Abstract

We have considered the quadratic nonlinear radiation from a thin dipole sheet in front of a mirror. Radiation at the second-harmonic (SH) frequency on incidence of a fundamental field can be inhibited or enhanced independently of the SH field intensity stored between the nonlinear layer and the mirror. We have shown that this apparent contradiction can be fully understood only if the quadratic nonlinear interaction includes terms with a momentum mismatch equal to the magnitude of the SH field wave vector, such as the term that accounts for transfer of energy from the reflected SH field back to the incident fundamental.

© 2000 Optical Society of America

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  1. H. Morawitz, Phys. Rev. 187, 1792 (1969).
    [CrossRef]
  2. H. Drexhage, J. Lumin. 1–2, 693 (1970).
    [CrossRef]
  3. H. Khun, J. Chem. Phys. 53, 101 (1970).
  4. D. Kleppner, Phys. Rev. Lett. 47, 233 (1981).
    [CrossRef]
  5. R. G. Hulet, E. S. Hilfer, and D. Kleppner, Phys. Rev. Lett. 55, 2137 (1985).
    [CrossRef] [PubMed]
  6. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
    [CrossRef] [PubMed]
  7. J. Martorell and N. M. Lawandy, Phys. Rev. Lett. 65, 1877 (1990).
    [CrossRef] [PubMed]
  8. J. P. Dowling and C. M. Bowden, Phys. Rev. A 46, 612 (1992).
    [CrossRef] [PubMed]
  9. L.-A. Wu and H. J. Kimple, J. Opt. Soc. Am. B 2, 697 (1985).
    [CrossRef]
  10. J. Trull, R. Vilaseca, J. Martorell, and R. Corbalán, Opt. Lett. 20, 17 (1995).
    [CrossRef]
  11. M. Kauranen, Y. Van Rompaey, J. J. Maki, and A. Persoons, Phys. Rev. Lett. 20, 952 (1998).
    [CrossRef]
  12. J. Martorell, R. Vilaseca, and R. Corbalán, Opt. Commun. 144, 65 (1997).
    [CrossRef]

1998 (1)

M. Kauranen, Y. Van Rompaey, J. J. Maki, and A. Persoons, Phys. Rev. Lett. 20, 952 (1998).
[CrossRef]

1997 (1)

J. Martorell, R. Vilaseca, and R. Corbalán, Opt. Commun. 144, 65 (1997).
[CrossRef]

1995 (1)

J. Trull, R. Vilaseca, J. Martorell, and R. Corbalán, Opt. Lett. 20, 17 (1995).
[CrossRef]

1992 (1)

J. P. Dowling and C. M. Bowden, Phys. Rev. A 46, 612 (1992).
[CrossRef] [PubMed]

1990 (1)

J. Martorell and N. M. Lawandy, Phys. Rev. Lett. 65, 1877 (1990).
[CrossRef] [PubMed]

1987 (1)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

1985 (2)

R. G. Hulet, E. S. Hilfer, and D. Kleppner, Phys. Rev. Lett. 55, 2137 (1985).
[CrossRef] [PubMed]

L.-A. Wu and H. J. Kimple, J. Opt. Soc. Am. B 2, 697 (1985).
[CrossRef]

1981 (1)

D. Kleppner, Phys. Rev. Lett. 47, 233 (1981).
[CrossRef]

1970 (2)

H. Drexhage, J. Lumin. 1–2, 693 (1970).
[CrossRef]

H. Khun, J. Chem. Phys. 53, 101 (1970).

1969 (1)

H. Morawitz, Phys. Rev. 187, 1792 (1969).
[CrossRef]

Bowden, C. M.

J. P. Dowling and C. M. Bowden, Phys. Rev. A 46, 612 (1992).
[CrossRef] [PubMed]

Corbalán, R.

J. Martorell, R. Vilaseca, and R. Corbalán, Opt. Commun. 144, 65 (1997).
[CrossRef]

J. Trull, R. Vilaseca, J. Martorell, and R. Corbalán, Opt. Lett. 20, 17 (1995).
[CrossRef]

Dowling, J. P.

J. P. Dowling and C. M. Bowden, Phys. Rev. A 46, 612 (1992).
[CrossRef] [PubMed]

Drexhage, H.

H. Drexhage, J. Lumin. 1–2, 693 (1970).
[CrossRef]

Hilfer, E. S.

R. G. Hulet, E. S. Hilfer, and D. Kleppner, Phys. Rev. Lett. 55, 2137 (1985).
[CrossRef] [PubMed]

Hulet, R. G.

R. G. Hulet, E. S. Hilfer, and D. Kleppner, Phys. Rev. Lett. 55, 2137 (1985).
[CrossRef] [PubMed]

Kauranen, M.

M. Kauranen, Y. Van Rompaey, J. J. Maki, and A. Persoons, Phys. Rev. Lett. 20, 952 (1998).
[CrossRef]

Khun, H.

H. Khun, J. Chem. Phys. 53, 101 (1970).

Kimple, H. J.

Kleppner, D.

R. G. Hulet, E. S. Hilfer, and D. Kleppner, Phys. Rev. Lett. 55, 2137 (1985).
[CrossRef] [PubMed]

D. Kleppner, Phys. Rev. Lett. 47, 233 (1981).
[CrossRef]

Lawandy, N. M.

J. Martorell and N. M. Lawandy, Phys. Rev. Lett. 65, 1877 (1990).
[CrossRef] [PubMed]

Maki, J. J.

M. Kauranen, Y. Van Rompaey, J. J. Maki, and A. Persoons, Phys. Rev. Lett. 20, 952 (1998).
[CrossRef]

Martorell, J.

J. Martorell, R. Vilaseca, and R. Corbalán, Opt. Commun. 144, 65 (1997).
[CrossRef]

J. Trull, R. Vilaseca, J. Martorell, and R. Corbalán, Opt. Lett. 20, 17 (1995).
[CrossRef]

J. Martorell and N. M. Lawandy, Phys. Rev. Lett. 65, 1877 (1990).
[CrossRef] [PubMed]

Morawitz, H.

H. Morawitz, Phys. Rev. 187, 1792 (1969).
[CrossRef]

Persoons, A.

M. Kauranen, Y. Van Rompaey, J. J. Maki, and A. Persoons, Phys. Rev. Lett. 20, 952 (1998).
[CrossRef]

Trull, J.

J. Trull, R. Vilaseca, J. Martorell, and R. Corbalán, Opt. Lett. 20, 17 (1995).
[CrossRef]

Van Rompaey, Y.

M. Kauranen, Y. Van Rompaey, J. J. Maki, and A. Persoons, Phys. Rev. Lett. 20, 952 (1998).
[CrossRef]

Vilaseca, R.

J. Martorell, R. Vilaseca, and R. Corbalán, Opt. Commun. 144, 65 (1997).
[CrossRef]

J. Trull, R. Vilaseca, J. Martorell, and R. Corbalán, Opt. Lett. 20, 17 (1995).
[CrossRef]

Wu, L.-A.

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

J. Chem. Phys. (1)

H. Khun, J. Chem. Phys. 53, 101 (1970).

J. Lumin. (1)

H. Drexhage, J. Lumin. 1–2, 693 (1970).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

J. Martorell, R. Vilaseca, and R. Corbalán, Opt. Commun. 144, 65 (1997).
[CrossRef]

Opt. Lett. (1)

J. Trull, R. Vilaseca, J. Martorell, and R. Corbalán, Opt. Lett. 20, 17 (1995).
[CrossRef]

Phys. Rev. (1)

H. Morawitz, Phys. Rev. 187, 1792 (1969).
[CrossRef]

Phys. Rev. A (1)

J. P. Dowling and C. M. Bowden, Phys. Rev. A 46, 612 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (5)

M. Kauranen, Y. Van Rompaey, J. J. Maki, and A. Persoons, Phys. Rev. Lett. 20, 952 (1998).
[CrossRef]

D. Kleppner, Phys. Rev. Lett. 47, 233 (1981).
[CrossRef]

R. G. Hulet, E. S. Hilfer, and D. Kleppner, Phys. Rev. Lett. 55, 2137 (1985).
[CrossRef] [PubMed]

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

J. Martorell and N. M. Lawandy, Phys. Rev. Lett. 65, 1877 (1990).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Thin layer of a nonlinear material adsorbed onto a substrate placed at a variable distance from a SH mirror.

Fig. 2
Fig. 2

SH field intensity radiated to the left outside the structure (solid curve), SH field intensity within the structure at a fixed position between the layer and the mirror (short-dashed curve), and difference between the total radiated FF—reflected and transmitted—and the incident FF intensities (dotted–dashed curve) as a function of distance of the mirror from the material–air interface. All three intensities are normalized to the SH radiation in free space, when no mirror is present (dotted line).

Fig. 3
Fig. 3

FF forward-transmitted intensity as a function of distance of the mirror from the material–air interface when all the interaction terms are included (solid curve), when only the contribution from the momentum-conserving terms is included (long-dashed curve), when only the contribution from the momentum-nonconserving terms is included (short-dashed curve), and when only the contribution of the term χ2E2-zE1+*z is included (dotted curve). We have subtracted the linear contribution to all four transmitted intensities. All four intensities are normalized to the SH radiation in free space.

Equations (3)

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

d2E1zdz2+ω2c2E1z=-ω2c2χ2E2zE1*z,
d2E2zdz2+2ω2c2E2z=-122ω2c2χ2E12z,
E1z=1/2E1+zexpik1z+E1-zexp-ik1z+c.c.,

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