Abstract

We demonstrate an experimental technique for isolating and enhancing quadrupolar second-harmonic generation in isotropic materials by using two orthogonally polarized laser beams that create wavelength-scale, forward-radiating gradients in the second-harmonic polarization.

© 2005 Optical Society of America

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References

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  1. J. E. Sipe, D. J. Moss, and H. M. van Driel, Phys. Rev. B 35, 1129 (1987).
    [CrossRef]
  2. H. Held, A. I. Lvovsky, X. Wei, and Y. R. Shen, Phys. Rev. B 66, 205110 (2002).
    [CrossRef]
  3. P. Guyot-Sionnest, W. Chen, and Y. R. Shen, Phys. Rev. B 33, 8254 (1986).
    [CrossRef]
  4. J. E. Sipe, V. Mizrahi, and G. I. Stegeman, Phys. Rev. B 35, 9091 (1987).
    [CrossRef]
  5. J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, Phys. Rev. Lett. 83, 4045 (1999).
    [CrossRef]
  6. W. L. Mochán, J. A. Maytorena, B. S. Mendoza, and V. L. Brudny, Phys. Rev. B 68, 085318 (2003).
    [CrossRef]
  7. V. L. Brudny, B. S. Mendoza, and W. L. Mochán, Phys. Rev. B 62, 11152 (2000).
    [CrossRef]
  8. P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, Phys. Rev. Lett. 94, 047401 (2005).
    [CrossRef]
  9. S. Bergfeld and W. Daum, Phys. Rev. Lett. 90, 036801 (2003).
    [CrossRef]
  10. Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, Appl. Phys. Lett. 70, 922 (1997).
    [CrossRef]
  11. D. S. Bethune, R. W. Smith, and Y. R. Shen, Phys. Rev. Lett. 37, 431 (1976).
    [CrossRef]
  12. S. Cattaneo and M. Kauranen, Opt. Lett. 28, 1445 (2003).
    [CrossRef] [PubMed]
  13. S. Cattaneo and M. Kauranen, “Polarization-based identification of bulk contributions in surface nonlinear optics,” Phys. Rev. B (to be published).
  14. S. Cattaneo, Ph.D. dissertation “Two-beam surface second-harmonic generation” (Tampere University of Technology, Tampere, Finland, 2004).
  15. S. Cattaneo, M. Siltanen, F. X. Wang, and M. Kauranen are working on a paper titled “Suppression of nonlinear optical signals in finite interaction volumes of bulk materials.”

2005 (1)

P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, Phys. Rev. Lett. 94, 047401 (2005).
[CrossRef]

2003 (3)

S. Bergfeld and W. Daum, Phys. Rev. Lett. 90, 036801 (2003).
[CrossRef]

W. L. Mochán, J. A. Maytorena, B. S. Mendoza, and V. L. Brudny, Phys. Rev. B 68, 085318 (2003).
[CrossRef]

S. Cattaneo and M. Kauranen, Opt. Lett. 28, 1445 (2003).
[CrossRef] [PubMed]

2002 (1)

H. Held, A. I. Lvovsky, X. Wei, and Y. R. Shen, Phys. Rev. B 66, 205110 (2002).
[CrossRef]

2000 (1)

V. L. Brudny, B. S. Mendoza, and W. L. Mochán, Phys. Rev. B 62, 11152 (2000).
[CrossRef]

1999 (1)

J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, Phys. Rev. Lett. 83, 4045 (1999).
[CrossRef]

1997 (1)

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, Appl. Phys. Lett. 70, 922 (1997).
[CrossRef]

1987 (2)

J. E. Sipe, D. J. Moss, and H. M. van Driel, Phys. Rev. B 35, 1129 (1987).
[CrossRef]

J. E. Sipe, V. Mizrahi, and G. I. Stegeman, Phys. Rev. B 35, 9091 (1987).
[CrossRef]

1986 (1)

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, Phys. Rev. B 33, 8254 (1986).
[CrossRef]

1976 (1)

D. S. Bethune, R. W. Smith, and Y. R. Shen, Phys. Rev. Lett. 37, 431 (1976).
[CrossRef]

Barad, Y.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, Appl. Phys. Lett. 70, 922 (1997).
[CrossRef]

Bergfeld, S.

S. Bergfeld and W. Daum, Phys. Rev. Lett. 90, 036801 (2003).
[CrossRef]

Bethune, D. S.

D. S. Bethune, R. W. Smith, and Y. R. Shen, Phys. Rev. Lett. 37, 431 (1976).
[CrossRef]

Brudny, V. L.

W. L. Mochán, J. A. Maytorena, B. S. Mendoza, and V. L. Brudny, Phys. Rev. B 68, 085318 (2003).
[CrossRef]

V. L. Brudny, B. S. Mendoza, and W. L. Mochán, Phys. Rev. B 62, 11152 (2000).
[CrossRef]

Cattaneo, S.

S. Cattaneo and M. Kauranen, Opt. Lett. 28, 1445 (2003).
[CrossRef] [PubMed]

S. Cattaneo, Ph.D. dissertation “Two-beam surface second-harmonic generation” (Tampere University of Technology, Tampere, Finland, 2004).

S. Cattaneo, M. Siltanen, F. X. Wang, and M. Kauranen are working on a paper titled “Suppression of nonlinear optical signals in finite interaction volumes of bulk materials.”

S. Cattaneo and M. Kauranen, “Polarization-based identification of bulk contributions in surface nonlinear optics,” Phys. Rev. B (to be published).

Chen, W.

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, Phys. Rev. B 33, 8254 (1986).
[CrossRef]

Dadap, J. I.

J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, Phys. Rev. Lett. 83, 4045 (1999).
[CrossRef]

Daum, W.

S. Bergfeld and W. Daum, Phys. Rev. Lett. 90, 036801 (2003).
[CrossRef]

Downer, M. C.

P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, Phys. Rev. Lett. 94, 047401 (2005).
[CrossRef]

Eisenberg, H.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, Appl. Phys. Lett. 70, 922 (1997).
[CrossRef]

Eisenthal, K. B.

J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, Phys. Rev. Lett. 83, 4045 (1999).
[CrossRef]

Figliozzi, P.

P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, Phys. Rev. Lett. 94, 047401 (2005).
[CrossRef]

Guyot-Sionnest, P.

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, Phys. Rev. B 33, 8254 (1986).
[CrossRef]

Heinz, T. F.

J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, Phys. Rev. Lett. 83, 4045 (1999).
[CrossRef]

Held, H.

H. Held, A. I. Lvovsky, X. Wei, and Y. R. Shen, Phys. Rev. B 66, 205110 (2002).
[CrossRef]

Horowitz, M.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, Appl. Phys. Lett. 70, 922 (1997).
[CrossRef]

Jiang, Y.

P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, Phys. Rev. Lett. 94, 047401 (2005).
[CrossRef]

Kauranen, M.

S. Cattaneo and M. Kauranen, Opt. Lett. 28, 1445 (2003).
[CrossRef] [PubMed]

S. Cattaneo and M. Kauranen, “Polarization-based identification of bulk contributions in surface nonlinear optics,” Phys. Rev. B (to be published).

S. Cattaneo, M. Siltanen, F. X. Wang, and M. Kauranen are working on a paper titled “Suppression of nonlinear optical signals in finite interaction volumes of bulk materials.”

Lvovsky, A. I.

H. Held, A. I. Lvovsky, X. Wei, and Y. R. Shen, Phys. Rev. B 66, 205110 (2002).
[CrossRef]

Matlis, N.

P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, Phys. Rev. Lett. 94, 047401 (2005).
[CrossRef]

Mattern, B.

P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, Phys. Rev. Lett. 94, 047401 (2005).
[CrossRef]

Maytorena, J. A.

W. L. Mochán, J. A. Maytorena, B. S. Mendoza, and V. L. Brudny, Phys. Rev. B 68, 085318 (2003).
[CrossRef]

Mendoza, B. S.

P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, Phys. Rev. Lett. 94, 047401 (2005).
[CrossRef]

W. L. Mochán, J. A. Maytorena, B. S. Mendoza, and V. L. Brudny, Phys. Rev. B 68, 085318 (2003).
[CrossRef]

V. L. Brudny, B. S. Mendoza, and W. L. Mochán, Phys. Rev. B 62, 11152 (2000).
[CrossRef]

Mizrahi, V.

J. E. Sipe, V. Mizrahi, and G. I. Stegeman, Phys. Rev. B 35, 9091 (1987).
[CrossRef]

Mochán, W. L.

P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, Phys. Rev. Lett. 94, 047401 (2005).
[CrossRef]

W. L. Mochán, J. A. Maytorena, B. S. Mendoza, and V. L. Brudny, Phys. Rev. B 68, 085318 (2003).
[CrossRef]

V. L. Brudny, B. S. Mendoza, and W. L. Mochán, Phys. Rev. B 62, 11152 (2000).
[CrossRef]

Moss, D. J.

J. E. Sipe, D. J. Moss, and H. M. van Driel, Phys. Rev. B 35, 1129 (1987).
[CrossRef]

Shan, J.

J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, Phys. Rev. Lett. 83, 4045 (1999).
[CrossRef]

Shen, Y. R.

H. Held, A. I. Lvovsky, X. Wei, and Y. R. Shen, Phys. Rev. B 66, 205110 (2002).
[CrossRef]

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, Phys. Rev. B 33, 8254 (1986).
[CrossRef]

D. S. Bethune, R. W. Smith, and Y. R. Shen, Phys. Rev. Lett. 37, 431 (1976).
[CrossRef]

Silberberg, Y.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, Appl. Phys. Lett. 70, 922 (1997).
[CrossRef]

Siltanen, M.

S. Cattaneo, M. Siltanen, F. X. Wang, and M. Kauranen are working on a paper titled “Suppression of nonlinear optical signals in finite interaction volumes of bulk materials.”

Sipe, J. E.

J. E. Sipe, V. Mizrahi, and G. I. Stegeman, Phys. Rev. B 35, 9091 (1987).
[CrossRef]

J. E. Sipe, D. J. Moss, and H. M. van Driel, Phys. Rev. B 35, 1129 (1987).
[CrossRef]

Smith, R. W.

D. S. Bethune, R. W. Smith, and Y. R. Shen, Phys. Rev. Lett. 37, 431 (1976).
[CrossRef]

Stegeman, G. I.

J. E. Sipe, V. Mizrahi, and G. I. Stegeman, Phys. Rev. B 35, 9091 (1987).
[CrossRef]

Sun, L.

P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, Phys. Rev. Lett. 94, 047401 (2005).
[CrossRef]

van Driel, H. M.

J. E. Sipe, D. J. Moss, and H. M. van Driel, Phys. Rev. B 35, 1129 (1987).
[CrossRef]

Wang, F. X.

S. Cattaneo, M. Siltanen, F. X. Wang, and M. Kauranen are working on a paper titled “Suppression of nonlinear optical signals in finite interaction volumes of bulk materials.”

Wei, X.

H. Held, A. I. Lvovsky, X. Wei, and Y. R. Shen, Phys. Rev. B 66, 205110 (2002).
[CrossRef]

White, C. W.

P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, Phys. Rev. Lett. 94, 047401 (2005).
[CrossRef]

Withrow, S. P.

P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, Phys. Rev. Lett. 94, 047401 (2005).
[CrossRef]

Appl. Phys. Lett. (1)

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, Appl. Phys. Lett. 70, 922 (1997).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (6)

J. E. Sipe, D. J. Moss, and H. M. van Driel, Phys. Rev. B 35, 1129 (1987).
[CrossRef]

H. Held, A. I. Lvovsky, X. Wei, and Y. R. Shen, Phys. Rev. B 66, 205110 (2002).
[CrossRef]

P. Guyot-Sionnest, W. Chen, and Y. R. Shen, Phys. Rev. B 33, 8254 (1986).
[CrossRef]

J. E. Sipe, V. Mizrahi, and G. I. Stegeman, Phys. Rev. B 35, 9091 (1987).
[CrossRef]

W. L. Mochán, J. A. Maytorena, B. S. Mendoza, and V. L. Brudny, Phys. Rev. B 68, 085318 (2003).
[CrossRef]

V. L. Brudny, B. S. Mendoza, and W. L. Mochán, Phys. Rev. B 62, 11152 (2000).
[CrossRef]

Phys. Rev. Lett. (4)

P. Figliozzi, L. Sun, Y. Jiang, N. Matlis, B. Mattern, M. C. Downer, S. P. Withrow, C. W. White, W. L. Mochán, and B. S. Mendoza, Phys. Rev. Lett. 94, 047401 (2005).
[CrossRef]

S. Bergfeld and W. Daum, Phys. Rev. Lett. 90, 036801 (2003).
[CrossRef]

J. I. Dadap, J. Shan, K. B. Eisenthal, and T. F. Heinz, Phys. Rev. Lett. 83, 4045 (1999).
[CrossRef]

D. S. Bethune, R. W. Smith, and Y. R. Shen, Phys. Rev. Lett. 37, 431 (1976).
[CrossRef]

Other (3)

S. Cattaneo and M. Kauranen, “Polarization-based identification of bulk contributions in surface nonlinear optics,” Phys. Rev. B (to be published).

S. Cattaneo, Ph.D. dissertation “Two-beam surface second-harmonic generation” (Tampere University of Technology, Tampere, Finland, 2004).

S. Cattaneo, M. Siltanen, F. X. Wang, and M. Kauranen are working on a paper titled “Suppression of nonlinear optical signals in finite interaction volumes of bulk materials.”

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Figures (3)

Fig. 1
Fig. 1

(a) Two-beam SHG with an unamplified laser as E 2 rotates from vertical ( y ̂ ) to horizontal (P polarized), with E 1 fixed along x ̂ . The SH radiation was completely y ̂ polarized. Dashed line, dark-count level Inset, two-beam SHG configuration. (b) Two-beam SHG signal for E 1 x ̂ and E 2 y ̂ observed through a polarization analyzer, showing a signal polarized along E 2 .

Fig. 2
Fig. 2

Two-beam SHG signal versus ellipticity of beam 1 polarization. Squares (dots) correspond to E 2 y ̂ ( E 2 P polarized). Curves are calculations based on Eq. (2).

Fig. 3
Fig. 3

Measured (solid squares) and calculated (solid curve) SHG intensity as the sample is scanned longitudinally through the two-beam overlap region of tightly focused unamplified beams. Dashed line, dark-count level. Inset, same measurement and calculation with loosely focused amplified beams.

Equations (3)

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

P Q ( 2 ) = ( δ β 2 γ ) ( E ) E + β E ( E ) .
P Q ( 2 ) = i ( δ β 2 γ ) { E 1 0 k 1 E 1 0 exp ( 2 i k 1 r ) + E 1 0 k 2 E 2 0 exp [ i ( k 1 + k 2 ) r ] + E 2 0 k 1 E 1 0 exp [ i ( k 1 + k 2 ) r ] + E 2 0 k 2 E 2 0 exp ( 2 i k 2 r ) } .
h 2 Z h 2 Z exp [ ( z tan α ) 2 w 1 2 + w 2 2 cos 2 α ] exp ( i Δ k z ) d z ,

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