Abstract

We present an analytical model for describing optical third-harmonic generation from a sphere that is small compared with the wavelength of light. Analysis of the problem shows that the power of the third harmonic from a sphere that is small compared with the waist size and the confocal parameter of the beam is proportional to the fourth power of a sphere’s size. Experiments with different spheres both in index-matching and non-index-matching liquids are performed and confirm theoretical predictions.

© 2005 Optical Society of America

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  1. J. W. Strut, “On the light from the sky, its polarization and color,” Philos. Mag.  41, 107–120 (1871).
  2. C. F. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
    [CrossRef]
  3. P. W. Barber and R. K. Chang, Optical Effects Associated with Small Particles (World Scientific, 1988).
  4. X. M. Hua and J. I. Gersten, “Theory of second harmonic generation by small metal spheres,” Phys. Rev. B  33, 3756–3764 (1986).
    [CrossRef]
  5. H. Wang, E. Yang, E. Borguet, and K. Eisenthal, “Second harmonic generation from the surface of centrosymmetric particles in bulk solution,” Chem. Phys. Lett.  259, 15–20 (1996).
    [CrossRef]
  6. J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-harmonic Rayleigh scattering from a centrosymmetric material,” Phys. Rev. Lett.  83, 4045–4048 (1999).
    [CrossRef]
  7. J. P. Dewitz, W. Hubner, and K. H. Bennemann, “Theory of nonlinear Mie-scattering from spherical metal clusters,” Z. Phys. D  37, 75–84 (1996).
    [CrossRef]
  8. J. Kasparian, B. Kramer, J. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hubner, J. Wolf, L. Woste, and K. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett.  78, 2952–2955 (1997).
    [CrossRef]
  9. D. Caroll and X. H. Zheng, “Spatial and angular distributions of third harmonic generation from metal surfaces,” Eur. Phys. J. D  5, 135–144 (1999).
    [CrossRef]
  10. C. Favre, V. Boutou, S. Hill, W. Zimmer, M. Krenz, H. Lambrecht, J. Yu, R. Chang, L. Woeste, and J. Wolf, “White-light nanosource with directional emission,” Phys. Rev. Lett.  89, 035002 (2002).
    [CrossRef] [PubMed]
  11. Z. Wang, B. Luk’yanchuk, M. Hong, Y. Lin, and T. Chong, “Energy flow around a small particle investigated by classical Mie theory,” Phys. Rev. B  70, 035418 (2004).
    [CrossRef]
  12. V. Shcheslavskiy, G. Petrov, S. Saltiel, and V. Yakovlev, “Quantitative characterization of aqueous solutions probed by the third-harmonic generation microscopy,” J. Struct. Biol.  147, 42–49 (2004).
    [CrossRef] [PubMed]
  13. M. Lippitz, M. A. van Dijk, and M. Orrit, “Third-harmonic generation from single gold nanoparticles,” Nano Lett.  5, 799–802 (2005).
    [CrossRef] [PubMed]
  14. L. Malmqvist and H. Hertz, “Second harmonic generation in optically trapped nonlinear particles with pulsed lasers,” Appl. Opt.  34, 3392–3397 (1995).
    [CrossRef] [PubMed]
  15. V. L. Brudny, B. S. Mendoza, and W. L. Mochan, “Second-harmonic generation from spherical particles,” Phys. Rev. B  62, 11152–11162 (2000).
    [CrossRef]
  16. J. I. Dadap, J. Shan, and T. F. Heinz, “Theory of optical second-harmonic generation from a sphere of centrosymmetric material: small-particle limit,” J. Opt. Soc. Am. B  21, 1328–1347 (2004).
    [CrossRef]
  17. V. I. Shcheslavskiy, G. I. Petrov, V. V. Yakovlev, S. M. Saltiel, B. S. Luk’yanchuk, Z. S. Nickolov, and J. D. Miller, “Third-harmonic generation from Rayleigh particles,” Phys. Rev. Lett., submitted for publication.
  18. J. F. Reintjes, Nonlinear Optical Parametric Processes in Liquids and Gases (Academic, 1984).
  19. S. M. Saltiel, K. Koynov, B. Agate, and W. Sibbett, “Second-harmonic generation with focused beams under conditions of large group-velocity mismatch,” J. Opt. Soc. Am. B  21, 591–598 (2004).
    [CrossRef]
  20. S. V. Fomichev, S. V. Popruzhenko, D. F. Zaretsky, and W. Becker, “Laser-induced nonlinear excitation of collective electron motion in a cluster,” J. Phys. B  36, 3817–3834 (2003).
    [CrossRef]
  21. V. Shcheslavskiy, V. Yakovlev, and A. Ivanov, “High-energy self-starting Cr4+:Mg2SiO4 oscillator operating at low repetition rate,” Opt. Lett.  26, 1999–2001 (2001).
    [CrossRef]
  22. V. Shcheslavskiy, G. Petrov, and V. V. Yakovlev, “Nonlinear susceptibility measurements of solutions using third-harmonic generation on the interface,” Appl. Phys. Lett.  82, 3982–3984 (2003).
    [CrossRef]
  23. D. Stroud and V. Wood, “Decoupling approximation for the nonlinear-optical response of composite media,” J. Opt. Soc. Am. B  6, 778–786 (1989).
    [CrossRef]
  24. G. I. Petrov, V. I. Shcheslavskiy, V. V. Yakovlev, I. Ozerov, E. Chelnokov, and W. Marine, “Efficient third-harmonic generation in a thin nanocrystalline film of ZnO,” Appl. Phys. Lett.  83, 3993–3995 (2003).
    [CrossRef]
  25. L. Malmqvist and H. M. Hertz, “Two-color trapped particle optical microscopy,” Opt. Lett.  19, 853–855 (1994).
    [CrossRef] [PubMed]

2005 (1)

M. Lippitz, M. A. van Dijk, and M. Orrit, “Third-harmonic generation from single gold nanoparticles,” Nano Lett.  5, 799–802 (2005).
[CrossRef] [PubMed]

2004 (4)

Z. Wang, B. Luk’yanchuk, M. Hong, Y. Lin, and T. Chong, “Energy flow around a small particle investigated by classical Mie theory,” Phys. Rev. B  70, 035418 (2004).
[CrossRef]

V. Shcheslavskiy, G. Petrov, S. Saltiel, and V. Yakovlev, “Quantitative characterization of aqueous solutions probed by the third-harmonic generation microscopy,” J. Struct. Biol.  147, 42–49 (2004).
[CrossRef] [PubMed]

S. M. Saltiel, K. Koynov, B. Agate, and W. Sibbett, “Second-harmonic generation with focused beams under conditions of large group-velocity mismatch,” J. Opt. Soc. Am. B  21, 591–598 (2004).
[CrossRef]

J. I. Dadap, J. Shan, and T. F. Heinz, “Theory of optical second-harmonic generation from a sphere of centrosymmetric material: small-particle limit,” J. Opt. Soc. Am. B  21, 1328–1347 (2004).
[CrossRef]

2003 (3)

S. V. Fomichev, S. V. Popruzhenko, D. F. Zaretsky, and W. Becker, “Laser-induced nonlinear excitation of collective electron motion in a cluster,” J. Phys. B  36, 3817–3834 (2003).
[CrossRef]

V. Shcheslavskiy, G. Petrov, and V. V. Yakovlev, “Nonlinear susceptibility measurements of solutions using third-harmonic generation on the interface,” Appl. Phys. Lett.  82, 3982–3984 (2003).
[CrossRef]

G. I. Petrov, V. I. Shcheslavskiy, V. V. Yakovlev, I. Ozerov, E. Chelnokov, and W. Marine, “Efficient third-harmonic generation in a thin nanocrystalline film of ZnO,” Appl. Phys. Lett.  83, 3993–3995 (2003).
[CrossRef]

2002 (1)

C. Favre, V. Boutou, S. Hill, W. Zimmer, M. Krenz, H. Lambrecht, J. Yu, R. Chang, L. Woeste, and J. Wolf, “White-light nanosource with directional emission,” Phys. Rev. Lett.  89, 035002 (2002).
[CrossRef] [PubMed]

2001 (1)

2000 (1)

V. L. Brudny, B. S. Mendoza, and W. L. Mochan, “Second-harmonic generation from spherical particles,” Phys. Rev. B  62, 11152–11162 (2000).
[CrossRef]

1999 (2)

D. Caroll and X. H. Zheng, “Spatial and angular distributions of third harmonic generation from metal surfaces,” Eur. Phys. J. D  5, 135–144 (1999).
[CrossRef]

J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-harmonic Rayleigh scattering from a centrosymmetric material,” Phys. Rev. Lett.  83, 4045–4048 (1999).
[CrossRef]

1997 (1)

J. Kasparian, B. Kramer, J. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hubner, J. Wolf, L. Woste, and K. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett.  78, 2952–2955 (1997).
[CrossRef]

1996 (2)

H. Wang, E. Yang, E. Borguet, and K. Eisenthal, “Second harmonic generation from the surface of centrosymmetric particles in bulk solution,” Chem. Phys. Lett.  259, 15–20 (1996).
[CrossRef]

J. P. Dewitz, W. Hubner, and K. H. Bennemann, “Theory of nonlinear Mie-scattering from spherical metal clusters,” Z. Phys. D  37, 75–84 (1996).
[CrossRef]

1995 (1)

1994 (1)

1989 (1)

1986 (1)

X. M. Hua and J. I. Gersten, “Theory of second harmonic generation by small metal spheres,” Phys. Rev. B  33, 3756–3764 (1986).
[CrossRef]

1871 (1)

J. W. Strut, “On the light from the sky, its polarization and color,” Philos. Mag.  41, 107–120 (1871).

Agate, B.

Barber, P. W.

P. W. Barber and R. K. Chang, Optical Effects Associated with Small Particles (World Scientific, 1988).

Becker, W.

S. V. Fomichev, S. V. Popruzhenko, D. F. Zaretsky, and W. Becker, “Laser-induced nonlinear excitation of collective electron motion in a cluster,” J. Phys. B  36, 3817–3834 (2003).
[CrossRef]

Bennemann, K.

J. Kasparian, B. Kramer, J. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hubner, J. Wolf, L. Woste, and K. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett.  78, 2952–2955 (1997).
[CrossRef]

Bennemann, K. H.

J. P. Dewitz, W. Hubner, and K. H. Bennemann, “Theory of nonlinear Mie-scattering from spherical metal clusters,” Z. Phys. D  37, 75–84 (1996).
[CrossRef]

Bohren, C. F.

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

Borguet, E.

H. Wang, E. Yang, E. Borguet, and K. Eisenthal, “Second harmonic generation from the surface of centrosymmetric particles in bulk solution,” Chem. Phys. Lett.  259, 15–20 (1996).
[CrossRef]

Boutou, V.

C. Favre, V. Boutou, S. Hill, W. Zimmer, M. Krenz, H. Lambrecht, J. Yu, R. Chang, L. Woeste, and J. Wolf, “White-light nanosource with directional emission,” Phys. Rev. Lett.  89, 035002 (2002).
[CrossRef] [PubMed]

J. Kasparian, B. Kramer, J. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hubner, J. Wolf, L. Woste, and K. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett.  78, 2952–2955 (1997).
[CrossRef]

Brudny, V. L.

V. L. Brudny, B. S. Mendoza, and W. L. Mochan, “Second-harmonic generation from spherical particles,” Phys. Rev. B  62, 11152–11162 (2000).
[CrossRef]

Caroll, D.

D. Caroll and X. H. Zheng, “Spatial and angular distributions of third harmonic generation from metal surfaces,” Eur. Phys. J. D  5, 135–144 (1999).
[CrossRef]

Chang, R.

C. Favre, V. Boutou, S. Hill, W. Zimmer, M. Krenz, H. Lambrecht, J. Yu, R. Chang, L. Woeste, and J. Wolf, “White-light nanosource with directional emission,” Phys. Rev. Lett.  89, 035002 (2002).
[CrossRef] [PubMed]

Chang, R. K.

P. W. Barber and R. K. Chang, Optical Effects Associated with Small Particles (World Scientific, 1988).

Chelnokov, E.

G. I. Petrov, V. I. Shcheslavskiy, V. V. Yakovlev, I. Ozerov, E. Chelnokov, and W. Marine, “Efficient third-harmonic generation in a thin nanocrystalline film of ZnO,” Appl. Phys. Lett.  83, 3993–3995 (2003).
[CrossRef]

Chong, T.

Z. Wang, B. Luk’yanchuk, M. Hong, Y. Lin, and T. Chong, “Energy flow around a small particle investigated by classical Mie theory,” Phys. Rev. B  70, 035418 (2004).
[CrossRef]

Dadap, J. I.

J. I. Dadap, J. Shan, and T. F. Heinz, “Theory of optical second-harmonic generation from a sphere of centrosymmetric material: small-particle limit,” J. Opt. Soc. Am. B  21, 1328–1347 (2004).
[CrossRef]

J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-harmonic Rayleigh scattering from a centrosymmetric material,” Phys. Rev. Lett.  83, 4045–4048 (1999).
[CrossRef]

Dewitz, J.

J. Kasparian, B. Kramer, J. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hubner, J. Wolf, L. Woste, and K. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett.  78, 2952–2955 (1997).
[CrossRef]

Dewitz, J. P.

J. P. Dewitz, W. Hubner, and K. H. Bennemann, “Theory of nonlinear Mie-scattering from spherical metal clusters,” Z. Phys. D  37, 75–84 (1996).
[CrossRef]

Eisenthal, K.

H. Wang, E. Yang, E. Borguet, and K. Eisenthal, “Second harmonic generation from the surface of centrosymmetric particles in bulk solution,” Chem. Phys. Lett.  259, 15–20 (1996).
[CrossRef]

Eisenthal, K. B.

J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-harmonic Rayleigh scattering from a centrosymmetric material,” Phys. Rev. Lett.  83, 4045–4048 (1999).
[CrossRef]

Favre, C.

C. Favre, V. Boutou, S. Hill, W. Zimmer, M. Krenz, H. Lambrecht, J. Yu, R. Chang, L. Woeste, and J. Wolf, “White-light nanosource with directional emission,” Phys. Rev. Lett.  89, 035002 (2002).
[CrossRef] [PubMed]

Fomichev, S. V.

S. V. Fomichev, S. V. Popruzhenko, D. F. Zaretsky, and W. Becker, “Laser-induced nonlinear excitation of collective electron motion in a cluster,” J. Phys. B  36, 3817–3834 (2003).
[CrossRef]

Gersten, J. I.

X. M. Hua and J. I. Gersten, “Theory of second harmonic generation by small metal spheres,” Phys. Rev. B  33, 3756–3764 (1986).
[CrossRef]

Heinz, T. F.

J. I. Dadap, J. Shan, and T. F. Heinz, “Theory of optical second-harmonic generation from a sphere of centrosymmetric material: small-particle limit,” J. Opt. Soc. Am. B  21, 1328–1347 (2004).
[CrossRef]

J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-harmonic Rayleigh scattering from a centrosymmetric material,” Phys. Rev. Lett.  83, 4045–4048 (1999).
[CrossRef]

Hertz, H.

Hertz, H. M.

Hill, S.

C. Favre, V. Boutou, S. Hill, W. Zimmer, M. Krenz, H. Lambrecht, J. Yu, R. Chang, L. Woeste, and J. Wolf, “White-light nanosource with directional emission,” Phys. Rev. Lett.  89, 035002 (2002).
[CrossRef] [PubMed]

Hong, M.

Z. Wang, B. Luk’yanchuk, M. Hong, Y. Lin, and T. Chong, “Energy flow around a small particle investigated by classical Mie theory,” Phys. Rev. B  70, 035418 (2004).
[CrossRef]

Hua, X. M.

X. M. Hua and J. I. Gersten, “Theory of second harmonic generation by small metal spheres,” Phys. Rev. B  33, 3756–3764 (1986).
[CrossRef]

Hubner, W.

J. Kasparian, B. Kramer, J. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hubner, J. Wolf, L. Woste, and K. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett.  78, 2952–2955 (1997).
[CrossRef]

J. P. Dewitz, W. Hubner, and K. H. Bennemann, “Theory of nonlinear Mie-scattering from spherical metal clusters,” Z. Phys. D  37, 75–84 (1996).
[CrossRef]

Huffman, D.

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

Ivanov, A.

Kasparian, J.

J. Kasparian, B. Kramer, J. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hubner, J. Wolf, L. Woste, and K. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett.  78, 2952–2955 (1997).
[CrossRef]

Koynov, K.

Kramer, B.

J. Kasparian, B. Kramer, J. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hubner, J. Wolf, L. Woste, and K. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett.  78, 2952–2955 (1997).
[CrossRef]

Krenz, M.

C. Favre, V. Boutou, S. Hill, W. Zimmer, M. Krenz, H. Lambrecht, J. Yu, R. Chang, L. Woeste, and J. Wolf, “White-light nanosource with directional emission,” Phys. Rev. Lett.  89, 035002 (2002).
[CrossRef] [PubMed]

Lambrecht, H.

C. Favre, V. Boutou, S. Hill, W. Zimmer, M. Krenz, H. Lambrecht, J. Yu, R. Chang, L. Woeste, and J. Wolf, “White-light nanosource with directional emission,” Phys. Rev. Lett.  89, 035002 (2002).
[CrossRef] [PubMed]

Leisner, T.

J. Kasparian, B. Kramer, J. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hubner, J. Wolf, L. Woste, and K. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett.  78, 2952–2955 (1997).
[CrossRef]

Lin, Y.

Z. Wang, B. Luk’yanchuk, M. Hong, Y. Lin, and T. Chong, “Energy flow around a small particle investigated by classical Mie theory,” Phys. Rev. B  70, 035418 (2004).
[CrossRef]

Lippitz, M.

M. Lippitz, M. A. van Dijk, and M. Orrit, “Third-harmonic generation from single gold nanoparticles,” Nano Lett.  5, 799–802 (2005).
[CrossRef] [PubMed]

Luk’yanchuk, B.

Z. Wang, B. Luk’yanchuk, M. Hong, Y. Lin, and T. Chong, “Energy flow around a small particle investigated by classical Mie theory,” Phys. Rev. B  70, 035418 (2004).
[CrossRef]

Luk’yanchuk, B. S.

V. I. Shcheslavskiy, G. I. Petrov, V. V. Yakovlev, S. M. Saltiel, B. S. Luk’yanchuk, Z. S. Nickolov, and J. D. Miller, “Third-harmonic generation from Rayleigh particles,” Phys. Rev. Lett., submitted for publication.

Malmqvist, L.

Marine, W.

G. I. Petrov, V. I. Shcheslavskiy, V. V. Yakovlev, I. Ozerov, E. Chelnokov, and W. Marine, “Efficient third-harmonic generation in a thin nanocrystalline film of ZnO,” Appl. Phys. Lett.  83, 3993–3995 (2003).
[CrossRef]

Mendoza, B. S.

V. L. Brudny, B. S. Mendoza, and W. L. Mochan, “Second-harmonic generation from spherical particles,” Phys. Rev. B  62, 11152–11162 (2000).
[CrossRef]

Miller, J. D.

V. I. Shcheslavskiy, G. I. Petrov, V. V. Yakovlev, S. M. Saltiel, B. S. Luk’yanchuk, Z. S. Nickolov, and J. D. Miller, “Third-harmonic generation from Rayleigh particles,” Phys. Rev. Lett., submitted for publication.

Mochan, W. L.

V. L. Brudny, B. S. Mendoza, and W. L. Mochan, “Second-harmonic generation from spherical particles,” Phys. Rev. B  62, 11152–11162 (2000).
[CrossRef]

Nickolov, Z. S.

V. I. Shcheslavskiy, G. I. Petrov, V. V. Yakovlev, S. M. Saltiel, B. S. Luk’yanchuk, Z. S. Nickolov, and J. D. Miller, “Third-harmonic generation from Rayleigh particles,” Phys. Rev. Lett., submitted for publication.

Orrit, M.

M. Lippitz, M. A. van Dijk, and M. Orrit, “Third-harmonic generation from single gold nanoparticles,” Nano Lett.  5, 799–802 (2005).
[CrossRef] [PubMed]

Ozerov, I.

G. I. Petrov, V. I. Shcheslavskiy, V. V. Yakovlev, I. Ozerov, E. Chelnokov, and W. Marine, “Efficient third-harmonic generation in a thin nanocrystalline film of ZnO,” Appl. Phys. Lett.  83, 3993–3995 (2003).
[CrossRef]

Petrov, G.

V. Shcheslavskiy, G. Petrov, S. Saltiel, and V. Yakovlev, “Quantitative characterization of aqueous solutions probed by the third-harmonic generation microscopy,” J. Struct. Biol.  147, 42–49 (2004).
[CrossRef] [PubMed]

V. Shcheslavskiy, G. Petrov, and V. V. Yakovlev, “Nonlinear susceptibility measurements of solutions using third-harmonic generation on the interface,” Appl. Phys. Lett.  82, 3982–3984 (2003).
[CrossRef]

Petrov, G. I.

G. I. Petrov, V. I. Shcheslavskiy, V. V. Yakovlev, I. Ozerov, E. Chelnokov, and W. Marine, “Efficient third-harmonic generation in a thin nanocrystalline film of ZnO,” Appl. Phys. Lett.  83, 3993–3995 (2003).
[CrossRef]

V. I. Shcheslavskiy, G. I. Petrov, V. V. Yakovlev, S. M. Saltiel, B. S. Luk’yanchuk, Z. S. Nickolov, and J. D. Miller, “Third-harmonic generation from Rayleigh particles,” Phys. Rev. Lett., submitted for publication.

Popruzhenko, S. V.

S. V. Fomichev, S. V. Popruzhenko, D. F. Zaretsky, and W. Becker, “Laser-induced nonlinear excitation of collective electron motion in a cluster,” J. Phys. B  36, 3817–3834 (2003).
[CrossRef]

Rairoux, P.

J. Kasparian, B. Kramer, J. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hubner, J. Wolf, L. Woste, and K. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett.  78, 2952–2955 (1997).
[CrossRef]

Reintjes, J. F.

J. F. Reintjes, Nonlinear Optical Parametric Processes in Liquids and Gases (Academic, 1984).

Saltiel, S.

V. Shcheslavskiy, G. Petrov, S. Saltiel, and V. Yakovlev, “Quantitative characterization of aqueous solutions probed by the third-harmonic generation microscopy,” J. Struct. Biol.  147, 42–49 (2004).
[CrossRef] [PubMed]

Saltiel, S. M.

S. M. Saltiel, K. Koynov, B. Agate, and W. Sibbett, “Second-harmonic generation with focused beams under conditions of large group-velocity mismatch,” J. Opt. Soc. Am. B  21, 591–598 (2004).
[CrossRef]

V. I. Shcheslavskiy, G. I. Petrov, V. V. Yakovlev, S. M. Saltiel, B. S. Luk’yanchuk, Z. S. Nickolov, and J. D. Miller, “Third-harmonic generation from Rayleigh particles,” Phys. Rev. Lett., submitted for publication.

Shan, J.

J. I. Dadap, J. Shan, and T. F. Heinz, “Theory of optical second-harmonic generation from a sphere of centrosymmetric material: small-particle limit,” J. Opt. Soc. Am. B  21, 1328–1347 (2004).
[CrossRef]

J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-harmonic Rayleigh scattering from a centrosymmetric material,” Phys. Rev. Lett.  83, 4045–4048 (1999).
[CrossRef]

Shcheslavskiy, V.

V. Shcheslavskiy, G. Petrov, S. Saltiel, and V. Yakovlev, “Quantitative characterization of aqueous solutions probed by the third-harmonic generation microscopy,” J. Struct. Biol.  147, 42–49 (2004).
[CrossRef] [PubMed]

V. Shcheslavskiy, G. Petrov, and V. V. Yakovlev, “Nonlinear susceptibility measurements of solutions using third-harmonic generation on the interface,” Appl. Phys. Lett.  82, 3982–3984 (2003).
[CrossRef]

V. Shcheslavskiy, V. Yakovlev, and A. Ivanov, “High-energy self-starting Cr4+:Mg2SiO4 oscillator operating at low repetition rate,” Opt. Lett.  26, 1999–2001 (2001).
[CrossRef]

Shcheslavskiy, V. I.

G. I. Petrov, V. I. Shcheslavskiy, V. V. Yakovlev, I. Ozerov, E. Chelnokov, and W. Marine, “Efficient third-harmonic generation in a thin nanocrystalline film of ZnO,” Appl. Phys. Lett.  83, 3993–3995 (2003).
[CrossRef]

V. I. Shcheslavskiy, G. I. Petrov, V. V. Yakovlev, S. M. Saltiel, B. S. Luk’yanchuk, Z. S. Nickolov, and J. D. Miller, “Third-harmonic generation from Rayleigh particles,” Phys. Rev. Lett., submitted for publication.

Sibbett, W.

Stroud, D.

Strut, J. W.

J. W. Strut, “On the light from the sky, its polarization and color,” Philos. Mag.  41, 107–120 (1871).

Vajda, S.

J. Kasparian, B. Kramer, J. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hubner, J. Wolf, L. Woste, and K. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett.  78, 2952–2955 (1997).
[CrossRef]

van Dijk, M. A.

M. Lippitz, M. A. van Dijk, and M. Orrit, “Third-harmonic generation from single gold nanoparticles,” Nano Lett.  5, 799–802 (2005).
[CrossRef] [PubMed]

Vezin, B.

J. Kasparian, B. Kramer, J. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hubner, J. Wolf, L. Woste, and K. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett.  78, 2952–2955 (1997).
[CrossRef]

Wang, H.

H. Wang, E. Yang, E. Borguet, and K. Eisenthal, “Second harmonic generation from the surface of centrosymmetric particles in bulk solution,” Chem. Phys. Lett.  259, 15–20 (1996).
[CrossRef]

Wang, Z.

Z. Wang, B. Luk’yanchuk, M. Hong, Y. Lin, and T. Chong, “Energy flow around a small particle investigated by classical Mie theory,” Phys. Rev. B  70, 035418 (2004).
[CrossRef]

Woeste, L.

C. Favre, V. Boutou, S. Hill, W. Zimmer, M. Krenz, H. Lambrecht, J. Yu, R. Chang, L. Woeste, and J. Wolf, “White-light nanosource with directional emission,” Phys. Rev. Lett.  89, 035002 (2002).
[CrossRef] [PubMed]

Wolf, J.

C. Favre, V. Boutou, S. Hill, W. Zimmer, M. Krenz, H. Lambrecht, J. Yu, R. Chang, L. Woeste, and J. Wolf, “White-light nanosource with directional emission,” Phys. Rev. Lett.  89, 035002 (2002).
[CrossRef] [PubMed]

J. Kasparian, B. Kramer, J. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hubner, J. Wolf, L. Woste, and K. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett.  78, 2952–2955 (1997).
[CrossRef]

Wood, V.

Woste, L.

J. Kasparian, B. Kramer, J. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hubner, J. Wolf, L. Woste, and K. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett.  78, 2952–2955 (1997).
[CrossRef]

Yakovlev, V.

V. Shcheslavskiy, G. Petrov, S. Saltiel, and V. Yakovlev, “Quantitative characterization of aqueous solutions probed by the third-harmonic generation microscopy,” J. Struct. Biol.  147, 42–49 (2004).
[CrossRef] [PubMed]

V. Shcheslavskiy, V. Yakovlev, and A. Ivanov, “High-energy self-starting Cr4+:Mg2SiO4 oscillator operating at low repetition rate,” Opt. Lett.  26, 1999–2001 (2001).
[CrossRef]

Yakovlev, V. V.

V. Shcheslavskiy, G. Petrov, and V. V. Yakovlev, “Nonlinear susceptibility measurements of solutions using third-harmonic generation on the interface,” Appl. Phys. Lett.  82, 3982–3984 (2003).
[CrossRef]

G. I. Petrov, V. I. Shcheslavskiy, V. V. Yakovlev, I. Ozerov, E. Chelnokov, and W. Marine, “Efficient third-harmonic generation in a thin nanocrystalline film of ZnO,” Appl. Phys. Lett.  83, 3993–3995 (2003).
[CrossRef]

V. I. Shcheslavskiy, G. I. Petrov, V. V. Yakovlev, S. M. Saltiel, B. S. Luk’yanchuk, Z. S. Nickolov, and J. D. Miller, “Third-harmonic generation from Rayleigh particles,” Phys. Rev. Lett., submitted for publication.

Yang, E.

H. Wang, E. Yang, E. Borguet, and K. Eisenthal, “Second harmonic generation from the surface of centrosymmetric particles in bulk solution,” Chem. Phys. Lett.  259, 15–20 (1996).
[CrossRef]

Yu, J.

C. Favre, V. Boutou, S. Hill, W. Zimmer, M. Krenz, H. Lambrecht, J. Yu, R. Chang, L. Woeste, and J. Wolf, “White-light nanosource with directional emission,” Phys. Rev. Lett.  89, 035002 (2002).
[CrossRef] [PubMed]

Zaretsky, D. F.

S. V. Fomichev, S. V. Popruzhenko, D. F. Zaretsky, and W. Becker, “Laser-induced nonlinear excitation of collective electron motion in a cluster,” J. Phys. B  36, 3817–3834 (2003).
[CrossRef]

Zheng, X. H.

D. Caroll and X. H. Zheng, “Spatial and angular distributions of third harmonic generation from metal surfaces,” Eur. Phys. J. D  5, 135–144 (1999).
[CrossRef]

Zimmer, W.

C. Favre, V. Boutou, S. Hill, W. Zimmer, M. Krenz, H. Lambrecht, J. Yu, R. Chang, L. Woeste, and J. Wolf, “White-light nanosource with directional emission,” Phys. Rev. Lett.  89, 035002 (2002).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

V. Shcheslavskiy, G. Petrov, and V. V. Yakovlev, “Nonlinear susceptibility measurements of solutions using third-harmonic generation on the interface,” Appl. Phys. Lett.  82, 3982–3984 (2003).
[CrossRef]

G. I. Petrov, V. I. Shcheslavskiy, V. V. Yakovlev, I. Ozerov, E. Chelnokov, and W. Marine, “Efficient third-harmonic generation in a thin nanocrystalline film of ZnO,” Appl. Phys. Lett.  83, 3993–3995 (2003).
[CrossRef]

Chem. Phys. Lett. (1)

H. Wang, E. Yang, E. Borguet, and K. Eisenthal, “Second harmonic generation from the surface of centrosymmetric particles in bulk solution,” Chem. Phys. Lett.  259, 15–20 (1996).
[CrossRef]

Eur. Phys. J. D (1)

D. Caroll and X. H. Zheng, “Spatial and angular distributions of third harmonic generation from metal surfaces,” Eur. Phys. J. D  5, 135–144 (1999).
[CrossRef]

J. Opt. Soc. Am. B (3)

J. Phys. B (1)

S. V. Fomichev, S. V. Popruzhenko, D. F. Zaretsky, and W. Becker, “Laser-induced nonlinear excitation of collective electron motion in a cluster,” J. Phys. B  36, 3817–3834 (2003).
[CrossRef]

J. Struct. Biol. (1)

V. Shcheslavskiy, G. Petrov, S. Saltiel, and V. Yakovlev, “Quantitative characterization of aqueous solutions probed by the third-harmonic generation microscopy,” J. Struct. Biol.  147, 42–49 (2004).
[CrossRef] [PubMed]

Nano Lett. (1)

M. Lippitz, M. A. van Dijk, and M. Orrit, “Third-harmonic generation from single gold nanoparticles,” Nano Lett.  5, 799–802 (2005).
[CrossRef] [PubMed]

Opt. Lett. (2)

Philos. Mag. (1)

J. W. Strut, “On the light from the sky, its polarization and color,” Philos. Mag.  41, 107–120 (1871).

Phys. Rev. B (3)

X. M. Hua and J. I. Gersten, “Theory of second harmonic generation by small metal spheres,” Phys. Rev. B  33, 3756–3764 (1986).
[CrossRef]

V. L. Brudny, B. S. Mendoza, and W. L. Mochan, “Second-harmonic generation from spherical particles,” Phys. Rev. B  62, 11152–11162 (2000).
[CrossRef]

Z. Wang, B. Luk’yanchuk, M. Hong, Y. Lin, and T. Chong, “Energy flow around a small particle investigated by classical Mie theory,” Phys. Rev. B  70, 035418 (2004).
[CrossRef]

Phys. Rev. Lett. (3)

J. Kasparian, B. Kramer, J. Dewitz, S. Vajda, P. Rairoux, B. Vezin, V. Boutou, T. Leisner, W. Hubner, J. Wolf, L. Woste, and K. Bennemann, “Angular dependences of third harmonic generation from microdroplets,” Phys. Rev. Lett.  78, 2952–2955 (1997).
[CrossRef]

C. Favre, V. Boutou, S. Hill, W. Zimmer, M. Krenz, H. Lambrecht, J. Yu, R. Chang, L. Woeste, and J. Wolf, “White-light nanosource with directional emission,” Phys. Rev. Lett.  89, 035002 (2002).
[CrossRef] [PubMed]

J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-harmonic Rayleigh scattering from a centrosymmetric material,” Phys. Rev. Lett.  83, 4045–4048 (1999).
[CrossRef]

Z. Phys. D (1)

J. P. Dewitz, W. Hubner, and K. H. Bennemann, “Theory of nonlinear Mie-scattering from spherical metal clusters,” Z. Phys. D  37, 75–84 (1996).
[CrossRef]

Other (4)

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

P. W. Barber and R. K. Chang, Optical Effects Associated with Small Particles (World Scientific, 1988).

V. I. Shcheslavskiy, G. I. Petrov, V. V. Yakovlev, S. M. Saltiel, B. S. Luk’yanchuk, Z. S. Nickolov, and J. D. Miller, “Third-harmonic generation from Rayleigh particles,” Phys. Rev. Lett., submitted for publication.

J. F. Reintjes, Nonlinear Optical Parametric Processes in Liquids and Gases (Academic, 1984).

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram illustrating the geometry of third harmonic generation by a small particle in a focused laser beam.

Fig. 2
Fig. 2

Results of theoretical calculations of THG in microspheres in an index-matching liquid. Third-harmonic power is in arbitrary units. R ω 0 , b = 32 μ m . Solid curve, χ s ( 3 ) χ m ( 3 ) = 0.5 ; dashed curve, χ s ( 3 ) χ m ( 3 ) = 2 ; dotted–dashed curve, χ s ( 3 ) χ m ( 3 ) = 3 . Inset, comparison of fourth-power dependence (dashed curve) and plot of analytical Eq. (12) for particles with small diameters.

Fig. 3
Fig. 3

Theoretical calculations of THG in microspheres in an index-matching liquid. Third-harmonic power is in arbitrary units. R ω 0 , b = 32 μ m . Solid curve, χ s ( 3 ) χ m ( 3 ) = 0.5 ; dashed curve, χ s ( 3 ) χ m ( 3 ) = 2 ; dotted–dashed curve, χ s ( 3 ) χ m ( 3 ) = 3 .

Fig. 4
Fig. 4

Power of the third harmonic generated from the solution of 0.750 μ m diameter fused-silica particles in the index-matching solution as a function of particle concentration. The dashed line provides a linear fit, used to calculate the effective power of the third harmonic generated by a single particle.

Fig. 5
Fig. 5

Third-harmonic intensity generated by a single particle in the index-matching liquid as a function of particle diameter. The dashed line shows the fourth-power dependence.

Fig. 6
Fig. 6

Power of the third harmonic generated by a single particle in the non-index-matching solution as a function of particle’s diameter. The dashed line shows the fourth-power dependence.

Fig. 7
Fig. 7

Time-dependent third-harmonic signal from the bulk of the flowing solution; each spike corresponds to a 200 nm diameter particle passing through a focal volume of a laser beam.

Equations (15)

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

P 3 = 1 4 χ ( 3 ) E 1 E 1 E 1 ,
2 i n 3 2 ω 3 c 2 E 3 t + 2 i k 3 E 3 z + T 2 E 3 = 4 π ω 3 2 c 2 P 3 exp ( i Δ k z ) ,
d A 3 d z = i γ A 10 3 exp ( i Δ k z ) ( 1 + i 2 z b ) 2 ,
A 3 ( z ) = i A 10 3 J ( Δ k , z 1 , z 2 ) ,
A 3 ( , ) = i A 10 3 [ I γ m exp ( i Δ k m z ) ( 1 + 2 i z b ) 2 d z + II γ s exp ( i Δ k s z ) ( 1 + 2 i z b ) 2 d z + III γ m exp ( i Δ k m z ) ( 1 + 2 i z b ) 2 d z ] .
A 3 ( , ) = i A 10 3 L ( ρ ) 2 + L ( ρ ) 2 ( γ s exp [ i ( Δ k s + 4 b ) z ] γ m exp [ i ( Δ k m + 4 b ) ] ) d z ,
I 3 = c n 3 2 π ( 8 π c n 1 I 1 ) 3 [ γ s Δ ̃ k s sin ( Δ ̃ k s L 2 ) γ m Δ ̃ k m sin 2 ( Δ ̃ k m L 2 ) ] ,
P 3 = 512 π 3 n 3 c 2 n 1 3 I 1 3 0 R ρ g 2 ( ρ ) [ γ s Δ ̃ k s sin ( Δ ̃ k s L 2 ) γ m Δ ̃ k m sin 2 ( Δ ̃ k m L 2 ) ] d ρ ,
P 3 = C ( T s + T m + T 3 ) ,
where C = 4096 n 3 c 2 n 1 3 ω 0 6 P 1 3 ,
T s , m = ( γ s 2 Δ ̃ k s , m 2 ) 2 [ R 2 Δ ̃ k s , m 2 R Δ ̃ k s , m sin ( 2 R Δ ̃ k s , m ) + sin 2 ( R Δ ̃ k s , m ) ] ,
T 3 = γ m γ s Δ ̃ k s Δ ̃ k m Δ k p 2 Δ k o 2 [ R Δ k o 2 Δ k p sin ( R Δ k p ) Δ k p 2 cos ( R Δ k o ) R Δ k o Δ k p 2 sin ( R Δ k o ) + Δ k o 2 cos ( R Δ k p ) + 4 Δ ̃ k m Δ ̃ k s ] ,
P 3 = 1024 n 3 c 2 n 1 3 ω 0 6 ( γ s γ m ) 2 R 4 P 1 3 .
P 3 I 1 3 ( π 6 ω 0 2 ) [ γ s Δ ̃ k s sin ( Δ ̃ k s R ) γ m Δ ̃ k m sin ( Δ ̃ k m R ) ] .
χ eff ( 3 ) = χ m ( 3 ) + p χ s ( 3 ) ,

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