. Tommasi, and M. Striccoli, “TiO2 nanorods/PMMA copolymer-based nanocomposites: highly homogeneous linear and nonlinear optical material,” Nanotechnology 19, 205705 (2008).
[CrossRef]

Deng, Y.

B. Weintraub, Y. Deng, and Z. L. Wang, “Position-controlled seedless growth of ZnO nanorod arrays on a polymer substrate via wet chemical synthesis,” J. Phys. Chem. C 111, 10162–10165 (2007).
[CrossRef]

Fuchs, D. T.

G. Chen, R. Rapaport, D. T. Fuchs, L. Lucas, A. J. Lovinger, S. Vilan, A. Aharoni, and U. Banin, “Optical gain from InAs nanocrystal quantum dots in a polymer matrix,” Appl. Phys. Lett. 87, 251108 (2005).
[CrossRef]

Y. K. Olsson, G. Chen, R. Rapaport, D. T. Fuchs, V. C. Sundara, J. S. Steckel, M. G. Bawendi, A. Aharoni, and U. Banin, “Fabrication and optical properties of polymeric waveguides containing nanocrystalline quantum dots,” Appl. Phys. Lett. 85, 4469–4471 (2004).
[CrossRef]

Geissler, P. L.

J. L. Baker, A. Widmer-Cooper, M. F. Toney, P. L. Geissler, and A. P. Alivisatos, “Device-scale perpendicular alignment of colloidal nanorods,” Nano Lett. 10, 195–201 (2010).
[CrossRef]

Giordano, S.

S. Giordano, “Effective medium theory for dispersions of dielectric ellipsoids,” J. Electrost. 58, 59–76 (2003).
[CrossRef]

Guyot-Sionnest, P.

M. Shim and P. Guyot-Sionnest, “Permanent dipole moment and charges in colloidal semiconductor quantum dots,” J. Chem. Phys. 111, 6955–6964 (1999).
[CrossRef]

Kong, J. A.

H. Sihvola and J. A. Kong, “Effective permittivity of dielectric mixtures,” IEEE Trans. Geosci. Remote Sens. 26, 420–429 (1988).
[CrossRef]

Lai, C.

C. Lai, Y. J. Lee, P. H. Yeh, and S. W. Lee, “Formation mechanism of SiGe nanorod arrays by combining nanosphere lithography and Au-assisted chemical etching,” Nanoscale Res. Lett. 7140 (2012).

Lamarre, J. M.

Landau, L. D.

L. D. Landau and E. M. Lifshitz, “A dielectric ellipsoid,” in Electrodynamics of Continuous Media, 2nd ed. (Pergamon, 1984), pp. 39–42.

Lee, S. W.

C. Lai, Y. J. Lee, P. H. Yeh, and S. W. Lee, “Formation mechanism of SiGe nanorod arrays by combining nanosphere lithography and Au-assisted chemical etching,” Nanoscale Res. Lett. 7140 (2012).

Lee, Y. J.

C. Lai, Y. J. Lee, P. H. Yeh, and S. W. Lee, “Formation mechanism of SiGe nanorod arrays by combining nanosphere lithography and Au-assisted chemical etching,” Nanoscale Res. Lett. 7140 (2012).

Li, L. S.

L. S. Li and A. P. Alivisatos, “Semiconductor nanorod liquid crystals and their assembly on a substrate,” Adv. Mater. 15, 408–411 (2003).
[CrossRef]

L. S. Li and A. P. Alivisatos, “Origin and scaling of the permanent dipole moment in CdSe nanorods,” Phys. Rev. Lett. 90, 097402 (2003).
[CrossRef]

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, “A dielectric ellipsoid,” in Electrodynamics of Continuous Media, 2nd ed. (Pergamon, 1984), pp. 39–42.

Linnros, J.

J. Valenta, B. Bruhn, and J. Linnros, “Polarization of photoluminescence excitation and emission spectra of silicon nanorods within single Si/SiO2 nanowires,” Phys. Status Solidi C 8, 1017–1020 (2011).
[CrossRef]

Liz-Marzán, L. M.

C. Pecharromán, J. Pérez-Juste, G. Mata-Osoro, L. M. Liz-Marzán, and P. Mulvaney, “Redshift of surface plasmon modes of small gold rods due to their atomic roughness and end-cap geometry,” Phys. Rev. B 77, 035418 (2008).
[CrossRef]

Lovinger, A. J.

G. Chen, R. Rapaport, D. T. Fuchs, L. Lucas, A. J. Lovinger, S. Vilan, A. Aharoni, and U. Banin, “Optical gain from InAs nanocrystal quantum dots in a polymer matrix,” Appl. Phys. Lett. 87, 251108 (2005).
[CrossRef]

Lucas, L.

G. Chen, R. Rapaport, D. T. Fuchs, L. Lucas, A. J. Lovinger, S. Vilan, A. Aharoni, and U. Banin, “Optical gain from InAs nanocrystal quantum dots in a polymer matrix,” Appl. Phys. Lett. 87, 251108 (2005).
[CrossRef]

Martinu, L.

Mata-Osoro, G.

C. Pecharromán, J. Pérez-Juste, G. Mata-Osoro, L. M. Liz-Marzán, and P. Mulvaney, “Redshift of surface plasmon modes of small gold rods due to their atomic roughness and end-cap geometry,” Phys. Rev. B 77, 035418 (2008).
[CrossRef]

Maxwell Garnett, J. C.

J. C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London Ser. A 203, 385–420 (1904).

Mecerreyes, D.

C. Sciancalepore, T. Cassano, M. L. Curri, D. Mecerreyes, A. Valentini, A. Agostiano, R. Tommasi, and M. Striccoli, “TiO2 nanorods/PMMA copolymer-based nanocomposites: highly homogeneous linear and nonlinear optical material,” Nanotechnology 19, 205705 (2008).
[CrossRef]

Mulvaney, P.

C. Pecharromán, J. Pérez-Juste, G. Mata-Osoro, L. M. Liz-Marzán, and P. Mulvaney, “Redshift of surface plasmon modes of small gold rods due to their atomic roughness and end-cap geometry,” Phys. Rev. B 77, 035418 (2008).
[CrossRef]

Nann, T.

T. Nann and J. Schneider, “Origin of permanent electric dipole moments in wurtzite nanocrystals,” Chem. Phys. Lett. 384, 150–152 (2004).
[CrossRef]

Narayana Rao, D.

Olsson, Y. K.

Y. K. Olsson, G. Chen, R. Rapaport, D. T. Fuchs, V. C. Sundara, J. S. Steckel, M. G. Bawendi, A. Aharoni, and U. Banin, “Fabrication and optical properties of polymeric waveguides containing nanocrystalline quantum dots,” Appl. Phys. Lett. 85, 4469–4471 (2004).
[CrossRef]

Pecharromán, C.

C. Pecharromán, J. Pérez-Juste, G. Mata-Osoro, L. M. Liz-Marzán, and P. Mulvaney, “Redshift of surface plasmon modes of small gold rods due to their atomic roughness and end-cap geometry,” Phys. Rev. B 77, 035418 (2008).
[CrossRef]

Pérez-Juste, J.

C. Pecharromán, J. Pérez-Juste, G. Mata-Osoro, L. M. Liz-Marzán, and P. Mulvaney, “Redshift of surface plasmon modes of small gold rods due to their atomic roughness and end-cap geometry,” Phys. Rev. B 77, 035418 (2008).
[CrossRef]

Rapaport, R.

G. Chen, R. Rapaport, D. T. Fuchs, L. Lucas, A. J. Lovinger, S. Vilan, A. Aharoni, and U. Banin, “Optical gain from InAs nanocrystal quantum dots in a polymer matrix,” Appl. Phys. Lett. 87, 251108 (2005).
[CrossRef]

Y. K. Olsson, G. Chen, R. Rapaport, D. T. Fuchs, V. C. Sundara, J. S. Steckel, M. G. Bawendi, A. Aharoni, and U. Banin, “Fabrication and optical properties of polymeric waveguides containing nanocrystalline quantum dots,” Appl. Phys. Lett. 85, 4469–4471 (2004).
[CrossRef]

Ruda, H. E.

H. E. Ruda and A. Shik, “Nanorod dynamics in ac electric fields” Nanotechnology 21, 235502 (2010).
[CrossRef]

Sathyavathi, R.

Schneider, J.

T. Nann and J. Schneider, “Origin of permanent electric dipole moments in wurtzite nanocrystals,” Chem. Phys. Lett. 384, 150–152 (2004).
[CrossRef]

Sciancalepore, C.

C. Sciancalepore, T. Cassano, M. L. Curri, D. Mecerreyes, A. Valentini, A. Agostiano, R. Tommasi, and M. Striccoli, “TiO2 nanorods/PMMA copolymer-based nanocomposites: highly homogeneous linear and nonlinear optical material,” Nanotechnology 19, 205705 (2008).
[CrossRef]

Shik, A.

H. E. Ruda and A. Shik, “Nanorod dynamics in ac electric fields” Nanotechnology 21, 235502 (2010).
[CrossRef]

Shim, M.

M. Shim and P. Guyot-Sionnest, “Permanent dipole moment and charges in colloidal semiconductor quantum dots,” J. Chem. Phys. 111, 6955–6964 (1999).
[CrossRef]

Sihvola, H.

H. Sihvola and J. A. Kong, “Effective permittivity of dielectric mixtures,” IEEE Trans. Geosci. Remote Sens. 26, 420–429 (1988).
[CrossRef]

H. Sihvola, Electromagnetic Mixing Formulas and Applications (Institution of Engineering and Technology, 2008).

Sipe, J. E.

J. E. Sipe and R. W. Boyd, “Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model,” Phys. Rev. A 46, 1614–1629 (1992).
[CrossRef]

Sönnichsen, C.

C. Sönnichsen and A. P. Alivisatos, “Gold nanorods as novel nonbleaching plasmon-based orientation sensors for polarized single-particle microscopy,” Nano Lett. 5, 301–304 (2005).
[CrossRef]

Steckel, J. S.

Y. K. Olsson, G. Chen, R. Rapaport, D. T. Fuchs, V. C. Sundara, J. S. Steckel, M. G. Bawendi, A. Aharoni, and U. Banin, “Fabrication and optical properties of polymeric waveguides containing nanocrystalline quantum dots,” Appl. Phys. Lett. 85, 4469–4471 (2004).
[CrossRef]

Striccoli, M.

C. Sciancalepore, T. Cassano, M. L. Curri, D. Mecerreyes, A. Valentini, A. Agostiano, R. Tommasi, and M. Striccoli, “TiO2 nanorods/PMMA copolymer-based nanocomposites: highly homogeneous linear and nonlinear optical material,” Nanotechnology 19, 205705 (2008).
[CrossRef]

Sundara, V. C.

Y. K. Olsson, G. Chen, R. Rapaport, D. T. Fuchs, V. C. Sundara, J. S. Steckel, M. G. Bawendi, A. Aharoni, and U. Banin, “Fabrication and optical properties of polymeric waveguides containing nanocrystalline quantum dots,” Appl. Phys. Lett. 85, 4469–4471 (2004).
[CrossRef]

Tommasi, R.

C. Sciancalepore, T. Cassano, M. L. Curri, D. Mecerreyes, A. Valentini, A. Agostiano, R. Tommasi, and M. Striccoli, “TiO2 nanorods/PMMA copolymer-based nanocomposites: highly homogeneous linear and nonlinear optical material,” Nanotechnology 19, 205705 (2008).
[CrossRef]

Toney, M. F.

J. L. Baker, A. Widmer-Cooper, M. F. Toney, P. L. Geissler, and A. P. Alivisatos, “Device-scale perpendicular alignment of colloidal nanorods,” Nano Lett. 10, 195–201 (2010).
[CrossRef]

Trani, F.

F. Trani, “Polarization anisotropy in the optical properties of silicon ellipsoids,” Surf. Sci. 601, 2702–2706 (2007).
[CrossRef]

Valenta, J.

J. Valenta, B. Bruhn, and J. Linnros, “Polarization of photoluminescence excitation and emission spectra of silicon nanorods within single Si/SiO2 nanowires,” Phys. Status Solidi C 8, 1017–1020 (2011).
[CrossRef]

Valentini, A.

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Figures (6)

Fig. 1.
Fig. 1.

Illustrations describing different NRs alignment degrees: (a) perfect nematic array of NRs, (b) randomly distributed NRs, and (c) partially aligned NRs.

Fig. 2.
Fig. 2.

Illustration depicting (a) the prolate spheroid shape and (b) the capsule shape proposed to describe the geometry of NRs. Both shapes have the same length (l=2·az) and diameter (d=2·ax).

Fig. 3.
Fig. 3.

Illustration depicting the alignment mechanism of the NRs by a DC electric field. (a) The aligning field causes induced dipole moments μ||, μ along NR major axes, parallel and normal to the NR LA, respectively. (b) The induced dipole moments cause a rotating moment M that acts on the NR. (c) The rotating moment tends to align the NR parallel to the aligning field.

Fig. 4.
Fig. 4.

(a) ADF of CdSe NRs without PDM inside PFCB: capsule shape versus prolate spheroid for different aligning electric field strengths under a temperature of 150°C, l=30nm, d=4.8nm. (b) The same for NRs with PDM. (c) Temperature dependency for different aligning fields (with PDM). (d) Different NRs with different volumes (for the NRs presented in Table 2, with PDM).

Fig. 5.
Fig. 5.

Illustration for the coordinate system and the definition of the angles φ and θ describing the NR orientation. The aligning field is also presented.

Fig. 6.
Fig. 6.

Results for the average optical properties of the composite: (a) effective permittivity εeff and (b) relative third-order NL susceptibility χeff(3)/χCdSe(3), as a function of the aligning field strength. Results for both the parallel (blue, upper) and transverse (red, lower) directions. Shaded areas are the average value ±1 STD.

Tables (3)

Tables Icon

Table 1. Polarizability of Prolate Spheroids and Capsule Shape for Different Dimensions, Axes Aspect Ratio, and Average Polarization Density

Tables Icon

Table 2. Comparison of Results of the PDM of the NRs Calculated by Li and Alivisatosa to Those in Our Analysis

Tables Icon

Table 3. Comparison between the Permittivity εeff and Relative Third-Order Susceptibility χeff(3)/χCdSe(3) in Parallel and Normal Directions of the Aligning Fielda

Equations (20)

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εeffj=εh+pεhεiεhεh+Lj(1p)(εiεh),
Lz=1e2e2[12eln(1+e1e)1],Lx=Ly=1Lz2,
αj=V(εiεh)εh+Lj(εiεh)εh,
γj=[εhεh+Lj(εiεh)]4ε0Vχi(3),
χeff(3),j=nγjε0=p[εhεh+Lj(εiεh)]4χi(3),
μ=(εiεh)Ein·dV,
μ=αEaligncosθ,μ=αEalignsinθ,
M=|μ×Ealign|=12(αα)Ealign2sin2θ+μpEalignsinθ.
ADF(θ)=exp[UNR(θ)KBT]0πexp[UNR(θ^)KBT]sinθ^dθ^,
εeffj=εh+εhp(αj/V)εhp(Ljαj/V),
α¯¯NR=(α000α000α),
L¯¯NR=(L000L000L),
Axyz(φ,θ)=R^z(φ)R^y(θ)ANRR^y(θ)R^z(φ),
ε¯¯eff=εhI¯¯+εhpα¯¯xyz/Vθ,φεhI¯¯p(L¯¯·α¯¯)xyz/Vθ,φ,
εeffz=εh+εhpαcos2θ+αsin2θθ/VεhpLαcos2θ+Lαsin2θθ/V,εeffx,y=εh+εhpαsin2θ+α(2sin2θ)θ/2VεhpLαcos2θ+Lα(2sin2θ)θ/2V.
εeffx,y=εeffz=εh+εhp(2α+α)/3Vεhp(2Lα+Lα)/3V,
χ¯¯eff(3)=pγ¯¯/Vθ,φε0.
χ¯¯eff(3)=p[εhεhI¯¯+L¯¯(εiεh)]4θ,φχi(3).
χeff(3),z=p(fx,y)4sin2θ+(fz)4cos2θθχi(3),χeff(3),x,y=p0.5(fz)4sin2θ+(fx,y)4(10.5×sin2θ)θχi(3),
χeff(3),x,y=χeff(3),z=p[2(fx,y)4+(fz)4]χi(3)/3.

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