Abstract

We show experimentally that in second-harmonic generation from a monolayer the radiation propagating in transmission and that in reflection can have very different magnitudes. The origin of this difference lies in destructive and constructive interference of the components of the nonlinear polarization that drive the field at the second-harmonic frequency.

© 1998 Optical Society of America

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References

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  1. G. A. Reider and T. F. Heinz, in Photonic Probes of Surfaces, P. Halevi, ed., Vol. 2 of Progress in Electromagnetics Research (North-Holland, Amsterdam, 1995), pp. 413–478.
    [CrossRef]
  2. R. W. J. Hollering and W. J. O. V. Teesselink, Opt. Commun. 79, 224 (1990).
    [CrossRef]
  3. M. Barmentlo, “Nonlinear optical studies on (liquid-) crystal surfaces,” Ph.D. dissertation (Leiden University, Leiden, The Netherlands, 1993).
  4. R. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).
  5. D. A. Kleinman, Phys. Rev. 126, 1977 (1962).
    [CrossRef]
  6. Y. R. Shen, Principles of Nonlinear Optics (Wiley, New York, 1984).
  7. P. Guyot-Sionnest and Y. R. Shen, Appl. Phys. B 42, 237 (1987).
    [CrossRef]
  8. C. S. Mullin, P. Guyot-Sionnest, and Y. R. Shen, Phys. Rev. A 39, 3745 (1989).
    [CrossRef] [PubMed]
  9. J. Y. Huang, R. Superfine, and Y. R. Shen, Phys. Rev. A 42, 3660 (1990).
    [CrossRef] [PubMed]
  10. N. Bloembergen and P. S. Pershan, Phys. Rev. 128, 606 (1962).
    [CrossRef]
  11. T. Dürr, R. Hildebrandt, G. Marowsky, and R. Stolle, Phys. Rev. A 56, 4139 (1997).
    [CrossRef]

1997 (1)

T. Dürr, R. Hildebrandt, G. Marowsky, and R. Stolle, Phys. Rev. A 56, 4139 (1997).
[CrossRef]

1990 (2)

J. Y. Huang, R. Superfine, and Y. R. Shen, Phys. Rev. A 42, 3660 (1990).
[CrossRef] [PubMed]

R. W. J. Hollering and W. J. O. V. Teesselink, Opt. Commun. 79, 224 (1990).
[CrossRef]

1989 (1)

C. S. Mullin, P. Guyot-Sionnest, and Y. R. Shen, Phys. Rev. A 39, 3745 (1989).
[CrossRef] [PubMed]

1987 (1)

P. Guyot-Sionnest and Y. R. Shen, Appl. Phys. B 42, 237 (1987).
[CrossRef]

1962 (2)

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

N. Bloembergen and P. S. Pershan, Phys. Rev. 128, 606 (1962).
[CrossRef]

Barmentlo, M.

M. Barmentlo, “Nonlinear optical studies on (liquid-) crystal surfaces,” Ph.D. dissertation (Leiden University, Leiden, The Netherlands, 1993).

Bloembergen, N.

N. Bloembergen and P. S. Pershan, Phys. Rev. 128, 606 (1962).
[CrossRef]

Boyd, R.

R. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).

Dürr, T.

T. Dürr, R. Hildebrandt, G. Marowsky, and R. Stolle, Phys. Rev. A 56, 4139 (1997).
[CrossRef]

Guyot-Sionnest, P.

C. S. Mullin, P. Guyot-Sionnest, and Y. R. Shen, Phys. Rev. A 39, 3745 (1989).
[CrossRef] [PubMed]

P. Guyot-Sionnest and Y. R. Shen, Appl. Phys. B 42, 237 (1987).
[CrossRef]

Heinz, T. F.

G. A. Reider and T. F. Heinz, in Photonic Probes of Surfaces, P. Halevi, ed., Vol. 2 of Progress in Electromagnetics Research (North-Holland, Amsterdam, 1995), pp. 413–478.
[CrossRef]

Hildebrandt, R.

T. Dürr, R. Hildebrandt, G. Marowsky, and R. Stolle, Phys. Rev. A 56, 4139 (1997).
[CrossRef]

Hollering, R. W. J.

R. W. J. Hollering and W. J. O. V. Teesselink, Opt. Commun. 79, 224 (1990).
[CrossRef]

Huang, J. Y.

J. Y. Huang, R. Superfine, and Y. R. Shen, Phys. Rev. A 42, 3660 (1990).
[CrossRef] [PubMed]

Kleinman, D. A.

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

Marowsky, G.

T. Dürr, R. Hildebrandt, G. Marowsky, and R. Stolle, Phys. Rev. A 56, 4139 (1997).
[CrossRef]

Mullin, C. S.

C. S. Mullin, P. Guyot-Sionnest, and Y. R. Shen, Phys. Rev. A 39, 3745 (1989).
[CrossRef] [PubMed]

Pershan, P. S.

N. Bloembergen and P. S. Pershan, Phys. Rev. 128, 606 (1962).
[CrossRef]

Reider, G. A.

G. A. Reider and T. F. Heinz, in Photonic Probes of Surfaces, P. Halevi, ed., Vol. 2 of Progress in Electromagnetics Research (North-Holland, Amsterdam, 1995), pp. 413–478.
[CrossRef]

Shen, Y. R.

J. Y. Huang, R. Superfine, and Y. R. Shen, Phys. Rev. A 42, 3660 (1990).
[CrossRef] [PubMed]

C. S. Mullin, P. Guyot-Sionnest, and Y. R. Shen, Phys. Rev. A 39, 3745 (1989).
[CrossRef] [PubMed]

P. Guyot-Sionnest and Y. R. Shen, Appl. Phys. B 42, 237 (1987).
[CrossRef]

Y. R. Shen, Principles of Nonlinear Optics (Wiley, New York, 1984).

Stolle, R.

T. Dürr, R. Hildebrandt, G. Marowsky, and R. Stolle, Phys. Rev. A 56, 4139 (1997).
[CrossRef]

Superfine, R.

J. Y. Huang, R. Superfine, and Y. R. Shen, Phys. Rev. A 42, 3660 (1990).
[CrossRef] [PubMed]

Teesselink, W. J. O. V.

R. W. J. Hollering and W. J. O. V. Teesselink, Opt. Commun. 79, 224 (1990).
[CrossRef]

Appl. Phys. B (1)

P. Guyot-Sionnest and Y. R. Shen, Appl. Phys. B 42, 237 (1987).
[CrossRef]

Opt. Commun. (1)

R. W. J. Hollering and W. J. O. V. Teesselink, Opt. Commun. 79, 224 (1990).
[CrossRef]

Phys. Rev. (2)

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

N. Bloembergen and P. S. Pershan, Phys. Rev. 128, 606 (1962).
[CrossRef]

Phys. Rev. A (3)

T. Dürr, R. Hildebrandt, G. Marowsky, and R. Stolle, Phys. Rev. A 56, 4139 (1997).
[CrossRef]

C. S. Mullin, P. Guyot-Sionnest, and Y. R. Shen, Phys. Rev. A 39, 3745 (1989).
[CrossRef] [PubMed]

J. Y. Huang, R. Superfine, and Y. R. Shen, Phys. Rev. A 42, 3660 (1990).
[CrossRef] [PubMed]

Other (4)

Y. R. Shen, Principles of Nonlinear Optics (Wiley, New York, 1984).

M. Barmentlo, “Nonlinear optical studies on (liquid-) crystal surfaces,” Ph.D. dissertation (Leiden University, Leiden, The Netherlands, 1993).

R. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).

G. A. Reider and T. F. Heinz, in Photonic Probes of Surfaces, P. Halevi, ed., Vol. 2 of Progress in Electromagnetics Research (North-Holland, Amsterdam, 1995), pp. 413–478.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Dependence of the intensity of the SH radiation on the angle of incidence of the radiation at the fundamental frequency when the latter is s polarized.

Fig. 2
Fig. 2

Dependence of the intensity of the SH radiation on the angle of incidence of the input field when the latter is p  polarized. The calculated (dashed) curves are scaled such that the optima coincide with those of the experimental data (solid curves). The inset shows the reflected signal on a different scale.

Fig. 3
Fig. 3

Wave vector of the input field kaω and the generated SH radiation in media a and b. Note that kza2ω and kzb2ω are of opposite sign. The inset shows the electric-field components of a p-polarized input field. Here Ex and Ez have opposite signs.

Fig. 4
Fig. 4

Microscopic picture of the SH radiation process for a p-polarized input field in an in-plane isotropic monolayer. The molecules, represented by arrows, are considered nonlinear dipoles. The radiation patterns of the nonlinear dipoles are indicated.

Equations (5)

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PiNL2ω=0j, kχijk22ω=ω+ωEjωEkω,
PzNL=0χzzzEzEz+χzxxExEx,
PxNL=0χxzxEzEz+χxxzExEz.
Epa=-ika0akzb-bkzakzbPxNL+bkxPzNL,
Epb=-ikb0akzb-bkzakzaPxNL+akxPzNL.

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