Abstract

The operation of photovoltaic (PV) tweezers, using the evanescent light-induced PV fields to trap and pattern nano- and micro-meter particles on a LiNbO3 crystal surface, is discussed. The case of a periodic light pattern is addressed in detail, including the role of particle shape and the modulation index of the light pattern. The use of a single Gaussian light beam is also considered. Illustrative experiments for the two situations are presented. The performance of such PV tweezers in comparison to the best established case of optical tweezers, using optical forces, is considered. Differential features between the two trapping approaches are remarked.

© 2011 OSA

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    [CrossRef]
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  6. P. Mokrý, M. Marvan, and J. Fousek, “Patterning of dielectric nanoparticles using dielectrophoretic forces generated by ferroelectric polydomain films,” J. Appl. Phys. 107(9), 094104 (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2011 (1)

A. Blázquez-Castro, J. C. Stockert, B. López-Arias, A. Juarranz, F. Agulló-López, A. García-Cabañes, and M. Carrascosa, “Tumour cell death induced by the bulk photovoltaic effect of LiNbO3:Fe under visible light irradiation,” Photochem. Photobiol. Sci. 10(6), 956–963 (2011).
[CrossRef] [PubMed]

2010 (2)

P. Mokrý, M. Marvan, and J. Fousek, “Patterning of dielectric nanoparticles using dielectrophoretic forces generated by ferroelectric polydomain films,” J. Appl. Phys. 107(9), 094104 (2010).
[CrossRef]

M. Esseling, F. Holtmann, M. Woerdemann, and C. Denz, “Two-dimensional dielectrophoretic particle trapping in a hybrid crystal/PDMS-system,” Opt. Express 18(16), 17404–17411 (2010).
[CrossRef] [PubMed]

2009 (1)

2008 (1)

A. Jonáš and P. Zemánek, “Light at work: the use of optical forces for particle manipulation, sorting, and analysis,” Electrophoresis 29(24), 4813–4851 (2008).
[CrossRef] [PubMed]

2007 (1)

H. A. Eggert, F. Y. Kuhnert, K. Buse, J. R. Adleman, and D. Psaltis, “Trapping of dielectric particles with light-induced space-charge fields,” Appl. Phys. Lett. 90(24), 241909 (2007).
[CrossRef]

2002 (2)

P. R. Gascoyne and J. Vykoukal, “Particle separation by dielectrophoresis,” Electrophoresis 23(13), 1973–1983 (2002).
[CrossRef] [PubMed]

T. Hao, “Electrorheological suspensions,” Adv. Colloid Interface Sci. 97(1-3), 1–35 (2002).
[CrossRef] [PubMed]

2001 (1)

S. S. Sarkisov, M. J. Curley, N. V. Kukhtarev, A. Fields, G. Adamovsky, C. C. Smith, and E. L. Moore, “Holographic surface gratings in iron-doped lithium niobate,” Appl. Phys. Lett. 79(7), 901–903 (2001).
[CrossRef]

1998 (1)

1997 (1)

F. Agulló-López, M. Carrascosa, and M. Aguilar, “An alternative design strategy for thin photorefractive polymer structures,” Adv. Mater. (Deerfield Beach Fla.) 9, 423–426 (1997).
[CrossRef]

1996 (3)

F. Agulló-López, M. Aguilar, and M. Carrascosa, “Photorefractive thin films,” Pure Appl. Opt. 5(5), 495–503 (1996).
[CrossRef]

L. Solymar, M. Aguilar, and F. Agulló-López, “Unified two-dimensional model for grating dynamics in photorefractive materials,” J. Appl. Phys. 80(3), 1268–1274 (1996).
[CrossRef]

M. Aguilar, M. Carrascosa, F. Agulló-López, L. F. Magaña, and L. Solymar, “Short-time photorefractive recording in multiple quantum wells: longitudinal geometry,” J. Opt. Soc. Am. B 13(11), 2630–2635 (1996).
[CrossRef]

1994 (2)

E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Recording and erasure kinetics in photorefractive materials at high modulation depths,” J. Opt. Soc. Am. B 11(4), 670–675 (1994).
[CrossRef]

E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Steady state photorefractive gratings in LiNbO3 for strong light modulation depths,” IEEE J. Quantum Electron. 30(4), 875–880 (1994).
[CrossRef]

1993 (1)

J. V. Alvarez-Bravo, M. Carrascosa, and L. Arizmendi, “Experimental effects of light intensity modulation on the recording and erasure of holographic gratings in BSO crystals,” Opt. Commun. 103(1-2), 22–28 (1993).
[CrossRef]

1970 (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
[CrossRef]

Adamovsky, G.

S. S. Sarkisov, M. J. Curley, N. V. Kukhtarev, A. Fields, G. Adamovsky, C. C. Smith, and E. L. Moore, “Holographic surface gratings in iron-doped lithium niobate,” Appl. Phys. Lett. 79(7), 901–903 (2001).
[CrossRef]

Adleman, J. R.

H. A. Eggert, F. Y. Kuhnert, K. Buse, J. R. Adleman, and D. Psaltis, “Trapping of dielectric particles with light-induced space-charge fields,” Appl. Phys. Lett. 90(24), 241909 (2007).
[CrossRef]

Aguilar, M.

F. Agulló-López, M. Carrascosa, and M. Aguilar, “An alternative design strategy for thin photorefractive polymer structures,” Adv. Mater. (Deerfield Beach Fla.) 9, 423–426 (1997).
[CrossRef]

F. Agulló-López, M. Aguilar, and M. Carrascosa, “Photorefractive thin films,” Pure Appl. Opt. 5(5), 495–503 (1996).
[CrossRef]

L. Solymar, M. Aguilar, and F. Agulló-López, “Unified two-dimensional model for grating dynamics in photorefractive materials,” J. Appl. Phys. 80(3), 1268–1274 (1996).
[CrossRef]

M. Aguilar, M. Carrascosa, F. Agulló-López, L. F. Magaña, and L. Solymar, “Short-time photorefractive recording in multiple quantum wells: longitudinal geometry,” J. Opt. Soc. Am. B 13(11), 2630–2635 (1996).
[CrossRef]

Agulló-López, F.

A. Blázquez-Castro, J. C. Stockert, B. López-Arias, A. Juarranz, F. Agulló-López, A. García-Cabañes, and M. Carrascosa, “Tumour cell death induced by the bulk photovoltaic effect of LiNbO3:Fe under visible light irradiation,” Photochem. Photobiol. Sci. 10(6), 956–963 (2011).
[CrossRef] [PubMed]

F. Agulló-López, M. Carrascosa, and M. Aguilar, “An alternative design strategy for thin photorefractive polymer structures,” Adv. Mater. (Deerfield Beach Fla.) 9, 423–426 (1997).
[CrossRef]

F. Agulló-López, M. Aguilar, and M. Carrascosa, “Photorefractive thin films,” Pure Appl. Opt. 5(5), 495–503 (1996).
[CrossRef]

L. Solymar, M. Aguilar, and F. Agulló-López, “Unified two-dimensional model for grating dynamics in photorefractive materials,” J. Appl. Phys. 80(3), 1268–1274 (1996).
[CrossRef]

M. Aguilar, M. Carrascosa, F. Agulló-López, L. F. Magaña, and L. Solymar, “Short-time photorefractive recording in multiple quantum wells: longitudinal geometry,” J. Opt. Soc. Am. B 13(11), 2630–2635 (1996).
[CrossRef]

E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Steady state photorefractive gratings in LiNbO3 for strong light modulation depths,” IEEE J. Quantum Electron. 30(4), 875–880 (1994).
[CrossRef]

E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Recording and erasure kinetics in photorefractive materials at high modulation depths,” J. Opt. Soc. Am. B 11(4), 670–675 (1994).
[CrossRef]

Alvarez-Bravo, J. V.

J. V. Alvarez-Bravo, M. Carrascosa, and L. Arizmendi, “Experimental effects of light intensity modulation on the recording and erasure of holographic gratings in BSO crystals,” Opt. Commun. 103(1-2), 22–28 (1993).
[CrossRef]

Arizmendi, L.

L. Arizmendi, E. M. de Miguel-Sanz, and M. Carrascosa, “Lifetimes of thermally fixed holograms in LiNbO(3):Fe crystals,” Opt. Lett. 23(12), 960–962 (1998).
[CrossRef] [PubMed]

J. V. Alvarez-Bravo, M. Carrascosa, and L. Arizmendi, “Experimental effects of light intensity modulation on the recording and erasure of holographic gratings in BSO crystals,” Opt. Commun. 103(1-2), 22–28 (1993).
[CrossRef]

Ashkin, A.

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
[CrossRef]

Blázquez-Castro, A.

A. Blázquez-Castro, J. C. Stockert, B. López-Arias, A. Juarranz, F. Agulló-López, A. García-Cabañes, and M. Carrascosa, “Tumour cell death induced by the bulk photovoltaic effect of LiNbO3:Fe under visible light irradiation,” Photochem. Photobiol. Sci. 10(6), 956–963 (2011).
[CrossRef] [PubMed]

Buse, K.

H. A. Eggert, F. Y. Kuhnert, K. Buse, J. R. Adleman, and D. Psaltis, “Trapping of dielectric particles with light-induced space-charge fields,” Appl. Phys. Lett. 90(24), 241909 (2007).
[CrossRef]

Carrascosa, M.

A. Blázquez-Castro, J. C. Stockert, B. López-Arias, A. Juarranz, F. Agulló-López, A. García-Cabañes, and M. Carrascosa, “Tumour cell death induced by the bulk photovoltaic effect of LiNbO3:Fe under visible light irradiation,” Photochem. Photobiol. Sci. 10(6), 956–963 (2011).
[CrossRef] [PubMed]

L. Arizmendi, E. M. de Miguel-Sanz, and M. Carrascosa, “Lifetimes of thermally fixed holograms in LiNbO(3):Fe crystals,” Opt. Lett. 23(12), 960–962 (1998).
[CrossRef] [PubMed]

F. Agulló-López, M. Carrascosa, and M. Aguilar, “An alternative design strategy for thin photorefractive polymer structures,” Adv. Mater. (Deerfield Beach Fla.) 9, 423–426 (1997).
[CrossRef]

F. Agulló-López, M. Aguilar, and M. Carrascosa, “Photorefractive thin films,” Pure Appl. Opt. 5(5), 495–503 (1996).
[CrossRef]

M. Aguilar, M. Carrascosa, F. Agulló-López, L. F. Magaña, and L. Solymar, “Short-time photorefractive recording in multiple quantum wells: longitudinal geometry,” J. Opt. Soc. Am. B 13(11), 2630–2635 (1996).
[CrossRef]

E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Steady state photorefractive gratings in LiNbO3 for strong light modulation depths,” IEEE J. Quantum Electron. 30(4), 875–880 (1994).
[CrossRef]

E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Recording and erasure kinetics in photorefractive materials at high modulation depths,” J. Opt. Soc. Am. B 11(4), 670–675 (1994).
[CrossRef]

J. V. Alvarez-Bravo, M. Carrascosa, and L. Arizmendi, “Experimental effects of light intensity modulation on the recording and erasure of holographic gratings in BSO crystals,” Opt. Commun. 103(1-2), 22–28 (1993).
[CrossRef]

Curley, M. J.

S. S. Sarkisov, M. J. Curley, N. V. Kukhtarev, A. Fields, G. Adamovsky, C. C. Smith, and E. L. Moore, “Holographic surface gratings in iron-doped lithium niobate,” Appl. Phys. Lett. 79(7), 901–903 (2001).
[CrossRef]

de Miguel-Sanz, E. M.

Denz, C.

Eggert, H. A.

H. A. Eggert, F. Y. Kuhnert, K. Buse, J. R. Adleman, and D. Psaltis, “Trapping of dielectric particles with light-induced space-charge fields,” Appl. Phys. Lett. 90(24), 241909 (2007).
[CrossRef]

Esseling, M.

Fields, A.

S. S. Sarkisov, M. J. Curley, N. V. Kukhtarev, A. Fields, G. Adamovsky, C. C. Smith, and E. L. Moore, “Holographic surface gratings in iron-doped lithium niobate,” Appl. Phys. Lett. 79(7), 901–903 (2001).
[CrossRef]

Fousek, J.

P. Mokrý, M. Marvan, and J. Fousek, “Patterning of dielectric nanoparticles using dielectrophoretic forces generated by ferroelectric polydomain films,” J. Appl. Phys. 107(9), 094104 (2010).
[CrossRef]

García-Cabañes, A.

A. Blázquez-Castro, J. C. Stockert, B. López-Arias, A. Juarranz, F. Agulló-López, A. García-Cabañes, and M. Carrascosa, “Tumour cell death induced by the bulk photovoltaic effect of LiNbO3:Fe under visible light irradiation,” Photochem. Photobiol. Sci. 10(6), 956–963 (2011).
[CrossRef] [PubMed]

Gascoyne, P. R.

P. R. Gascoyne and J. Vykoukal, “Particle separation by dielectrophoresis,” Electrophoresis 23(13), 1973–1983 (2002).
[CrossRef] [PubMed]

Hao, T.

T. Hao, “Electrorheological suspensions,” Adv. Colloid Interface Sci. 97(1-3), 1–35 (2002).
[CrossRef] [PubMed]

Holtmann, F.

Jonáš, A.

A. Jonáš and P. Zemánek, “Light at work: the use of optical forces for particle manipulation, sorting, and analysis,” Electrophoresis 29(24), 4813–4851 (2008).
[CrossRef] [PubMed]

Juarranz, A.

A. Blázquez-Castro, J. C. Stockert, B. López-Arias, A. Juarranz, F. Agulló-López, A. García-Cabañes, and M. Carrascosa, “Tumour cell death induced by the bulk photovoltaic effect of LiNbO3:Fe under visible light irradiation,” Photochem. Photobiol. Sci. 10(6), 956–963 (2011).
[CrossRef] [PubMed]

Kong, Y.

Kuhnert, F. Y.

H. A. Eggert, F. Y. Kuhnert, K. Buse, J. R. Adleman, and D. Psaltis, “Trapping of dielectric particles with light-induced space-charge fields,” Appl. Phys. Lett. 90(24), 241909 (2007).
[CrossRef]

Kukhtarev, N. V.

S. S. Sarkisov, M. J. Curley, N. V. Kukhtarev, A. Fields, G. Adamovsky, C. C. Smith, and E. L. Moore, “Holographic surface gratings in iron-doped lithium niobate,” Appl. Phys. Lett. 79(7), 901–903 (2001).
[CrossRef]

López, V.

E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Recording and erasure kinetics in photorefractive materials at high modulation depths,” J. Opt. Soc. Am. B 11(4), 670–675 (1994).
[CrossRef]

E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Steady state photorefractive gratings in LiNbO3 for strong light modulation depths,” IEEE J. Quantum Electron. 30(4), 875–880 (1994).
[CrossRef]

López-Arias, B.

A. Blázquez-Castro, J. C. Stockert, B. López-Arias, A. Juarranz, F. Agulló-López, A. García-Cabañes, and M. Carrascosa, “Tumour cell death induced by the bulk photovoltaic effect of LiNbO3:Fe under visible light irradiation,” Photochem. Photobiol. Sci. 10(6), 956–963 (2011).
[CrossRef] [PubMed]

Magaña, L. F.

Marvan, M.

P. Mokrý, M. Marvan, and J. Fousek, “Patterning of dielectric nanoparticles using dielectrophoretic forces generated by ferroelectric polydomain films,” J. Appl. Phys. 107(9), 094104 (2010).
[CrossRef]

Mokrý, P.

P. Mokrý, M. Marvan, and J. Fousek, “Patterning of dielectric nanoparticles using dielectrophoretic forces generated by ferroelectric polydomain films,” J. Appl. Phys. 107(9), 094104 (2010).
[CrossRef]

Moore, E. L.

S. S. Sarkisov, M. J. Curley, N. V. Kukhtarev, A. Fields, G. Adamovsky, C. C. Smith, and E. L. Moore, “Holographic surface gratings in iron-doped lithium niobate,” Appl. Phys. Lett. 79(7), 901–903 (2001).
[CrossRef]

Pan, L.

Psaltis, D.

H. A. Eggert, F. Y. Kuhnert, K. Buse, J. R. Adleman, and D. Psaltis, “Trapping of dielectric particles with light-induced space-charge fields,” Appl. Phys. Lett. 90(24), 241909 (2007).
[CrossRef]

Rupp, R. A.

Sarkisov, S. S.

S. S. Sarkisov, M. J. Curley, N. V. Kukhtarev, A. Fields, G. Adamovsky, C. C. Smith, and E. L. Moore, “Holographic surface gratings in iron-doped lithium niobate,” Appl. Phys. Lett. 79(7), 901–903 (2001).
[CrossRef]

Serrano, E.

E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Recording and erasure kinetics in photorefractive materials at high modulation depths,” J. Opt. Soc. Am. B 11(4), 670–675 (1994).
[CrossRef]

E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Steady state photorefractive gratings in LiNbO3 for strong light modulation depths,” IEEE J. Quantum Electron. 30(4), 875–880 (1994).
[CrossRef]

Smith, C. C.

S. S. Sarkisov, M. J. Curley, N. V. Kukhtarev, A. Fields, G. Adamovsky, C. C. Smith, and E. L. Moore, “Holographic surface gratings in iron-doped lithium niobate,” Appl. Phys. Lett. 79(7), 901–903 (2001).
[CrossRef]

Solymar, L.

L. Solymar, M. Aguilar, and F. Agulló-López, “Unified two-dimensional model for grating dynamics in photorefractive materials,” J. Appl. Phys. 80(3), 1268–1274 (1996).
[CrossRef]

M. Aguilar, M. Carrascosa, F. Agulló-López, L. F. Magaña, and L. Solymar, “Short-time photorefractive recording in multiple quantum wells: longitudinal geometry,” J. Opt. Soc. Am. B 13(11), 2630–2635 (1996).
[CrossRef]

Stockert, J. C.

A. Blázquez-Castro, J. C. Stockert, B. López-Arias, A. Juarranz, F. Agulló-López, A. García-Cabañes, and M. Carrascosa, “Tumour cell death induced by the bulk photovoltaic effect of LiNbO3:Fe under visible light irradiation,” Photochem. Photobiol. Sci. 10(6), 956–963 (2011).
[CrossRef] [PubMed]

Sun, Q.

Tan, X.

Tang, B.

Vykoukal, J.

P. R. Gascoyne and J. Vykoukal, “Particle separation by dielectrophoresis,” Electrophoresis 23(13), 1973–1983 (2002).
[CrossRef] [PubMed]

Wang, J.

Woerdemann, M.

Xu, J.

Zemánek, P.

A. Jonáš and P. Zemánek, “Light at work: the use of optical forces for particle manipulation, sorting, and analysis,” Electrophoresis 29(24), 4813–4851 (2008).
[CrossRef] [PubMed]

Zhang, X.

Adv. Colloid Interface Sci. (1)

T. Hao, “Electrorheological suspensions,” Adv. Colloid Interface Sci. 97(1-3), 1–35 (2002).
[CrossRef] [PubMed]

Adv. Mater. (Deerfield Beach Fla.) (1)

F. Agulló-López, M. Carrascosa, and M. Aguilar, “An alternative design strategy for thin photorefractive polymer structures,” Adv. Mater. (Deerfield Beach Fla.) 9, 423–426 (1997).
[CrossRef]

Appl. Phys. Lett. (2)

S. S. Sarkisov, M. J. Curley, N. V. Kukhtarev, A. Fields, G. Adamovsky, C. C. Smith, and E. L. Moore, “Holographic surface gratings in iron-doped lithium niobate,” Appl. Phys. Lett. 79(7), 901–903 (2001).
[CrossRef]

H. A. Eggert, F. Y. Kuhnert, K. Buse, J. R. Adleman, and D. Psaltis, “Trapping of dielectric particles with light-induced space-charge fields,” Appl. Phys. Lett. 90(24), 241909 (2007).
[CrossRef]

Electrophoresis (2)

A. Jonáš and P. Zemánek, “Light at work: the use of optical forces for particle manipulation, sorting, and analysis,” Electrophoresis 29(24), 4813–4851 (2008).
[CrossRef] [PubMed]

P. R. Gascoyne and J. Vykoukal, “Particle separation by dielectrophoresis,” Electrophoresis 23(13), 1973–1983 (2002).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Steady state photorefractive gratings in LiNbO3 for strong light modulation depths,” IEEE J. Quantum Electron. 30(4), 875–880 (1994).
[CrossRef]

J. Appl. Phys. (2)

L. Solymar, M. Aguilar, and F. Agulló-López, “Unified two-dimensional model for grating dynamics in photorefractive materials,” J. Appl. Phys. 80(3), 1268–1274 (1996).
[CrossRef]

P. Mokrý, M. Marvan, and J. Fousek, “Patterning of dielectric nanoparticles using dielectrophoretic forces generated by ferroelectric polydomain films,” J. Appl. Phys. 107(9), 094104 (2010).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

J. V. Alvarez-Bravo, M. Carrascosa, and L. Arizmendi, “Experimental effects of light intensity modulation on the recording and erasure of holographic gratings in BSO crystals,” Opt. Commun. 103(1-2), 22–28 (1993).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Photochem. Photobiol. Sci. (1)

A. Blázquez-Castro, J. C. Stockert, B. López-Arias, A. Juarranz, F. Agulló-López, A. García-Cabañes, and M. Carrascosa, “Tumour cell death induced by the bulk photovoltaic effect of LiNbO3:Fe under visible light irradiation,” Photochem. Photobiol. Sci. 10(6), 956–963 (2011).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24(4), 156–159 (1970).
[CrossRef]

Pure Appl. Opt. (1)

F. Agulló-López, M. Aguilar, and M. Carrascosa, “Photorefractive thin films,” Pure Appl. Opt. 5(5), 495–503 (1996).
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Other (6)

M. Carrascosa, L. Arizmendi, and J. M. Cabrera, “Thermal fixing of photoinduced gratings”, in Photrefractive Materials and Their Applications 1, P. Günter and J.-P. Huignard, eds, (Springer, New York 2006).

T. B. Jones, Electrokinetics of particles (Cambridge University Press, 1995).

F. Agulló-López, G. F. Calvo, and M. Carrascosa, “Fundamentals of photorefractive phenomena” in Photorefractive Materials and Applications 1, P. Günter and J.-P. Huignard, eds. (Springer, New York 2006), Chap 1.

H. A. Pohl, Dielectrophoresis: the Behavior of Neutral Matter in Nonuniform Electric Fields (Cambridge University Press, Cambridge, 1978).

B. I. Sturmann and V. M. Fridkin, Photovoltaic and Photorefractive Effects in Noncentrosymetric Materials (Gordon & Breach, Philadelphia 1992).

F. Agulló-López, J. M. Cabrera, and F. Agulló-Rueda, Electrooptics: Phenomena, Materials and Applications (Academic, New York 1994).

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Figures (4)

Fig. 1
Fig. 1

Chalk micro-particles trapped on the surface of LiNbO3:Fe after illumination with the interference of two beams with periodicity 30 μm and modulation m ≈1 (a) and with a single laser beam (b). In (b) the illuminated region (diameter 4σ) has been indicated with a circular dashed line.

Fig. 2
Fig. 2

Evanescent photovoltaic electric fields E (represented by arrows) as a function of the position (x,z) generated by a sinusoidal light pattern.

Fig. 3
Fig. 3

Dielectrophoretic forces for isotropic spherical particles under periodic photovoltaic fields: (a) sinusoidal electric field pattern inside the crystal and (b) non-sinusoidal field pattern, that are illustrated in the bottom part of the figures.

Fig. 4
Fig. 4

Two-dimensional plot of the Gaussian light intensity distribution (a) and the square of the calculated photovoltaic electric field generated by that beam illumination (b). Note that x stands for the PV axis.

Equations (26)

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j PV =q(I/hν)σ N D l PV
E PV = J PV qμn = σI N D l PV hνμn = l PV γ N A μ
j PV =500 nA/cm 2 , n=5× 10 9 cm 3 = 10 9 cm 3 , E PV =100000 V/cm
I= I 0 (1+mcosKx)
E PV = j PV ε ε 0 t= σ N D I 0 e l PV hνε ε 0 (1+mcosKx)t
E 0 =im E D +i E PV 1+ E D +ir E PV E q m E q E PV E q +ir E PV m E PV
E D = k B KT q (diffusion field) E q = q N D r ε ε 0 K (limiting field) r= N A N D + N A (oxidation/reduction ratio)
E X (x,z)=K e Kz V 0 cosKx
E Z (x,z)=K e Kz V 0 sinKx
E X in (x,z)=( E 0 E B e Kz )cosKx
E Z in (x,z)= E B e Kz sinKx
E B = E 0 ε ε1 , V 0 = E B K
f =W=( p E )
α=2 π r 3 ε M (0) ε P (0)ε (0) M ε P (0)+2 ε M (0)
α XX = α YY =V( ε P ε M )
α ZZ =V ε M ε P ε M ε P =V ε M ( 1 ε M ε P )
f =( p E )= ε 0 ( α XX E X 2 + α ZZ E Z 2 )
E 2 = E X 2 + E Y 2 = E 0 2 ( ε ε1 ) 2 e Kz
W= ε 0 α(ω)< E (ω) 2 >= 1 2 ε 0 α(ω)( E o 2 )
f = 1 2 ε 0 α(ω)( E 0 2 )
f = 1 2 ε 0 α(ω) E 2 = 1 2 ε 0 α(ω)m E 0 2 sinKx
E X (x,z)= V 0 K e Kz cosKx2 V 1 K e 2Kz cos2Kx E Z (x,z)= V 0 K e Kz sinKx+2 V 1 K e 2Kz sin2Kx
f X = ε 0 ( α XX E X 2 x + α ZZ E Z 2 x )
E X 2 x = V 0 2 K 3 e 2Kz sin2Kx4 V 1 2 K 3 e 4Kz sin4Kx4 V 0 V 1 K 3 e 3Kz cos2Kx 8 V 0 V 1 K 3 e 3Kz cosKxsin2Kx E Z 2 x = V 0 2 K 3 e 2Kz sin2Kx+4 V 1 2 K 3 e 4Kz sin2Kx+4 V 0 V 1 K 3 e 3Kz cosKxsin2Kx 8 V 0 V 1 K 3 e 3Kz sinKxcos2Kx
f X = ε 0 ( α ZZ α XX ) K 3 [ V 0 2 e 2Kz sin2Kx+6 V 0 V 1 e 3Kz sin3Kx+4 V 1 2 e 4Kz sin4Kx ] 2 V 0 V 1 ε 0 ( α ZZ + α XX ) K 3 e 3Kz sinKx
f X =4 ε 0 α ZZ V 0 V 1 K 3 e 3Kz sinKx

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