Abstract

Based on a combination of the multiple-multipole method and nonlinear coupled-wave equations, a rigorous three-dimensional numerical simulation of nonlinear optical interactions between an optical near field and a nonlinear medium is performed, allowing us to study the dependence of second-harmonic (SH) near-field intensity on tip–sample distance and the polarization state of the incident fundamental wave. It is demonstrated that allowed and forbidden light make different contributions to the SH near-field intensity.

© 2000 Optical Society of America

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References

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  1. E. Betzig and J. Trautman, Science 257, 189 (1992).
    [CrossRef] [PubMed]
  2. H. Heinzelmann and D. W. Pohl, Appl. Phys. A 59, 89 (1994).
    [CrossRef]
  3. J. F. McGilp, Prog. Surf. Sci. 49, 1 (1995).
  4. Zh. Li, B. Gu, and G. Yang, Phys. Rev. B 59, 12622 (1999).
    [CrossRef]
  5. L. Novotny, D. W. Pohl, and B. Hecht, Ultramicroscopy 61, 1 (1995).
    [CrossRef]
  6. D. W. Pohl, L. Novotny, B. Hecht, and H. Heinzelmann, Thin Solid Films 273, 161 (1996).
    [CrossRef]
  7. J. Zyss, J. F. Nicoud, and M. Coquillay, J. Chem. Phys. 81, 4160 (1984).
  8. C. Hafner and L. H. Bomholt, The 3D Electrodynamic Wave Simulator (Wiley, New York, 1993).
  9. L. Novotny, “Light propagation and light confinement in near-field optics,” Ph.D. dissertation (ETH, Zurich, 1996).
  10. P. Andreazza, D. Josse, and J. Zyss, Phys. Rev. B 45, 7640 (1992).
    [CrossRef]
  11. D. W. Pohl, Thin Solid Films 264, 250 (1995).
    [CrossRef]
  12. D. A. Kleimman, Phys. Rev. 126, 1977 (1962).
    [CrossRef]
  13. I. I. Smolyaninov, A. V. Zayats, and C. C. Davis, Phys. Rev. B 56, 9290 (1997).
    [CrossRef]

1999 (1)

Zh. Li, B. Gu, and G. Yang, Phys. Rev. B 59, 12622 (1999).
[CrossRef]

1997 (1)

I. I. Smolyaninov, A. V. Zayats, and C. C. Davis, Phys. Rev. B 56, 9290 (1997).
[CrossRef]

1996 (1)

D. W. Pohl, L. Novotny, B. Hecht, and H. Heinzelmann, Thin Solid Films 273, 161 (1996).
[CrossRef]

1995 (3)

J. F. McGilp, Prog. Surf. Sci. 49, 1 (1995).

L. Novotny, D. W. Pohl, and B. Hecht, Ultramicroscopy 61, 1 (1995).
[CrossRef]

D. W. Pohl, Thin Solid Films 264, 250 (1995).
[CrossRef]

1994 (1)

H. Heinzelmann and D. W. Pohl, Appl. Phys. A 59, 89 (1994).
[CrossRef]

1992 (2)

E. Betzig and J. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

P. Andreazza, D. Josse, and J. Zyss, Phys. Rev. B 45, 7640 (1992).
[CrossRef]

1984 (1)

J. Zyss, J. F. Nicoud, and M. Coquillay, J. Chem. Phys. 81, 4160 (1984).

1962 (1)

D. A. Kleimman, Phys. Rev. 126, 1977 (1962).
[CrossRef]

Andreazza, P.

P. Andreazza, D. Josse, and J. Zyss, Phys. Rev. B 45, 7640 (1992).
[CrossRef]

Betzig, E.

E. Betzig and J. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

Bomholt, L. H.

C. Hafner and L. H. Bomholt, The 3D Electrodynamic Wave Simulator (Wiley, New York, 1993).

Coquillay, M.

J. Zyss, J. F. Nicoud, and M. Coquillay, J. Chem. Phys. 81, 4160 (1984).

Davis, C. C.

I. I. Smolyaninov, A. V. Zayats, and C. C. Davis, Phys. Rev. B 56, 9290 (1997).
[CrossRef]

Gu, B.

Zh. Li, B. Gu, and G. Yang, Phys. Rev. B 59, 12622 (1999).
[CrossRef]

Hafner, C.

C. Hafner and L. H. Bomholt, The 3D Electrodynamic Wave Simulator (Wiley, New York, 1993).

Hecht, B.

D. W. Pohl, L. Novotny, B. Hecht, and H. Heinzelmann, Thin Solid Films 273, 161 (1996).
[CrossRef]

L. Novotny, D. W. Pohl, and B. Hecht, Ultramicroscopy 61, 1 (1995).
[CrossRef]

Heinzelmann, H.

D. W. Pohl, L. Novotny, B. Hecht, and H. Heinzelmann, Thin Solid Films 273, 161 (1996).
[CrossRef]

H. Heinzelmann and D. W. Pohl, Appl. Phys. A 59, 89 (1994).
[CrossRef]

Josse, D.

P. Andreazza, D. Josse, and J. Zyss, Phys. Rev. B 45, 7640 (1992).
[CrossRef]

Kleimman, D. A.

D. A. Kleimman, Phys. Rev. 126, 1977 (1962).
[CrossRef]

Li, Zh.

Zh. Li, B. Gu, and G. Yang, Phys. Rev. B 59, 12622 (1999).
[CrossRef]

McGilp, J. F.

J. F. McGilp, Prog. Surf. Sci. 49, 1 (1995).

Nicoud, J. F.

J. Zyss, J. F. Nicoud, and M. Coquillay, J. Chem. Phys. 81, 4160 (1984).

Novotny, L.

D. W. Pohl, L. Novotny, B. Hecht, and H. Heinzelmann, Thin Solid Films 273, 161 (1996).
[CrossRef]

L. Novotny, D. W. Pohl, and B. Hecht, Ultramicroscopy 61, 1 (1995).
[CrossRef]

L. Novotny, “Light propagation and light confinement in near-field optics,” Ph.D. dissertation (ETH, Zurich, 1996).

Pohl, D. W.

D. W. Pohl, L. Novotny, B. Hecht, and H. Heinzelmann, Thin Solid Films 273, 161 (1996).
[CrossRef]

L. Novotny, D. W. Pohl, and B. Hecht, Ultramicroscopy 61, 1 (1995).
[CrossRef]

D. W. Pohl, Thin Solid Films 264, 250 (1995).
[CrossRef]

H. Heinzelmann and D. W. Pohl, Appl. Phys. A 59, 89 (1994).
[CrossRef]

Smolyaninov, I. I.

I. I. Smolyaninov, A. V. Zayats, and C. C. Davis, Phys. Rev. B 56, 9290 (1997).
[CrossRef]

Trautman, J.

E. Betzig and J. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

Yang, G.

Zh. Li, B. Gu, and G. Yang, Phys. Rev. B 59, 12622 (1999).
[CrossRef]

Zayats, A. V.

I. I. Smolyaninov, A. V. Zayats, and C. C. Davis, Phys. Rev. B 56, 9290 (1997).
[CrossRef]

Zyss, J.

P. Andreazza, D. Josse, and J. Zyss, Phys. Rev. B 45, 7640 (1992).
[CrossRef]

J. Zyss, J. F. Nicoud, and M. Coquillay, J. Chem. Phys. 81, 4160 (1984).

Appl. Phys. A (1)

H. Heinzelmann and D. W. Pohl, Appl. Phys. A 59, 89 (1994).
[CrossRef]

J. Chem. Phys. (1)

J. Zyss, J. F. Nicoud, and M. Coquillay, J. Chem. Phys. 81, 4160 (1984).

Phys. Rev. (1)

D. A. Kleimman, Phys. Rev. 126, 1977 (1962).
[CrossRef]

Phys. Rev. B (3)

I. I. Smolyaninov, A. V. Zayats, and C. C. Davis, Phys. Rev. B 56, 9290 (1997).
[CrossRef]

P. Andreazza, D. Josse, and J. Zyss, Phys. Rev. B 45, 7640 (1992).
[CrossRef]

Zh. Li, B. Gu, and G. Yang, Phys. Rev. B 59, 12622 (1999).
[CrossRef]

Prog. Surf. Sci. (1)

J. F. McGilp, Prog. Surf. Sci. 49, 1 (1995).

Science (1)

E. Betzig and J. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

Thin Solid Films (2)

D. W. Pohl, L. Novotny, B. Hecht, and H. Heinzelmann, Thin Solid Films 273, 161 (1996).
[CrossRef]

D. W. Pohl, Thin Solid Films 264, 250 (1995).
[CrossRef]

Ultramicroscopy (1)

L. Novotny, D. W. Pohl, and B. Hecht, Ultramicroscopy 61, 1 (1995).
[CrossRef]

Other (2)

C. Hafner and L. H. Bomholt, The 3D Electrodynamic Wave Simulator (Wiley, New York, 1993).

L. Novotny, “Light propagation and light confinement in near-field optics,” Ph.D. dissertation (ETH, Zurich, 1996).

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Figures (4)

Fig. 1
Fig. 1

Three-dimensional view of the optical near-field intensities of (a) the FW and (b) the SHG. The calculations of the intensities are performed for p polarization and for d=10 nm.

Fig. 2
Fig. 2

Electric field intensities of (a) the FW and (b) the SHG along the x coordinate for y=0 at different d. Solid curves, field intensities of the allowed light; dashed curves, field intensities of the forbidden light.

Fig. 3
Fig. 3

Dependence of the SH near-field intensity on the polarization direction of the incident light. The calculation is performed for d=10 nm.

Fig. 4
Fig. 4

Effect of d on the near-field intensity of the SHG for (filled circles) p polarization of the total field, (open squares) allowed light, (open triangles) forbidden light, and (filled diamonds) s polarization of the total field.

Equations (7)

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

Esk=A0kexpikrexpikzd,
kz=k2-k21/2=k01-n12 sin2 θ1/2,
fir,ω0jAjifjr,ω0.
-××fjr,ω0+qj2fjr,ω0=0.
××Er,ωi-ωi2c2ωiEr,ωi=4πωi2c2P2r,ωi,  i=1,2,
Px2r,2ω0=2d21Exr,ω0Eyr,ω0,
Py2r,2ω0=d21Exr,ω02+d22Eyr,ω02,

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