Abstract

We study the generation of second-harmonic radiation in the interaction of light with an infinite cylinder illuminated perpendicular to its axis by an s- or p-polarized monochromatic electromagnetic wave. With the assumption of a homogeneous and isotropic medium, we derive analytical expressions for the second-harmonic field radiated by the cylinder. The theoretical results are illustrated through calculations of the total scattered power and its angular distribution by employment of a free-electron model for the linear and nonlinear susceptibilities. The scattering cross sections at the harmonic frequency display peaks due to the excitation of resonances.

© 2004 Optical Society of America

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    [CrossRef]
  2. D. Rogovin and T. P. Shen, “Microparticle surface-enhanced second-harmonic generation,” J. Opt. Soc. Am. B 5, 1886–1889 (1988).
    [CrossRef]
  3. K. Hayata and M. Koshiba, “Theory of surface-emitting second-harmonic generation from optically trapped microspheres,” Phys. Rev. A 46, 6104–1889 (1992).
    [CrossRef] [PubMed]
  4. J. Martorell, R. Vilaseca, and R. Crobalán, “Scattering of second-harmonic light from small spherical particles ordered in a crystalline lattice,” Phys. Rev. A 55, 4520–4525 (1997).
    [CrossRef]
  5. J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, “Second-harmonic Rayleigh scattering from a sphere of centrosymmetric material,” Phys. Rev. Lett. 83, 4045–4048 (1999).
    [CrossRef]
  6. V. L. Brudny, B. S. Mendoza, and W. L. Mochán, “Second-harmonic generation from spherical particles,” Phys. Rev. B 62, 11152–11162 (2000).
    [CrossRef]
  7. J. F. McGilp, “Optical characterization of semiconductor surfaces and interfaces,” Prog. Surf. Sci. 49, 1–106 (1995).
    [CrossRef]
  8. Y. R. Shen, “Wave mixing spectroscopy for surface studies,” Solid State Commun. 102, 221–229 (1997).
    [CrossRef]
  9. G. Lüpke, “Characterization of semiconductor interfaces by second-harmonic generation,” Surf. Sci. Rep. 35, 75–161 (1999).
    [CrossRef]
  10. M. C. Downer, B. S. Mendoza, and V. I. Gavrilenko, “Optical second harmonic spectroscopy of semiconductor surfaces: advances in microscopic understanding,” Surf. Interface Anal. 31, 966–986 (2001).
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  11. F. Brown, R. E. Parks, and A. M. Sleeper, “Nonlinear optical reflection from a metallic boundary,” Phys. Rev. Lett. 14, 1029–1031 (1965).
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  12. F. Brown and R. E. Parks, “Magnetic-dipole contribution to optical harmonics in silver,” Phys. Rev. Lett. 16, 507–509 (1966).
    [CrossRef]
  13. N. Bloembergen, R. K. Chang, and C. H. Lee, “Second-harmonic generation of light in reflection from media with inversion symmetry,” Phys. Rev. Lett. 16, 986–989 (1966).
    [CrossRef]
  14. N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion simmetry,” Phys. Rev. 174, 813–822 (1968).
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  15. J. Rudnick and E. A. Stern, “Second-harmonic radiation from metal surfaces,” Phys. Rev. B 4, 4274–4290 (1971).
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  16. P. Guyot-Sionnest and Y. R. Shen, “Bulk contribution in surface second-harmonic generation,” Phys. Rev. B 38, 7985–7989 (1988).
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  17. B. S. Mendoza and W. L. Mochán, “Exactly solvable model of surface second-harmonic generation,” Phys. Rev. B 53, 4999–5006 (1996).
    [CrossRef]
  18. B. S. Mendoza and W. L. Mochán, “Erratum: exactly solvable model of surface second-harmonic generation,” Phys. Rev. B 53, 4999 (1996); Phys. Rev. B 61, 16243 (2000).
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  22. A. R. McGurn, V. M. Agranovich, and T. A. Leskova, “Weak-localization effects in the generation of second harmonics of light at a randomly rough vacuum–metal grating,” Phys. Rev. B 44, 11441–11456 (1991).
    [CrossRef]
  23. K. A. O’Donnell, R. Torre, and C. S. West, “Observations of backscattering effects in second-harmonic generation from a weakly rough metal surface,” Opt. Lett. 21, 1738–1740 (1996).
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  26. M. Leyva-Lucero, E. R. Méndez, T. A. Leskova, A. A. Maradudin, and J. Q. Lu, “Multiple-scattering effects in the second-harmonic generation of light in reflection from a randomly rough metal surface,” Opt. Lett. 21, 1809–1811 (1996).
    [CrossRef] [PubMed]
  27. M. A. Leyva-Lucero, E. R. Méndez, T. A. Leskova, and A. A. Maradudin, “Destructive interference effects in the second harmonic light generated at randomly rough metal surfaces,” Opt. Commun. 161, 79–94 (1999).
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    [CrossRef]
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    [CrossRef]
  36. S. C. Hill and R. E. Benner, “Morphology-dependent resonances,” in Optical Effects Associated with Small Particles, P. W. Barber and R. K. Chang, eds. (World Scientific, Singapore, 1988), pp. 3–61.

2003 (1)

2001 (1)

M. C. Downer, B. S. Mendoza, and V. I. Gavrilenko, “Optical second harmonic spectroscopy of semiconductor surfaces: advances in microscopic understanding,” Surf. Interface Anal. 31, 966–986 (2001).
[CrossRef]

2000 (1)

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

1999 (3)

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

G. Lüpke, “Characterization of semiconductor interfaces by second-harmonic generation,” Surf. Sci. Rep. 35, 75–161 (1999).
[CrossRef]

M. A. Leyva-Lucero, E. R. Méndez, T. A. Leskova, and A. A. Maradudin, “Destructive interference effects in the second harmonic light generated at randomly rough metal surfaces,” Opt. Commun. 161, 79–94 (1999).
[CrossRef]

1997 (4)

K. A. O’Donnell, R. Torre, and C. S. West, “Observations of second-harmonic generation from randomly rough metal surface,” Phys. Rev. B 55, 7985–7992 (1997).
[CrossRef]

K. A. O’Donnell and R. Torre, “Second-harmonic generation from strongly rough metal surfaces,” Opt. Commun. 138, 341–344 (1997).
[CrossRef]

Y. R. Shen, “Wave mixing spectroscopy for surface studies,” Solid State Commun. 102, 221–229 (1997).
[CrossRef]

J. Martorell, R. Vilaseca, and R. Crobalán, “Scattering of second-harmonic light from small spherical particles ordered in a crystalline lattice,” Phys. Rev. A 55, 4520–4525 (1997).
[CrossRef]

1996 (3)

1995 (1)

J. F. McGilp, “Optical characterization of semiconductor surfaces and interfaces,” Prog. Surf. Sci. 49, 1–106 (1995).
[CrossRef]

1992 (1)

K. Hayata and M. Koshiba, “Theory of surface-emitting second-harmonic generation from optically trapped microspheres,” Phys. Rev. A 46, 6104–1889 (1992).
[CrossRef] [PubMed]

1991 (1)

A. R. McGurn, V. M. Agranovich, and T. A. Leskova, “Weak-localization effects in the generation of second harmonics of light at a randomly rough vacuum–metal grating,” Phys. Rev. B 44, 11441–11456 (1991).
[CrossRef]

1988 (2)

D. Rogovin and T. P. Shen, “Microparticle surface-enhanced second-harmonic generation,” J. Opt. Soc. Am. B 5, 1886–1889 (1988).
[CrossRef]

P. Guyot-Sionnest and Y. R. Shen, “Bulk contribution in surface second-harmonic generation,” Phys. Rev. B 38, 7985–7989 (1988).
[CrossRef]

1986 (2)

D. Maystre, M. Neviere, and R. Reinisch, “Nonlinear polarisation inside metals: a mathematical study of the free electron model,” Appl. Phys. A 39, 115–121 (1986).
[CrossRef]

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

1985 (1)

J. L. Coutaz, M. Neviere, E. Pic, and R. Reinisch, “Experimental study of surface-enhanced second-harmonic generation on silver gratings,” Phys. Rev. B 32, 2227–2232 (1985).
[CrossRef]

1984 (2)

R. T. Deck and R. K. Grygier, “Surface-plasmon enhanced harmonic generation at a rough metal surface,” Appl. Opt. 23, 3202–3213 (1984).
[CrossRef] [PubMed]

G. A. Farias and A. A. Maradudin, “Second-harmonic generation in reflection from a metallic grating,” Phys. Rev. B 30, 3002–3012 (1984).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

1971 (1)

J. Rudnick and E. A. Stern, “Second-harmonic radiation from metal surfaces,” Phys. Rev. B 4, 4274–4290 (1971).
[CrossRef]

1968 (1)

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion simmetry,” Phys. Rev. 174, 813–822 (1968).
[CrossRef]

1966 (2)

F. Brown and R. E. Parks, “Magnetic-dipole contribution to optical harmonics in silver,” Phys. Rev. Lett. 16, 507–509 (1966).
[CrossRef]

N. Bloembergen, R. K. Chang, and C. H. Lee, “Second-harmonic generation of light in reflection from media with inversion symmetry,” Phys. Rev. Lett. 16, 986–989 (1966).
[CrossRef]

1965 (1)

F. Brown, R. E. Parks, and A. M. Sleeper, “Nonlinear optical reflection from a metallic boundary,” Phys. Rev. Lett. 14, 1029–1031 (1965).
[CrossRef]

Agranovich, V. M.

A. R. McGurn, V. M. Agranovich, and T. A. Leskova, “Weak-localization effects in the generation of second harmonics of light at a randomly rough vacuum–metal grating,” Phys. Rev. B 44, 11441–11456 (1991).
[CrossRef]

Bloembergen, N.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion simmetry,” Phys. Rev. 174, 813–822 (1968).
[CrossRef]

N. Bloembergen, R. K. Chang, and C. H. Lee, “Second-harmonic generation of light in reflection from media with inversion symmetry,” Phys. Rev. Lett. 16, 986–989 (1966).
[CrossRef]

Brown, F.

F. Brown and R. E. Parks, “Magnetic-dipole contribution to optical harmonics in silver,” Phys. Rev. Lett. 16, 507–509 (1966).
[CrossRef]

F. Brown, R. E. Parks, and A. M. Sleeper, “Nonlinear optical reflection from a metallic boundary,” Phys. Rev. Lett. 14, 1029–1031 (1965).
[CrossRef]

Brudny, V. L.

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

Chang, R. K.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion simmetry,” Phys. Rev. 174, 813–822 (1968).
[CrossRef]

N. Bloembergen, R. K. Chang, and C. H. Lee, “Second-harmonic generation of light in reflection from media with inversion symmetry,” Phys. Rev. Lett. 16, 986–989 (1966).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Coutaz, J. L.

J. L. Coutaz, M. Neviere, E. Pic, and R. Reinisch, “Experimental study of surface-enhanced second-harmonic generation on silver gratings,” Phys. Rev. B 32, 2227–2232 (1985).
[CrossRef]

Crobalán, R.

J. Martorell, R. Vilaseca, and R. Crobalán, “Scattering of second-harmonic light from small spherical particles ordered in a crystalline lattice,” Phys. Rev. A 55, 4520–4525 (1997).
[CrossRef]

Dadap, J. I.

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

Deck, R. T.

Downer, M. C.

M. C. Downer, B. S. Mendoza, and V. I. Gavrilenko, “Optical second harmonic spectroscopy of semiconductor surfaces: advances in microscopic understanding,” Surf. Interface Anal. 31, 966–986 (2001).
[CrossRef]

Eisenthal, K. B.

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

Farias, G. A.

G. A. Farias and A. A. Maradudin, “Second-harmonic generation in reflection from a metallic grating,” Phys. Rev. B 30, 3002–3012 (1984).
[CrossRef]

Gavrilenko, V. I.

M. C. Downer, B. S. Mendoza, and V. I. Gavrilenko, “Optical second harmonic spectroscopy of semiconductor surfaces: advances in microscopic understanding,” Surf. Interface Anal. 31, 966–986 (2001).
[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]

Grygier, R. K.

Guyot-Sionnest, P.

P. Guyot-Sionnest and Y. R. Shen, “Bulk contribution in surface second-harmonic generation,” Phys. Rev. B 38, 7985–7989 (1988).
[CrossRef]

Hayata, K.

K. Hayata and M. Koshiba, “Theory of surface-emitting second-harmonic generation from optically trapped microspheres,” Phys. Rev. A 46, 6104–1889 (1992).
[CrossRef] [PubMed]

Heinz, T. F.

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

Jha, S. S.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion simmetry,” Phys. Rev. 174, 813–822 (1968).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Koshiba, M.

K. Hayata and M. Koshiba, “Theory of surface-emitting second-harmonic generation from optically trapped microspheres,” Phys. Rev. A 46, 6104–1889 (1992).
[CrossRef] [PubMed]

Lee, C. H.

N. Bloembergen, R. K. Chang, S. S. Jha, and C. H. Lee, “Optical second-harmonic generation in reflection from media with inversion simmetry,” Phys. Rev. 174, 813–822 (1968).
[CrossRef]

N. Bloembergen, R. K. Chang, and C. H. Lee, “Second-harmonic generation of light in reflection from media with inversion symmetry,” Phys. Rev. Lett. 16, 986–989 (1966).
[CrossRef]

Leskova, T. A.

M. A. Leyva-Lucero, E. R. Méndez, T. A. Leskova, and A. A. Maradudin, “Destructive interference effects in the second harmonic light generated at randomly rough metal surfaces,” Opt. Commun. 161, 79–94 (1999).
[CrossRef]

M. Leyva-Lucero, E. R. Méndez, T. A. Leskova, A. A. Maradudin, and J. Q. Lu, “Multiple-scattering effects in the second-harmonic generation of light in reflection from a randomly rough metal surface,” Opt. Lett. 21, 1809–1811 (1996).
[CrossRef] [PubMed]

A. R. McGurn, V. M. Agranovich, and T. A. Leskova, “Weak-localization effects in the generation of second harmonics of light at a randomly rough vacuum–metal grating,” Phys. Rev. B 44, 11441–11456 (1991).
[CrossRef]

Leyva-Lucero, M.

Leyva-Lucero, M. A.

M. A. Leyva-Lucero, E. R. Méndez, T. A. Leskova, and A. A. Maradudin, “Destructive interference effects in the second harmonic light generated at randomly rough metal surfaces,” Opt. Commun. 161, 79–94 (1999).
[CrossRef]

Lu, J. Q.

Lüpke, G.

G. Lüpke, “Characterization of semiconductor interfaces by second-harmonic generation,” Surf. Sci. Rep. 35, 75–161 (1999).
[CrossRef]

Maradudin, A. A.

M. A. Leyva-Lucero, E. R. Méndez, T. A. Leskova, and A. A. Maradudin, “Destructive interference effects in the second harmonic light generated at randomly rough metal surfaces,” Opt. Commun. 161, 79–94 (1999).
[CrossRef]

M. Leyva-Lucero, E. R. Méndez, T. A. Leskova, A. A. Maradudin, and J. Q. Lu, “Multiple-scattering effects in the second-harmonic generation of light in reflection from a randomly rough metal surface,” Opt. Lett. 21, 1809–1811 (1996).
[CrossRef] [PubMed]

G. A. Farias and A. A. Maradudin, “Second-harmonic generation in reflection from a metallic grating,” Phys. Rev. B 30, 3002–3012 (1984).
[CrossRef]

Martorell, J.

J. Martorell, R. Vilaseca, and R. Crobalán, “Scattering of second-harmonic light from small spherical particles ordered in a crystalline lattice,” Phys. Rev. A 55, 4520–4525 (1997).
[CrossRef]

Maystre, D.

D. Maystre, M. Neviere, and R. Reinisch, “Nonlinear polarisation inside metals: a mathematical study of the free electron model,” Appl. Phys. A 39, 115–121 (1986).
[CrossRef]

McGilp, J. F.

J. F. McGilp, “Optical characterization of semiconductor surfaces and interfaces,” Prog. Surf. Sci. 49, 1–106 (1995).
[CrossRef]

McGurn, A. R.

A. R. McGurn, V. M. Agranovich, and T. A. Leskova, “Weak-localization effects in the generation of second harmonics of light at a randomly rough vacuum–metal grating,” Phys. Rev. B 44, 11441–11456 (1991).
[CrossRef]

Méndez, E. R.

Mendoza, B. S.

C. I. Valencia, E. R. Méndez, and B. S. Mendoza, “Second-harmonic generation in the scattering of light by two-dimensional particles,” J. Opt. Soc. Am. B 20, 2150–2161 (2003).
[CrossRef]

M. C. Downer, B. S. Mendoza, and V. I. Gavrilenko, “Optical second harmonic spectroscopy of semiconductor surfaces: advances in microscopic understanding,” Surf. Interface Anal. 31, 966–986 (2001).
[CrossRef]

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

B. S. Mendoza and W. L. Mochán, “Exactly solvable model of surface second-harmonic generation,” Phys. Rev. B 53, 4999–5006 (1996).
[CrossRef]

B. S. Mendoza and W. L. Mochán, “Erratum: exactly solvable model of surface second-harmonic generation,” Phys. Rev. B 53, 4999 (1996); Phys. Rev. B 61, 16243 (2000).
[CrossRef]

Mochán, W. L.

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

B. S. Mendoza and W. L. Mochán, “Exactly solvable model of surface second-harmonic generation,” Phys. Rev. B 53, 4999–5006 (1996).
[CrossRef]

B. S. Mendoza and W. L. Mochán, “Erratum: exactly solvable model of surface second-harmonic generation,” Phys. Rev. B 53, 4999 (1996); Phys. Rev. B 61, 16243 (2000).
[CrossRef]

Neviere, M.

D. Maystre, M. Neviere, and R. Reinisch, “Nonlinear polarisation inside metals: a mathematical study of the free electron model,” Appl. Phys. A 39, 115–121 (1986).
[CrossRef]

J. L. Coutaz, M. Neviere, E. Pic, and R. Reinisch, “Experimental study of surface-enhanced second-harmonic generation on silver gratings,” Phys. Rev. B 32, 2227–2232 (1985).
[CrossRef]

O’Donnell, K. A.

K. A. O’Donnell and R. Torre, “Second-harmonic generation from strongly rough metal surfaces,” Opt. Commun. 138, 341–344 (1997).
[CrossRef]

K. A. O’Donnell, R. Torre, and C. S. West, “Observations of second-harmonic generation from randomly rough metal surface,” Phys. Rev. B 55, 7985–7992 (1997).
[CrossRef]

K. A. O’Donnell, R. Torre, and C. S. West, “Observations of backscattering effects in second-harmonic generation from a weakly rough metal surface,” Opt. Lett. 21, 1738–1740 (1996).
[CrossRef] [PubMed]

Parks, R. E.

F. Brown and R. E. Parks, “Magnetic-dipole contribution to optical harmonics in silver,” Phys. Rev. Lett. 16, 507–509 (1966).
[CrossRef]

F. Brown, R. E. Parks, and A. M. Sleeper, “Nonlinear optical reflection from a metallic boundary,” Phys. Rev. Lett. 14, 1029–1031 (1965).
[CrossRef]

Pic, E.

J. L. Coutaz, M. Neviere, E. Pic, and R. Reinisch, “Experimental study of surface-enhanced second-harmonic generation on silver gratings,” Phys. Rev. B 32, 2227–2232 (1985).
[CrossRef]

Reinisch, R.

D. Maystre, M. Neviere, and R. Reinisch, “Nonlinear polarisation inside metals: a mathematical study of the free electron model,” Appl. Phys. A 39, 115–121 (1986).
[CrossRef]

J. L. Coutaz, M. Neviere, E. Pic, and R. Reinisch, “Experimental study of surface-enhanced second-harmonic generation on silver gratings,” Phys. Rev. B 32, 2227–2232 (1985).
[CrossRef]

Rogovin, D.

Rudnick, J.

J. Rudnick and E. A. Stern, “Second-harmonic radiation from metal surfaces,” Phys. Rev. B 4, 4274–4290 (1971).
[CrossRef]

Shan, J.

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

Shen, T. P.

Shen, Y. R.

Y. R. Shen, “Wave mixing spectroscopy for surface studies,” Solid State Commun. 102, 221–229 (1997).
[CrossRef]

P. Guyot-Sionnest and Y. R. Shen, “Bulk contribution in surface second-harmonic generation,” Phys. Rev. B 38, 7985–7989 (1988).
[CrossRef]

Sleeper, A. M.

F. Brown, R. E. Parks, and A. M. Sleeper, “Nonlinear optical reflection from a metallic boundary,” Phys. Rev. Lett. 14, 1029–1031 (1965).
[CrossRef]

Stern, E. A.

J. Rudnick and E. A. Stern, “Second-harmonic radiation from metal surfaces,” Phys. Rev. B 4, 4274–4290 (1971).
[CrossRef]

Torre, R.

K. A. O’Donnell and R. Torre, “Second-harmonic generation from strongly rough metal surfaces,” Opt. Commun. 138, 341–344 (1997).
[CrossRef]

K. A. O’Donnell, R. Torre, and C. S. West, “Observations of second-harmonic generation from randomly rough metal surface,” Phys. Rev. B 55, 7985–7992 (1997).
[CrossRef]

K. A. O’Donnell, R. Torre, and C. S. West, “Observations of backscattering effects in second-harmonic generation from a weakly rough metal surface,” Opt. Lett. 21, 1738–1740 (1996).
[CrossRef] [PubMed]

Valencia, C. I.

Vilaseca, R.

J. Martorell, R. Vilaseca, and R. Crobalán, “Scattering of second-harmonic light from small spherical particles ordered in a crystalline lattice,” Phys. Rev. A 55, 4520–4525 (1997).
[CrossRef]

West, C. S.

K. A. O’Donnell, R. Torre, and C. S. West, “Observations of second-harmonic generation from randomly rough metal surface,” Phys. Rev. B 55, 7985–7992 (1997).
[CrossRef]

K. A. O’Donnell, R. Torre, and C. S. West, “Observations of backscattering effects in second-harmonic generation from a weakly rough metal surface,” Opt. Lett. 21, 1738–1740 (1996).
[CrossRef] [PubMed]

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Figures (10)

Fig. 1
Fig. 1

Schematic diagram of the geometry considered.

Fig. 2
Fig. 2

Scattering cross section for a cylinder of radius R=0.5 µm illuminated with p-polarized light in the range 0.42<λ<1.05 µm. (a) Fundamental frequency and (b) second-harmonic frequency.

Fig. 3
Fig. 3

Scattering cross section for a cylinder of radius R=0.3µm illuminated with p-polarized light in the range 0.62<λ<1.24µm. (a) Fundamental frequency and (b) second-harmonic frequency.

Fig. 4
Fig. 4

Scattering cross section for a cylinder of radius R=0.3µm illuminated with s-polarized light in the range 0.62<λ<1.24µm. (a) Fundamental frequency and (b) second-harmonic frequency.

Fig. 5
Fig. 5

Linear scattering by a cylinder of radius R=0.5µm illuminated with p-polarized light of wavelength λ=0.567µm (frequency ωa). (a) Logarithmic intensity map inside the cylinder and relative strength of the coefficients gRm(p). (b) Differential scattering cross section.

Fig. 6
Fig. 6

Second-harmonic generation by a cylinder of radius R=0.5µm illuminated with p-polarized light of wavelength λ=0.567µm (frequency ωa). (a) Logarithmic intensity map inside the cylinder at the frequency 2ωa and relative strength of the coefficients cRm. (b) Differential scattering cross section at 2ωa.

Fig. 7
Fig. 7

Differential scattering cross section for a cylinder of radius R=0.3µm illuminated with p-polarized light of wavelength λb=0.658µm (frequency ωb).

Fig. 8
Fig. 8

P-polarized second-harmonic differential scattering cross section for a cylinder of radius R=0.3µm illuminated with p-polarized light of wavelength λb=0.658µm (second-harmonic frequency 2ωb).

Fig. 9
Fig. 9

Differential scattering cross section for a cylinder of radius R=0.3µm illuminated with s-polarized light of wavelength λ=0.658µm (frequency ωb).

Fig. 10
Fig. 10

P-polarized second-harmonic differential scattering cross section for a cylinder of radius R=0.3µm illuminated with s-polarized light of wavelength λ=0.658µm (second-harmonic frequency 2ωb).

Equations (63)

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rs(t)=R[sin t, cos t].
Z=R[sin t, cos t],X=R[cos t,-sin t],
Z=Rsin t x1+cos t x3,
X=Rcos t x1-sin t x3.
ψs,p(R)(t|Ω)=ψs,p(R)(r|Ω)|r=rs,
Υs,p(R)(t|Ω)=ψs,p(R)(r|Ω)Zr=rs.
PNL(r|2ω)=α[E(r|ω)·]E(r|ω)+βE(r|ω)×[·E(r|ω)]+γ[E(r|ω)·E(r|ω)],
Pzs(rs|2ω)=limτ0 -ττ PzNL(rs, z|2ω)II(z|2ω) dz,
Pts(rs|2ω)=limτ0 -ττPtNL(rs, z|2ω)dz,
ψp(I)(t|2ω)-ψp(II)(t|2ω)=4π 2iωcPxs(t|2ω),
Υp(I)(t|2ω)-1II(2ω)Υp(II)(t|2ω)=-4π 2iωc dPzs(t|2ω)dt
+RPxNL(t|2ω)II(2ω),
RPxNL(t|2ω)=-(α/2+γ) c2ω2 1R2 ddt[Υp(I)(t|ω)]2+1II2(ω) ddt dψp(I)(t|ω)dt2-α2II(ω) ddt[ψp(I)(t|ω)]2+γ ddt[ψs(I)(t|ω)]2,
Pxs(t|2ω)=χttzscω2 1R2Υp(I)(t|ω) dψp(I)(t|ω)dt,
Pzs(t|2ω)=-χzzzscω2 1R2 dψp(I)(t|ω)dt2-χzttscω2 1R2[Υp(I)(t|ω)]2-[ψs(I)(t|ω)]2,
1r r r ψ(r, θ|Ω)r+1r2 2ψ(r, θ|Ω)θ2
+nR(Ω) Ωc2ψ(r, θ|Ω)=0,
κΩ(R) ddκΩ(R) κΩ(R) dZldκΩ(R)+{[κΩ(R)]2-l2}Zl=0,
ψς(I)(r, θ|ω)=±ψ0ςl=-il[Jl(κω(I))+al(ς)×Hl(1)(κω(I))]exp(ilθ),
ψς(II)(r, θ|ω)=±ψ0ςl=-ilgl(ς)Jl(κω(II))exp(ilθ),
al(s)=nωJl(ρ)Jl(nωρ)-Jl(nωρ)Jl(ρ)Jl(nωρ)[Hl(1)(ρ)]-nωJl(nωρ)Hl(1)(ρ),
gl(s)=Jl(ρ)[Hl(1)(ρ)]-Jl(ρ)Hl(1)(ρ)Jl(nωρ)[Hl(1)(ρ)]-nωJl(nωρ)Hl(1)(ρ)
al(p)=Jl(ρ)Jl(nωρ)-nωJl(nωρ)Jl(ρ)nωJl(nωρ)[Hl(1)(ρ)]-Jl(nωρ)Hl(1)(ρ),
gl(p)=nω{Jl(ρ)[Hl(1)(ρ)]-Jl(ρ)Hl(1)(ρ)}nωJl(nωρ)[Hl(1)(ρ)]-Jl(nωρ)Hl(1)(ρ)
ψp(I)(r, θ|2ω)=l=-blHl(1)(κ2ω(I))exp(ilθ),
ψp(II)(r, θ|2ω)=l=-clJl(κ2ω(II))exp(ilθ).
l=-[blHl(1)(2ρ)-clJl(2n2ωρ)]exp(ilθ)
=KC1l,k=-il+klTl(p)(ρ)Uk(p)(ρ)exp[i(l+k)θ],
l=-bl[Hl(1)(2ρ)]-1n2ωclJl(2n2ωρ)exp(ilθ)
=K2C2l,k=-il+klk2Tl(p)(ρ)Tk(p)(ρ)exp[i(l+k)θ]
-C3l,k=-il+kkUl(p)(ρ)Uk(p)(ρ)exp[i(l+k)θ]+C4l,k=-il+kkTl(s)(ρ)Tk(s)(ρ)exp[i(l+k)θ]-C5l,k=-il+kkTl(p)(ρ)Tk(p)(ρ)exp[i(l+k)θ],
C1=-χttzs,
C2=12ρ2 χzzzs+α/2+γnω4n2ω2,
C3=-χztts+α/2+γn2ω2,
C4=χztts+γn2ω2,
C5=-α2nω2n2ω2.
bmHm(1)(2ρ)-cmJm(2n2ωρ)=imKC1V1m,
bm[Hm(1)(2ρ)]-1n2ωcmJm(2n2ωρ)
=imK(C2V2m+C3V3m+C4V4m+C5V5m)
V1m=k=-kTk(p)(ρ)Um-k(p)(ρ),
V2m=2k=-k(m-k)2Tk(p)(ρ)Tm-k(p)(ρ),
V3m=k=-(m-k)Uk(p)(ρ)Um-k(p)(ρ),
V4m=k=-(m-k)Tk(s)(ρ)Tm-k(s)(ρ),
V5m=k=-(m-k)Tk(p)(ρ)Tm-k(p)(ρ).
bm=imKΔm (C2V2m+C3V3m+C4V4m+C5V5m)Jm(2n2ωρ)-C1V1mn2ωJm(2n2ωρ),
cm=imKΔm{(C2V2m+C3V3m+C4V4m+C5V5m)Hm(1)(2ρ)-C1V1m[Hm(1)(2ρ)]},
Δm=Jm(2n2ωρ)[Hm(1)(2ρ)]-1n2ωJm(2n2ωρ)Hm(1)(2ρ).
P(Ω)sc=r0L02πSsc(r0, θ|Ω)·eˆrdθ,
Pς(Ω)sc=r0Lc8π Ωc  Rei02πψς(I)(r0, θ|Ω)sc×ψς(I)(r0, θ|Ω)scr*dθ.
Pς(ω)inc=σ c8π|ψ0ς|2.
a-m(ς)=am(ς).
Qς(ω)=Pς(ω)scPς(ω)inc=02πqς(θ|ω)dθ=2ρ |a0(ς)|2+2m=1|am(ς)|2,
qς(θ|ω)=1πρ a0+2m=1am(ς) cos(mθ)2.
b-m=(-1)m+1bm
Qpς(2ω)=σ Pp(2ω)sc[Pς(ω)inc]2=02πqpς(θ|2ω)dθ=8πρc|ψ0ς|4 m=1|bm|2,
qpς(θ|2ω)=16ρc|ψ0ς|4 m=1(-i)mbm sin(mθ)2
α=0,β=e8πm0ω2,γ=β4[1-II(ω)],
χzzzs=-23β[II(ω)-1][II(ω)-3]2II2(ω)-23 lnII(ω)II(2ω),
χztts=0,
χttzs=βII(ω)-1II(ω).
Jm(nωρ)[Hm(1)(ρ)]-nωJm(nωρ)Hm(1)(ρ)=0
nωJm(nωρ)[Hm(1)(ρ)]-Jm(nωρ)Hm(1)(ρ)=0
n2ωJm(2n2ωρ)[Hm(1)(2ρ)]-Jm(2n2ωρ)Hm(1)(2ρ)=0.

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