Abstract

The electro-optical Pockels response from a single non-centrosymmetric nanocrystal is reported. High sensitivity to the weak electric-field dependent nonlinear scattering is achieved through a dedicated imaging interferometric microscope and the linear dependence of electro-optical signal upon the applied field is checked. Using different incident light polarization states, a priori random spatial orientation of the crystal can be inferred. The electro-optical response from a nanocrystal provides local subwavelength sensor of quasi-static electric fields with potential applications in physics and biology. It also leads to a new sub-wavelength microscopy towards the nanoscale investigation of interesting phenomena such as nanoferroelectricity.

©2011 Optical Society of America

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    [Crossref] [PubMed]
  21. L. M. Zhang, F. J. Zhang, Y. Q. Wang, and R. O. Claus, “Linear electro-optic tensor ratio determination and quadratic electro-optic modulation of electrostatically self-assembled CdSe quantum dot films,” J. Chem. Phys. 116(14), 6297–6304 (2002).
    [Crossref]
  22. A. R. Johnston, “The strain-free electrooptic effect in single crystal barium titanate,” Appl. Phys. Lett. 7(7), 195–198 (1965).
    [Crossref]
  23. N. Sandeau, L. Le Xuan, D. Chauvat, C. Zhou, J. F. Roch, and S. Brasselet, “Defocused imaging of second harmonic generation from a single nanocrystal,” Opt. Express 15(24), 16051–16060 (2007).
    [Crossref] [PubMed]
  24. M. Sigelle and R. Hierle, “Determination of the electrooptic coefficients of 3-methyl 4-nitropyridine 1-oxide by an interferometric phase-modulation technique,” J. Appl. Phys. 52(6), 4199–4204 (1981).
    [Crossref]
  25. J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W. Tian, M. E. Hawley, B. Craigo, A. K. Tagantsev, X. Q. Pan, S. K. Streiffer, L. Q. Chen, S. W. Kirchoefer, J. Levy, and D. G. Schlom, “Room-temperature ferroelectricity in strained SrTiO3,” Nature 430(7001), 758–761 (2004).
    [Crossref] [PubMed]
  26. H. Z. Ma, J. Levy, M. D. Biegalski, S. Trolier-McKinstry, and D. G. Schlom, “Room-temperature electro-optic properties of strained SrTiO3 films grown on DyScO3,” J. Appl. Phys. 105(1), 014102 (2009).
    [Crossref]

2009 (2)

B. Hajj, S. De Reguardati, L. Hugonin, B. Le Pioufle, T. Osaki, H. Suzuki, S. Takeuchi, H. Mojzisova, D. Chauvat, and J. Zyss, “Electro-optical imaging microscopy of dye-doped artificial lipidic membranes,” Biophys. J. 97(11), 2913–2921 (2009).
[Crossref] [PubMed]

H. Z. Ma, J. Levy, M. D. Biegalski, S. Trolier-McKinstry, and D. G. Schlom, “Room-temperature electro-optic properties of strained SrTiO3 films grown on DyScO3,” J. Appl. Phys. 105(1), 014102 (2009).
[Crossref]

2008 (1)

X. L. Le, C. Zhou, A. Slablab, D. Chauvat, C. Tard, S. Perruchas, T. Gacoin, P. Villeval, and J. F. Roch, “Photostable second-harmonic generation from a single KTiOPO4 nanocrystal for nonlinear microscopy,” Small 4(9), 1332–1336 (2008).
[Crossref] [PubMed]

2007 (1)

2006 (2)

H. Z. Ma and J. Levy, “GHz apertureless near-field scanning optical microscopy of ferroelectric nanodomain dynamics,” Nano Lett. 6(3), 341–344 (2006).
[Crossref] [PubMed]

T. Toury, S. Brasselet, and J. Zyss, “Electro-optical microscopy: mapping nonlinear polymer films with micrometric resolution,” Opt. Lett. 31(10), 1468–1470 (2006).
[Crossref] [PubMed]

2005 (1)

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[Crossref] [PubMed]

2004 (3)

B. Garrido, M. Lopez, A. Perez-Rodriguez, C. Garcia, P. Pellegrino, R. Ferre, J. A. Moreno, J. R. Morante, C. Bonafos, M. Carrada, A. Claverie, J. de la Torre, and A. Souifi, “Optical and electrical properties of Si-nanocrystals ion beam synthesized in SiO2,” Nucl. Instrum. Methods Phys. Res. B 216, 213–221 (2004).
[Crossref]

D. A. Dombeck, M. Blanchard-Desce, and W. W. Webb, “Optical recording of action potentials with second-harmonic generation microscopy,” J. Neurosci. 24(4), 999–1003 (2004).
[Crossref] [PubMed]

J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W. Tian, M. E. Hawley, B. Craigo, A. K. Tagantsev, X. Q. Pan, S. K. Streiffer, L. Q. Chen, S. W. Kirchoefer, J. Levy, and D. G. Schlom, “Room-temperature ferroelectricity in strained SrTiO3,” Nature 430(7001), 758–761 (2004).
[Crossref] [PubMed]

2003 (1)

2002 (1)

L. M. Zhang, F. J. Zhang, Y. Q. Wang, and R. O. Claus, “Linear electro-optic tensor ratio determination and quadratic electro-optic modulation of electrostatically self-assembled CdSe quantum dot films,” J. Chem. Phys. 116(14), 6297–6304 (2002).
[Crossref]

2001 (2)

Y. S. Wang, R. Z. Wang, P. Sun, Q. Y. Tu, Q. L. Yan, and P. Huang, “Electro-optical properties of CdS0.1Se0.9 nanocrystals,” Physica E 9(2), 310–313 (2001).
[Crossref]

H. Zhang, M. C. Oh, A. Szep, W. H. Steier, C. Zhang, L. R. Dalton, H. Erlig, Y. Chang, D. H. Chang, and H. R. Fetterman, “Push-pull electro-optic polymer modulators with low half-wave voltage and low loss at both 1310 and 1550 nm,” Appl. Phys. Lett. 78(20), 3136–3138 (2001).
[Crossref]

2000 (2)

A. Donval, E. Toussaere, R. Hierle, and J. Zyss, “Polarization insensitive electro-optic polymer modulator,” J. Appl. Phys. 87(7), 3258–3262 (2000).
[Crossref]

Y. S. Wang, R. Z. Wang, P. Sun, Q. Y. Tu, Q. L. Yan, and P. Huang, “Effects of modulated electric field form and frequency on the electro-optical properties of CdS0.1Se0.9 nanocrystals,” J. Appl. Phys. 88(3), 1473–1475 (2000).
[Crossref]

1998 (1)

1995 (1)

C. Bosshard, G. Knopfle, P. Pretre, S. Follonier, C. Serbutoviez, and P. Gunter, “Molecular-crystals and polymers for nonlinear optics,” Opt. Eng. 34(7), 1951–1960 (1995).
[Crossref]

1994 (1)

E. Gross, R. S. Bedlack, and L. M. Loew, “Dual-wavelength ratiometric fluorescence measurement of the membrane dipole potential,” Biophys. J. 67(1), 208–216 (1994).
[Crossref] [PubMed]

1993 (1)

U. Woggon, S. V. Bogdanov, O. Wind, K. H. Schlaad, H. Pier, C. Klingshirn, P. Chatziagorastou, and H. P. Fritz, “Electrooptic properties of CdS embedded in a polymer,” Phys. Rev. B 48(16), 11979–11986 (1993).
[Crossref]

1986 (1)

J. D. Bierlein and C. B. Arweiler, “Electrooptic and dielectric-properties of KTiOPO4,” Appl. Phys. Lett. 49(15), 917–919 (1986).
[Crossref]

1981 (1)

M. Sigelle and R. Hierle, “Determination of the electrooptic coefficients of 3-methyl 4-nitropyridine 1-oxide by an interferometric phase-modulation technique,” J. Appl. Phys. 52(6), 4199–4204 (1981).
[Crossref]

1965 (1)

A. R. Johnston, “The strain-free electrooptic effect in single crystal barium titanate,” Appl. Phys. Lett. 7(7), 195–198 (1965).
[Crossref]

Arweiler, C. B.

J. D. Bierlein and C. B. Arweiler, “Electrooptic and dielectric-properties of KTiOPO4,” Appl. Phys. Lett. 49(15), 917–919 (1986).
[Crossref]

Bedlack, R. S.

E. Gross, R. S. Bedlack, and L. M. Loew, “Dual-wavelength ratiometric fluorescence measurement of the membrane dipole potential,” Biophys. J. 67(1), 208–216 (1994).
[Crossref] [PubMed]

Biegalski, M. D.

H. Z. Ma, J. Levy, M. D. Biegalski, S. Trolier-McKinstry, and D. G. Schlom, “Room-temperature electro-optic properties of strained SrTiO3 films grown on DyScO3,” J. Appl. Phys. 105(1), 014102 (2009).
[Crossref]

Bierlein, J. D.

J. D. Bierlein and C. B. Arweiler, “Electrooptic and dielectric-properties of KTiOPO4,” Appl. Phys. Lett. 49(15), 917–919 (1986).
[Crossref]

Blanchard-Desce, M.

D. A. Dombeck, M. Blanchard-Desce, and W. W. Webb, “Optical recording of action potentials with second-harmonic generation microscopy,” J. Neurosci. 24(4), 999–1003 (2004).
[Crossref] [PubMed]

L. Moreaux, T. Pons, V. Dambrin, M. Blanchard-Desce, and J. Mertz, “Electro-optic response of second-harmonic generation membrane potential sensors,” Opt. Lett. 28(8), 625–627 (2003).
[Crossref] [PubMed]

Bogdanov, S. V.

U. Woggon, S. V. Bogdanov, O. Wind, K. H. Schlaad, H. Pier, C. Klingshirn, P. Chatziagorastou, and H. P. Fritz, “Electrooptic properties of CdS embedded in a polymer,” Phys. Rev. B 48(16), 11979–11986 (1993).
[Crossref]

Bonafos, C.

B. Garrido, M. Lopez, A. Perez-Rodriguez, C. Garcia, P. Pellegrino, R. Ferre, J. A. Moreno, J. R. Morante, C. Bonafos, M. Carrada, A. Claverie, J. de la Torre, and A. Souifi, “Optical and electrical properties of Si-nanocrystals ion beam synthesized in SiO2,” Nucl. Instrum. Methods Phys. Res. B 216, 213–221 (2004).
[Crossref]

Bosshard, C.

C. Bosshard, G. Knopfle, P. Pretre, S. Follonier, C. Serbutoviez, and P. Gunter, “Molecular-crystals and polymers for nonlinear optics,” Opt. Eng. 34(7), 1951–1960 (1995).
[Crossref]

Brasselet, S.

Carrada, M.

B. Garrido, M. Lopez, A. Perez-Rodriguez, C. Garcia, P. Pellegrino, R. Ferre, J. A. Moreno, J. R. Morante, C. Bonafos, M. Carrada, A. Claverie, J. de la Torre, and A. Souifi, “Optical and electrical properties of Si-nanocrystals ion beam synthesized in SiO2,” Nucl. Instrum. Methods Phys. Res. B 216, 213–221 (2004).
[Crossref]

Chang, D. H.

H. Zhang, M. C. Oh, A. Szep, W. H. Steier, C. Zhang, L. R. Dalton, H. Erlig, Y. Chang, D. H. Chang, and H. R. Fetterman, “Push-pull electro-optic polymer modulators with low half-wave voltage and low loss at both 1310 and 1550 nm,” Appl. Phys. Lett. 78(20), 3136–3138 (2001).
[Crossref]

Chang, W.

J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W. Tian, M. E. Hawley, B. Craigo, A. K. Tagantsev, X. Q. Pan, S. K. Streiffer, L. Q. Chen, S. W. Kirchoefer, J. Levy, and D. G. Schlom, “Room-temperature ferroelectricity in strained SrTiO3,” Nature 430(7001), 758–761 (2004).
[Crossref] [PubMed]

Chang, Y.

H. Zhang, M. C. Oh, A. Szep, W. H. Steier, C. Zhang, L. R. Dalton, H. Erlig, Y. Chang, D. H. Chang, and H. R. Fetterman, “Push-pull electro-optic polymer modulators with low half-wave voltage and low loss at both 1310 and 1550 nm,” Appl. Phys. Lett. 78(20), 3136–3138 (2001).
[Crossref]

Chatziagorastou, P.

U. Woggon, S. V. Bogdanov, O. Wind, K. H. Schlaad, H. Pier, C. Klingshirn, P. Chatziagorastou, and H. P. Fritz, “Electrooptic properties of CdS embedded in a polymer,” Phys. Rev. B 48(16), 11979–11986 (1993).
[Crossref]

Chauvat, D.

B. Hajj, S. De Reguardati, L. Hugonin, B. Le Pioufle, T. Osaki, H. Suzuki, S. Takeuchi, H. Mojzisova, D. Chauvat, and J. Zyss, “Electro-optical imaging microscopy of dye-doped artificial lipidic membranes,” Biophys. J. 97(11), 2913–2921 (2009).
[Crossref] [PubMed]

X. L. Le, C. Zhou, A. Slablab, D. Chauvat, C. Tard, S. Perruchas, T. Gacoin, P. Villeval, and J. F. Roch, “Photostable second-harmonic generation from a single KTiOPO4 nanocrystal for nonlinear microscopy,” Small 4(9), 1332–1336 (2008).
[Crossref] [PubMed]

N. Sandeau, L. Le Xuan, D. Chauvat, C. Zhou, J. F. Roch, and S. Brasselet, “Defocused imaging of second harmonic generation from a single nanocrystal,” Opt. Express 15(24), 16051–16060 (2007).
[Crossref] [PubMed]

Chen, L. Q.

J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W. Tian, M. E. Hawley, B. Craigo, A. K. Tagantsev, X. Q. Pan, S. K. Streiffer, L. Q. Chen, S. W. Kirchoefer, J. Levy, and D. G. Schlom, “Room-temperature ferroelectricity in strained SrTiO3,” Nature 430(7001), 758–761 (2004).
[Crossref] [PubMed]

Choudhury, S.

J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W. Tian, M. E. Hawley, B. Craigo, A. K. Tagantsev, X. Q. Pan, S. K. Streiffer, L. Q. Chen, S. W. Kirchoefer, J. Levy, and D. G. Schlom, “Room-temperature ferroelectricity in strained SrTiO3,” Nature 430(7001), 758–761 (2004).
[Crossref] [PubMed]

Claus, R. O.

L. M. Zhang, F. J. Zhang, Y. Q. Wang, and R. O. Claus, “Linear electro-optic tensor ratio determination and quadratic electro-optic modulation of electrostatically self-assembled CdSe quantum dot films,” J. Chem. Phys. 116(14), 6297–6304 (2002).
[Crossref]

Claverie, A.

B. Garrido, M. Lopez, A. Perez-Rodriguez, C. Garcia, P. Pellegrino, R. Ferre, J. A. Moreno, J. R. Morante, C. Bonafos, M. Carrada, A. Claverie, J. de la Torre, and A. Souifi, “Optical and electrical properties of Si-nanocrystals ion beam synthesized in SiO2,” Nucl. Instrum. Methods Phys. Res. B 216, 213–221 (2004).
[Crossref]

Craigo, B.

J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W. Tian, M. E. Hawley, B. Craigo, A. K. Tagantsev, X. Q. Pan, S. K. Streiffer, L. Q. Chen, S. W. Kirchoefer, J. Levy, and D. G. Schlom, “Room-temperature ferroelectricity in strained SrTiO3,” Nature 430(7001), 758–761 (2004).
[Crossref] [PubMed]

Dalton, L. R.

H. Zhang, M. C. Oh, A. Szep, W. H. Steier, C. Zhang, L. R. Dalton, H. Erlig, Y. Chang, D. H. Chang, and H. R. Fetterman, “Push-pull electro-optic polymer modulators with low half-wave voltage and low loss at both 1310 and 1550 nm,” Appl. Phys. Lett. 78(20), 3136–3138 (2001).
[Crossref]

Dambrin, V.

de la Torre, J.

B. Garrido, M. Lopez, A. Perez-Rodriguez, C. Garcia, P. Pellegrino, R. Ferre, J. A. Moreno, J. R. Morante, C. Bonafos, M. Carrada, A. Claverie, J. de la Torre, and A. Souifi, “Optical and electrical properties of Si-nanocrystals ion beam synthesized in SiO2,” Nucl. Instrum. Methods Phys. Res. B 216, 213–221 (2004).
[Crossref]

De Reguardati, S.

B. Hajj, S. De Reguardati, L. Hugonin, B. Le Pioufle, T. Osaki, H. Suzuki, S. Takeuchi, H. Mojzisova, D. Chauvat, and J. Zyss, “Electro-optical imaging microscopy of dye-doped artificial lipidic membranes,” Biophys. J. 97(11), 2913–2921 (2009).
[Crossref] [PubMed]

Dombeck, D. A.

D. A. Dombeck, M. Blanchard-Desce, and W. W. Webb, “Optical recording of action potentials with second-harmonic generation microscopy,” J. Neurosci. 24(4), 999–1003 (2004).
[Crossref] [PubMed]

Donval, A.

A. Donval, E. Toussaere, R. Hierle, and J. Zyss, “Polarization insensitive electro-optic polymer modulator,” J. Appl. Phys. 87(7), 3258–3262 (2000).
[Crossref]

Erlig, H.

H. Zhang, M. C. Oh, A. Szep, W. H. Steier, C. Zhang, L. R. Dalton, H. Erlig, Y. Chang, D. H. Chang, and H. R. Fetterman, “Push-pull electro-optic polymer modulators with low half-wave voltage and low loss at both 1310 and 1550 nm,” Appl. Phys. Lett. 78(20), 3136–3138 (2001).
[Crossref]

Ferre, R.

B. Garrido, M. Lopez, A. Perez-Rodriguez, C. Garcia, P. Pellegrino, R. Ferre, J. A. Moreno, J. R. Morante, C. Bonafos, M. Carrada, A. Claverie, J. de la Torre, and A. Souifi, “Optical and electrical properties of Si-nanocrystals ion beam synthesized in SiO2,” Nucl. Instrum. Methods Phys. Res. B 216, 213–221 (2004).
[Crossref]

Fetterman, H. R.

H. Zhang, M. C. Oh, A. Szep, W. H. Steier, C. Zhang, L. R. Dalton, H. Erlig, Y. Chang, D. H. Chang, and H. R. Fetterman, “Push-pull electro-optic polymer modulators with low half-wave voltage and low loss at both 1310 and 1550 nm,” Appl. Phys. Lett. 78(20), 3136–3138 (2001).
[Crossref]

Follonier, S.

C. Bosshard, G. Knopfle, P. Pretre, S. Follonier, C. Serbutoviez, and P. Gunter, “Molecular-crystals and polymers for nonlinear optics,” Opt. Eng. 34(7), 1951–1960 (1995).
[Crossref]

Fritz, H. P.

U. Woggon, S. V. Bogdanov, O. Wind, K. H. Schlaad, H. Pier, C. Klingshirn, P. Chatziagorastou, and H. P. Fritz, “Electrooptic properties of CdS embedded in a polymer,” Phys. Rev. B 48(16), 11979–11986 (1993).
[Crossref]

Gacoin, T.

X. L. Le, C. Zhou, A. Slablab, D. Chauvat, C. Tard, S. Perruchas, T. Gacoin, P. Villeval, and J. F. Roch, “Photostable second-harmonic generation from a single KTiOPO4 nanocrystal for nonlinear microscopy,” Small 4(9), 1332–1336 (2008).
[Crossref] [PubMed]

Garcia, C.

B. Garrido, M. Lopez, A. Perez-Rodriguez, C. Garcia, P. Pellegrino, R. Ferre, J. A. Moreno, J. R. Morante, C. Bonafos, M. Carrada, A. Claverie, J. de la Torre, and A. Souifi, “Optical and electrical properties of Si-nanocrystals ion beam synthesized in SiO2,” Nucl. Instrum. Methods Phys. Res. B 216, 213–221 (2004).
[Crossref]

Garrido, B.

B. Garrido, M. Lopez, A. Perez-Rodriguez, C. Garcia, P. Pellegrino, R. Ferre, J. A. Moreno, J. R. Morante, C. Bonafos, M. Carrada, A. Claverie, J. de la Torre, and A. Souifi, “Optical and electrical properties of Si-nanocrystals ion beam synthesized in SiO2,” Nucl. Instrum. Methods Phys. Res. B 216, 213–221 (2004).
[Crossref]

Gross, E.

E. Gross, R. S. Bedlack, and L. M. Loew, “Dual-wavelength ratiometric fluorescence measurement of the membrane dipole potential,” Biophys. J. 67(1), 208–216 (1994).
[Crossref] [PubMed]

Gunter, P.

C. Bosshard, G. Knopfle, P. Pretre, S. Follonier, C. Serbutoviez, and P. Gunter, “Molecular-crystals and polymers for nonlinear optics,” Opt. Eng. 34(7), 1951–1960 (1995).
[Crossref]

Haeni, J. H.

J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W. Tian, M. E. Hawley, B. Craigo, A. K. Tagantsev, X. Q. Pan, S. K. Streiffer, L. Q. Chen, S. W. Kirchoefer, J. Levy, and D. G. Schlom, “Room-temperature ferroelectricity in strained SrTiO3,” Nature 430(7001), 758–761 (2004).
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B. Hajj, S. De Reguardati, L. Hugonin, B. Le Pioufle, T. Osaki, H. Suzuki, S. Takeuchi, H. Mojzisova, D. Chauvat, and J. Zyss, “Electro-optical imaging microscopy of dye-doped artificial lipidic membranes,” Biophys. J. 97(11), 2913–2921 (2009).
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J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W. Tian, M. E. Hawley, B. Craigo, A. K. Tagantsev, X. Q. Pan, S. K. Streiffer, L. Q. Chen, S. W. Kirchoefer, J. Levy, and D. G. Schlom, “Room-temperature ferroelectricity in strained SrTiO3,” Nature 430(7001), 758–761 (2004).
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A. Donval, E. Toussaere, R. Hierle, and J. Zyss, “Polarization insensitive electro-optic polymer modulator,” J. Appl. Phys. 87(7), 3258–3262 (2000).
[Crossref]

M. Sigelle and R. Hierle, “Determination of the electrooptic coefficients of 3-methyl 4-nitropyridine 1-oxide by an interferometric phase-modulation technique,” J. Appl. Phys. 52(6), 4199–4204 (1981).
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Huang, P.

Y. S. Wang, R. Z. Wang, P. Sun, Q. Y. Tu, Q. L. Yan, and P. Huang, “Electro-optical properties of CdS0.1Se0.9 nanocrystals,” Physica E 9(2), 310–313 (2001).
[Crossref]

Y. S. Wang, R. Z. Wang, P. Sun, Q. Y. Tu, Q. L. Yan, and P. Huang, “Effects of modulated electric field form and frequency on the electro-optical properties of CdS0.1Se0.9 nanocrystals,” J. Appl. Phys. 88(3), 1473–1475 (2000).
[Crossref]

Hugonin, L.

B. Hajj, S. De Reguardati, L. Hugonin, B. Le Pioufle, T. Osaki, H. Suzuki, S. Takeuchi, H. Mojzisova, D. Chauvat, and J. Zyss, “Electro-optical imaging microscopy of dye-doped artificial lipidic membranes,” Biophys. J. 97(11), 2913–2921 (2009).
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J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W. Tian, M. E. Hawley, B. Craigo, A. K. Tagantsev, X. Q. Pan, S. K. Streiffer, L. Q. Chen, S. W. Kirchoefer, J. Levy, and D. G. Schlom, “Room-temperature ferroelectricity in strained SrTiO3,” Nature 430(7001), 758–761 (2004).
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J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W. Tian, M. E. Hawley, B. Craigo, A. K. Tagantsev, X. Q. Pan, S. K. Streiffer, L. Q. Chen, S. W. Kirchoefer, J. Levy, and D. G. Schlom, “Room-temperature ferroelectricity in strained SrTiO3,” Nature 430(7001), 758–761 (2004).
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U. Woggon, S. V. Bogdanov, O. Wind, K. H. Schlaad, H. Pier, C. Klingshirn, P. Chatziagorastou, and H. P. Fritz, “Electrooptic properties of CdS embedded in a polymer,” Phys. Rev. B 48(16), 11979–11986 (1993).
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C. Bosshard, G. Knopfle, P. Pretre, S. Follonier, C. Serbutoviez, and P. Gunter, “Molecular-crystals and polymers for nonlinear optics,” Opt. Eng. 34(7), 1951–1960 (1995).
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X. L. Le, C. Zhou, A. Slablab, D. Chauvat, C. Tard, S. Perruchas, T. Gacoin, P. Villeval, and J. F. Roch, “Photostable second-harmonic generation from a single KTiOPO4 nanocrystal for nonlinear microscopy,” Small 4(9), 1332–1336 (2008).
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Le Pioufle, B.

B. Hajj, S. De Reguardati, L. Hugonin, B. Le Pioufle, T. Osaki, H. Suzuki, S. Takeuchi, H. Mojzisova, D. Chauvat, and J. Zyss, “Electro-optical imaging microscopy of dye-doped artificial lipidic membranes,” Biophys. J. 97(11), 2913–2921 (2009).
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Le Xuan, L.

Levy, J.

H. Z. Ma, J. Levy, M. D. Biegalski, S. Trolier-McKinstry, and D. G. Schlom, “Room-temperature electro-optic properties of strained SrTiO3 films grown on DyScO3,” J. Appl. Phys. 105(1), 014102 (2009).
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H. Z. Ma and J. Levy, “GHz apertureless near-field scanning optical microscopy of ferroelectric nanodomain dynamics,” Nano Lett. 6(3), 341–344 (2006).
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J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W. Tian, M. E. Hawley, B. Craigo, A. K. Tagantsev, X. Q. Pan, S. K. Streiffer, L. Q. Chen, S. W. Kirchoefer, J. Levy, and D. G. Schlom, “Room-temperature ferroelectricity in strained SrTiO3,” Nature 430(7001), 758–761 (2004).
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Li, Y. L.

J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W. Tian, M. E. Hawley, B. Craigo, A. K. Tagantsev, X. Q. Pan, S. K. Streiffer, L. Q. Chen, S. W. Kirchoefer, J. Levy, and D. G. Schlom, “Room-temperature ferroelectricity in strained SrTiO3,” Nature 430(7001), 758–761 (2004).
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Lipson, M.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
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E. Gross, R. S. Bedlack, and L. M. Loew, “Dual-wavelength ratiometric fluorescence measurement of the membrane dipole potential,” Biophys. J. 67(1), 208–216 (1994).
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Lopez, M.

B. Garrido, M. Lopez, A. Perez-Rodriguez, C. Garcia, P. Pellegrino, R. Ferre, J. A. Moreno, J. R. Morante, C. Bonafos, M. Carrada, A. Claverie, J. de la Torre, and A. Souifi, “Optical and electrical properties of Si-nanocrystals ion beam synthesized in SiO2,” Nucl. Instrum. Methods Phys. Res. B 216, 213–221 (2004).
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Ma, H. Z.

H. Z. Ma, J. Levy, M. D. Biegalski, S. Trolier-McKinstry, and D. G. Schlom, “Room-temperature electro-optic properties of strained SrTiO3 films grown on DyScO3,” J. Appl. Phys. 105(1), 014102 (2009).
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H. Z. Ma and J. Levy, “GHz apertureless near-field scanning optical microscopy of ferroelectric nanodomain dynamics,” Nano Lett. 6(3), 341–344 (2006).
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Mertz, J.

Mitomi, O.

Miyazawa, H.

Mojzisova, H.

B. Hajj, S. De Reguardati, L. Hugonin, B. Le Pioufle, T. Osaki, H. Suzuki, S. Takeuchi, H. Mojzisova, D. Chauvat, and J. Zyss, “Electro-optical imaging microscopy of dye-doped artificial lipidic membranes,” Biophys. J. 97(11), 2913–2921 (2009).
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Morante, J. R.

B. Garrido, M. Lopez, A. Perez-Rodriguez, C. Garcia, P. Pellegrino, R. Ferre, J. A. Moreno, J. R. Morante, C. Bonafos, M. Carrada, A. Claverie, J. de la Torre, and A. Souifi, “Optical and electrical properties of Si-nanocrystals ion beam synthesized in SiO2,” Nucl. Instrum. Methods Phys. Res. B 216, 213–221 (2004).
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Moreaux, L.

Moreno, J. A.

B. Garrido, M. Lopez, A. Perez-Rodriguez, C. Garcia, P. Pellegrino, R. Ferre, J. A. Moreno, J. R. Morante, C. Bonafos, M. Carrada, A. Claverie, J. de la Torre, and A. Souifi, “Optical and electrical properties of Si-nanocrystals ion beam synthesized in SiO2,” Nucl. Instrum. Methods Phys. Res. B 216, 213–221 (2004).
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Noguchi, K.

Oh, M. C.

H. Zhang, M. C. Oh, A. Szep, W. H. Steier, C. Zhang, L. R. Dalton, H. Erlig, Y. Chang, D. H. Chang, and H. R. Fetterman, “Push-pull electro-optic polymer modulators with low half-wave voltage and low loss at both 1310 and 1550 nm,” Appl. Phys. Lett. 78(20), 3136–3138 (2001).
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Osaki, T.

B. Hajj, S. De Reguardati, L. Hugonin, B. Le Pioufle, T. Osaki, H. Suzuki, S. Takeuchi, H. Mojzisova, D. Chauvat, and J. Zyss, “Electro-optical imaging microscopy of dye-doped artificial lipidic membranes,” Biophys. J. 97(11), 2913–2921 (2009).
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Pan, X. Q.

J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W. Tian, M. E. Hawley, B. Craigo, A. K. Tagantsev, X. Q. Pan, S. K. Streiffer, L. Q. Chen, S. W. Kirchoefer, J. Levy, and D. G. Schlom, “Room-temperature ferroelectricity in strained SrTiO3,” Nature 430(7001), 758–761 (2004).
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Pellegrino, P.

B. Garrido, M. Lopez, A. Perez-Rodriguez, C. Garcia, P. Pellegrino, R. Ferre, J. A. Moreno, J. R. Morante, C. Bonafos, M. Carrada, A. Claverie, J. de la Torre, and A. Souifi, “Optical and electrical properties of Si-nanocrystals ion beam synthesized in SiO2,” Nucl. Instrum. Methods Phys. Res. B 216, 213–221 (2004).
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Perez-Rodriguez, A.

B. Garrido, M. Lopez, A. Perez-Rodriguez, C. Garcia, P. Pellegrino, R. Ferre, J. A. Moreno, J. R. Morante, C. Bonafos, M. Carrada, A. Claverie, J. de la Torre, and A. Souifi, “Optical and electrical properties of Si-nanocrystals ion beam synthesized in SiO2,” Nucl. Instrum. Methods Phys. Res. B 216, 213–221 (2004).
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Perruchas, S.

X. L. Le, C. Zhou, A. Slablab, D. Chauvat, C. Tard, S. Perruchas, T. Gacoin, P. Villeval, and J. F. Roch, “Photostable second-harmonic generation from a single KTiOPO4 nanocrystal for nonlinear microscopy,” Small 4(9), 1332–1336 (2008).
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Pier, H.

U. Woggon, S. V. Bogdanov, O. Wind, K. H. Schlaad, H. Pier, C. Klingshirn, P. Chatziagorastou, and H. P. Fritz, “Electrooptic properties of CdS embedded in a polymer,” Phys. Rev. B 48(16), 11979–11986 (1993).
[Crossref]

Pons, T.

Pradhan, S.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[Crossref] [PubMed]

Pretre, P.

C. Bosshard, G. Knopfle, P. Pretre, S. Follonier, C. Serbutoviez, and P. Gunter, “Molecular-crystals and polymers for nonlinear optics,” Opt. Eng. 34(7), 1951–1960 (1995).
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Reiche, P.

J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W. Tian, M. E. Hawley, B. Craigo, A. K. Tagantsev, X. Q. Pan, S. K. Streiffer, L. Q. Chen, S. W. Kirchoefer, J. Levy, and D. G. Schlom, “Room-temperature ferroelectricity in strained SrTiO3,” Nature 430(7001), 758–761 (2004).
[Crossref] [PubMed]

Roch, J. F.

X. L. Le, C. Zhou, A. Slablab, D. Chauvat, C. Tard, S. Perruchas, T. Gacoin, P. Villeval, and J. F. Roch, “Photostable second-harmonic generation from a single KTiOPO4 nanocrystal for nonlinear microscopy,” Small 4(9), 1332–1336 (2008).
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N. Sandeau, L. Le Xuan, D. Chauvat, C. Zhou, J. F. Roch, and S. Brasselet, “Defocused imaging of second harmonic generation from a single nanocrystal,” Opt. Express 15(24), 16051–16060 (2007).
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Schlaad, K. H.

U. Woggon, S. V. Bogdanov, O. Wind, K. H. Schlaad, H. Pier, C. Klingshirn, P. Chatziagorastou, and H. P. Fritz, “Electrooptic properties of CdS embedded in a polymer,” Phys. Rev. B 48(16), 11979–11986 (1993).
[Crossref]

Schlom, D. G.

H. Z. Ma, J. Levy, M. D. Biegalski, S. Trolier-McKinstry, and D. G. Schlom, “Room-temperature electro-optic properties of strained SrTiO3 films grown on DyScO3,” J. Appl. Phys. 105(1), 014102 (2009).
[Crossref]

J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W. Tian, M. E. Hawley, B. Craigo, A. K. Tagantsev, X. Q. Pan, S. K. Streiffer, L. Q. Chen, S. W. Kirchoefer, J. Levy, and D. G. Schlom, “Room-temperature ferroelectricity in strained SrTiO3,” Nature 430(7001), 758–761 (2004).
[Crossref] [PubMed]

Schmidt, B.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[Crossref] [PubMed]

Serbutoviez, C.

C. Bosshard, G. Knopfle, P. Pretre, S. Follonier, C. Serbutoviez, and P. Gunter, “Molecular-crystals and polymers for nonlinear optics,” Opt. Eng. 34(7), 1951–1960 (1995).
[Crossref]

Sigelle, M.

M. Sigelle and R. Hierle, “Determination of the electrooptic coefficients of 3-methyl 4-nitropyridine 1-oxide by an interferometric phase-modulation technique,” J. Appl. Phys. 52(6), 4199–4204 (1981).
[Crossref]

Slablab, A.

X. L. Le, C. Zhou, A. Slablab, D. Chauvat, C. Tard, S. Perruchas, T. Gacoin, P. Villeval, and J. F. Roch, “Photostable second-harmonic generation from a single KTiOPO4 nanocrystal for nonlinear microscopy,” Small 4(9), 1332–1336 (2008).
[Crossref] [PubMed]

Souifi, A.

B. Garrido, M. Lopez, A. Perez-Rodriguez, C. Garcia, P. Pellegrino, R. Ferre, J. A. Moreno, J. R. Morante, C. Bonafos, M. Carrada, A. Claverie, J. de la Torre, and A. Souifi, “Optical and electrical properties of Si-nanocrystals ion beam synthesized in SiO2,” Nucl. Instrum. Methods Phys. Res. B 216, 213–221 (2004).
[Crossref]

Steier, W. H.

H. Zhang, M. C. Oh, A. Szep, W. H. Steier, C. Zhang, L. R. Dalton, H. Erlig, Y. Chang, D. H. Chang, and H. R. Fetterman, “Push-pull electro-optic polymer modulators with low half-wave voltage and low loss at both 1310 and 1550 nm,” Appl. Phys. Lett. 78(20), 3136–3138 (2001).
[Crossref]

Streiffer, S. K.

J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W. Tian, M. E. Hawley, B. Craigo, A. K. Tagantsev, X. Q. Pan, S. K. Streiffer, L. Q. Chen, S. W. Kirchoefer, J. Levy, and D. G. Schlom, “Room-temperature ferroelectricity in strained SrTiO3,” Nature 430(7001), 758–761 (2004).
[Crossref] [PubMed]

Sun, P.

Y. S. Wang, R. Z. Wang, P. Sun, Q. Y. Tu, Q. L. Yan, and P. Huang, “Electro-optical properties of CdS0.1Se0.9 nanocrystals,” Physica E 9(2), 310–313 (2001).
[Crossref]

Y. S. Wang, R. Z. Wang, P. Sun, Q. Y. Tu, Q. L. Yan, and P. Huang, “Effects of modulated electric field form and frequency on the electro-optical properties of CdS0.1Se0.9 nanocrystals,” J. Appl. Phys. 88(3), 1473–1475 (2000).
[Crossref]

Suzuki, H.

B. Hajj, S. De Reguardati, L. Hugonin, B. Le Pioufle, T. Osaki, H. Suzuki, S. Takeuchi, H. Mojzisova, D. Chauvat, and J. Zyss, “Electro-optical imaging microscopy of dye-doped artificial lipidic membranes,” Biophys. J. 97(11), 2913–2921 (2009).
[Crossref] [PubMed]

Szep, A.

H. Zhang, M. C. Oh, A. Szep, W. H. Steier, C. Zhang, L. R. Dalton, H. Erlig, Y. Chang, D. H. Chang, and H. R. Fetterman, “Push-pull electro-optic polymer modulators with low half-wave voltage and low loss at both 1310 and 1550 nm,” Appl. Phys. Lett. 78(20), 3136–3138 (2001).
[Crossref]

Tagantsev, A. K.

J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W. Tian, M. E. Hawley, B. Craigo, A. K. Tagantsev, X. Q. Pan, S. K. Streiffer, L. Q. Chen, S. W. Kirchoefer, J. Levy, and D. G. Schlom, “Room-temperature ferroelectricity in strained SrTiO3,” Nature 430(7001), 758–761 (2004).
[Crossref] [PubMed]

Takeuchi, S.

B. Hajj, S. De Reguardati, L. Hugonin, B. Le Pioufle, T. Osaki, H. Suzuki, S. Takeuchi, H. Mojzisova, D. Chauvat, and J. Zyss, “Electro-optical imaging microscopy of dye-doped artificial lipidic membranes,” Biophys. J. 97(11), 2913–2921 (2009).
[Crossref] [PubMed]

Tard, C.

X. L. Le, C. Zhou, A. Slablab, D. Chauvat, C. Tard, S. Perruchas, T. Gacoin, P. Villeval, and J. F. Roch, “Photostable second-harmonic generation from a single KTiOPO4 nanocrystal for nonlinear microscopy,” Small 4(9), 1332–1336 (2008).
[Crossref] [PubMed]

Tian, W.

J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W. Tian, M. E. Hawley, B. Craigo, A. K. Tagantsev, X. Q. Pan, S. K. Streiffer, L. Q. Chen, S. W. Kirchoefer, J. Levy, and D. G. Schlom, “Room-temperature ferroelectricity in strained SrTiO3,” Nature 430(7001), 758–761 (2004).
[Crossref] [PubMed]

Toury, T.

Toussaere, E.

A. Donval, E. Toussaere, R. Hierle, and J. Zyss, “Polarization insensitive electro-optic polymer modulator,” J. Appl. Phys. 87(7), 3258–3262 (2000).
[Crossref]

Trolier-McKinstry, S.

H. Z. Ma, J. Levy, M. D. Biegalski, S. Trolier-McKinstry, and D. G. Schlom, “Room-temperature electro-optic properties of strained SrTiO3 films grown on DyScO3,” J. Appl. Phys. 105(1), 014102 (2009).
[Crossref]

Tu, Q. Y.

Y. S. Wang, R. Z. Wang, P. Sun, Q. Y. Tu, Q. L. Yan, and P. Huang, “Electro-optical properties of CdS0.1Se0.9 nanocrystals,” Physica E 9(2), 310–313 (2001).
[Crossref]

Y. S. Wang, R. Z. Wang, P. Sun, Q. Y. Tu, Q. L. Yan, and P. Huang, “Effects of modulated electric field form and frequency on the electro-optical properties of CdS0.1Se0.9 nanocrystals,” J. Appl. Phys. 88(3), 1473–1475 (2000).
[Crossref]

Uecker, R.

J. H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y. L. Li, S. Choudhury, W. Tian, M. E. Hawley, B. Craigo, A. K. Tagantsev, X. Q. Pan, S. K. Streiffer, L. Q. Chen, S. W. Kirchoefer, J. Levy, and D. G. Schlom, “Room-temperature ferroelectricity in strained SrTiO3,” Nature 430(7001), 758–761 (2004).
[Crossref] [PubMed]

Villeval, P.

X. L. Le, C. Zhou, A. Slablab, D. Chauvat, C. Tard, S. Perruchas, T. Gacoin, P. Villeval, and J. F. Roch, “Photostable second-harmonic generation from a single KTiOPO4 nanocrystal for nonlinear microscopy,” Small 4(9), 1332–1336 (2008).
[Crossref] [PubMed]

Wang, R. Z.

Y. S. Wang, R. Z. Wang, P. Sun, Q. Y. Tu, Q. L. Yan, and P. Huang, “Electro-optical properties of CdS0.1Se0.9 nanocrystals,” Physica E 9(2), 310–313 (2001).
[Crossref]

Y. S. Wang, R. Z. Wang, P. Sun, Q. Y. Tu, Q. L. Yan, and P. Huang, “Effects of modulated electric field form and frequency on the electro-optical properties of CdS0.1Se0.9 nanocrystals,” J. Appl. Phys. 88(3), 1473–1475 (2000).
[Crossref]

Wang, Y. Q.

L. M. Zhang, F. J. Zhang, Y. Q. Wang, and R. O. Claus, “Linear electro-optic tensor ratio determination and quadratic electro-optic modulation of electrostatically self-assembled CdSe quantum dot films,” J. Chem. Phys. 116(14), 6297–6304 (2002).
[Crossref]

Wang, Y. S.

Y. S. Wang, R. Z. Wang, P. Sun, Q. Y. Tu, Q. L. Yan, and P. Huang, “Electro-optical properties of CdS0.1Se0.9 nanocrystals,” Physica E 9(2), 310–313 (2001).
[Crossref]

Y. S. Wang, R. Z. Wang, P. Sun, Q. Y. Tu, Q. L. Yan, and P. Huang, “Effects of modulated electric field form and frequency on the electro-optical properties of CdS0.1Se0.9 nanocrystals,” J. Appl. Phys. 88(3), 1473–1475 (2000).
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Webb, W. W.

D. A. Dombeck, M. Blanchard-Desce, and W. W. Webb, “Optical recording of action potentials with second-harmonic generation microscopy,” J. Neurosci. 24(4), 999–1003 (2004).
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Wind, O.

U. Woggon, S. V. Bogdanov, O. Wind, K. H. Schlaad, H. Pier, C. Klingshirn, P. Chatziagorastou, and H. P. Fritz, “Electrooptic properties of CdS embedded in a polymer,” Phys. Rev. B 48(16), 11979–11986 (1993).
[Crossref]

Woggon, U.

U. Woggon, S. V. Bogdanov, O. Wind, K. H. Schlaad, H. Pier, C. Klingshirn, P. Chatziagorastou, and H. P. Fritz, “Electrooptic properties of CdS embedded in a polymer,” Phys. Rev. B 48(16), 11979–11986 (1993).
[Crossref]

Xu, Q.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[Crossref] [PubMed]

Yan, Q. L.

Y. S. Wang, R. Z. Wang, P. Sun, Q. Y. Tu, Q. L. Yan, and P. Huang, “Electro-optical properties of CdS0.1Se0.9 nanocrystals,” Physica E 9(2), 310–313 (2001).
[Crossref]

Y. S. Wang, R. Z. Wang, P. Sun, Q. Y. Tu, Q. L. Yan, and P. Huang, “Effects of modulated electric field form and frequency on the electro-optical properties of CdS0.1Se0.9 nanocrystals,” J. Appl. Phys. 88(3), 1473–1475 (2000).
[Crossref]

Zhang, C.

H. Zhang, M. C. Oh, A. Szep, W. H. Steier, C. Zhang, L. R. Dalton, H. Erlig, Y. Chang, D. H. Chang, and H. R. Fetterman, “Push-pull electro-optic polymer modulators with low half-wave voltage and low loss at both 1310 and 1550 nm,” Appl. Phys. Lett. 78(20), 3136–3138 (2001).
[Crossref]

Zhang, F. J.

L. M. Zhang, F. J. Zhang, Y. Q. Wang, and R. O. Claus, “Linear electro-optic tensor ratio determination and quadratic electro-optic modulation of electrostatically self-assembled CdSe quantum dot films,” J. Chem. Phys. 116(14), 6297–6304 (2002).
[Crossref]

Zhang, H.

H. Zhang, M. C. Oh, A. Szep, W. H. Steier, C. Zhang, L. R. Dalton, H. Erlig, Y. Chang, D. H. Chang, and H. R. Fetterman, “Push-pull electro-optic polymer modulators with low half-wave voltage and low loss at both 1310 and 1550 nm,” Appl. Phys. Lett. 78(20), 3136–3138 (2001).
[Crossref]

Zhang, L. M.

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Small (1)

X. L. Le, C. Zhou, A. Slablab, D. Chauvat, C. Tard, S. Perruchas, T. Gacoin, P. Villeval, and J. F. Roch, “Photostable second-harmonic generation from a single KTiOPO4 nanocrystal for nonlinear microscopy,” Small 4(9), 1332–1336 (2008).
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Figures (4)

Fig. 1
Fig. 1 Principle of EO detection: a) the different fields participating to the experiment; Ein: incident optical field, EΩ: quasi-static field applied by lateral gold electrodes, P: crystal polarization; b) Simplified representation of the interferometer scheme; L: cw HeNe laser, P: photodiode.

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Fig. 2
Fig. 2 Dynamic light scattering of the KTP solution used in this experiment. A mean value of 150nm size is found.

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Fig. 3
Fig. 3 (a) Typical spatial response distribution from a single nanocrystal; (b) the linear dependence of the signal on the applied electric field amplitude.

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Fig. 4
Fig. 4 (a) Theoretical polar response for the simplified case where the crystal Z-axis and the applied electric field are long the x-axis of the laboratory frame; b,c,d)Polar response for three different nanocrystal orientations. The black dots stand for the experimental data and the red line for the simulation which Euler angle are respectively (114,45,150), (70,110,50) and (140,45,315). The corresponding crystal 3D orientation is presented under each polar graph.

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Equations (9)

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

P i ∝ ε 0 ∑ j ∑ k r i j k E j ω E k Ω
[ r i j ] = ( 0 0 r 13 0 0 r 23 0 0 r 33 0 r 42 0 r 51 0 0 0 0 0 )
E → S C ∝ ∂ 2 P → ∂ t 2 = − ( ω + Ω ) 2 P →
I = | E r e f ω + E s i g ω + E s c a t t e r i n g ω + Ω | 2
S ∝ 2 Re [ ( E r e f ω + E s i g ω ) * E s c ω + Ω ]
E → i n c = E 0 ( cos θ   u → x + sin θ   u → y )
E → s c ∝ P → ∝ ε 0 E 0 E 1 Ω [ ( r 33 cos θ + r 52 sin θ ) u → x + ( r 53 cos θ + r 13 sin θ ) u → y ]
I int e r f e r e n c e ≈ 2 ( E r e f + E s ) E S C ∝ ε 0 E 0 E 1 Ω ( E r e f ω + E s ) [ r 33 cos 2 θ + r 13 sin 2 θ ]
r i , j , k = ∑ i ' , j ' , k ' r i ' , j ' , k ' ( i ^ ' , i ^ ) ( j ^ ' , j ^ ) ( k ^ ' , k ^ )

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