Abstract

We present a method, based on noncollinear second-harmonic generation, to evaluate the nonzero elements of the nonlinear optical susceptibility. At a fixed incidence angle, the generated signal is investigated by varying the polarization state of both fundamental beams. The resulting polarization charts allows us to verify if Kleinman’s symmetry rules can be applied to a given material or to retrieve the absolute value of the nonlinear optical tensor terms, from a reference measurement. Experimental measurements obtained from gallium nitride layers are reported. The proposed method does not require an angular scan and thus is useful when the generated signal is strongly affected by sample rotation.

© 2009 Optical Society of America

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  1. R. E. Muenchausen, R. A. Keller, and N. S. Nogar, J. Opt. Soc. Am. B 4, 237 (1987).
    [CrossRef]
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    [CrossRef]
  3. D. Faccio, V. Pruneri, and P. G. Kazansky, Opt. Lett. 25, 1376 (2000).
    [CrossRef]
  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] [PubMed]
  5. S. Cattaneo and M. Kauranen, Phys. Rev. B 72, 033412 (2005).
    [CrossRef]
  6. S. Cattaneo and M. Kauranen, Opt. Lett. 28, 1445 (2003).
    [CrossRef] [PubMed]
  7. S. Cattaneo, E. Vuorimaa, H. Lemmetyinen, and M. Kauranen, J. Chem. Phys. 120, 9245 (2004).
    [CrossRef] [PubMed]
  8. M. C. Larciprete, M. Centini, A. Belardini, L. Sciscione, M. Bertolotti, C. Sibilia, M. Scalora, A. Passaseo, and B. Potì, Appl. Phys. Lett. 89, 131105 (2006).
    [CrossRef]
  9. J. Miragliotta, D. K. Wickenden, T. J. Kistenmacher, and W. A Bryden, J. Opt. Soc. Am. B 10, 1447 (1993).
    [CrossRef]
  10. N. A. Sanford, A. V. Davydov, D. V. Tsvetkov, A. V. Dmitriev, S. Keller, U. K. Mishra, S. P. DenBaars, S. S. Park, J. Y. Han, and R. J. Molnar, J. Appl. Phys. 97, 053512 (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. B. F. Levine, Phys. Rev. B 55, 13630 (1997).
    [CrossRef]
  15. P. A. Franken and J. F. Ward, Rev. Mod. Phys. 35, 23 (1963).
    [CrossRef]

2006 (1)

M. C. Larciprete, M. Centini, A. Belardini, L. Sciscione, M. Bertolotti, C. Sibilia, M. Scalora, A. Passaseo, and B. Potì, Appl. Phys. Lett. 89, 131105 (2006).
[CrossRef]

2005 (3)

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] [PubMed]

S. Cattaneo and M. Kauranen, Phys. Rev. B 72, 033412 (2005).
[CrossRef]

N. A. Sanford, A. V. Davydov, D. V. Tsvetkov, A. V. Dmitriev, S. Keller, U. K. Mishra, S. P. DenBaars, S. S. Park, J. Y. Han, and R. J. Molnar, J. Appl. Phys. 97, 053512 (2005).
[CrossRef]

2004 (1)

S. Cattaneo, E. Vuorimaa, H. Lemmetyinen, and M. Kauranen, J. Chem. Phys. 120, 9245 (2004).
[CrossRef] [PubMed]

2003 (1)

2000 (1)

1997 (1)

B. F. Levine, Phys. Rev. B 55, 13630 (1997).
[CrossRef]

1995 (1)

J. Chen, Z. H. Levine, and J. W. Wilkins, Appl. Phys. Lett. 66, 1129 (1995).
[CrossRef]

1993 (2)

J. Miragliotta, D. K. Wickenden, T. J. Kistenmacher, and W. A Bryden, J. Opt. Soc. Am. B 10, 1447 (1993).
[CrossRef]

P. Provencher, C. Y. Côté, and M. M. Denariez-Roberge, Can. J. Phys. 71, 66 (1993).
[CrossRef]

1987 (1)

1970 (1)

J. Jerphagnon and S. K. Kurtz, J. Appl. Phys. 41, 1667 (1970).
[CrossRef]

1963 (1)

P. A. Franken and J. F. Ward, Rev. Mod. Phys. 35, 23 (1963).
[CrossRef]

Belardini, A.

M. C. Larciprete, M. Centini, A. Belardini, L. Sciscione, M. Bertolotti, C. Sibilia, M. Scalora, A. Passaseo, and B. Potì, Appl. Phys. Lett. 89, 131105 (2006).
[CrossRef]

Bertolotti, M.

M. C. Larciprete, M. Centini, A. Belardini, L. Sciscione, M. Bertolotti, C. Sibilia, M. Scalora, A. Passaseo, and B. Potì, Appl. Phys. Lett. 89, 131105 (2006).
[CrossRef]

Bryden, W. A

Cattaneo, S.

S. Cattaneo and M. Kauranen, Phys. Rev. B 72, 033412 (2005).
[CrossRef]

S. Cattaneo, E. Vuorimaa, H. Lemmetyinen, and M. Kauranen, J. Chem. Phys. 120, 9245 (2004).
[CrossRef] [PubMed]

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

Centini, M.

M. C. Larciprete, M. Centini, A. Belardini, L. Sciscione, M. Bertolotti, C. Sibilia, M. Scalora, A. Passaseo, and B. Potì, Appl. Phys. Lett. 89, 131105 (2006).
[CrossRef]

Chen, J.

J. Chen, Z. H. Levine, and J. W. Wilkins, Appl. Phys. Lett. 66, 1129 (1995).
[CrossRef]

Côté, C. Y.

P. Provencher, C. Y. Côté, and M. M. Denariez-Roberge, Can. J. Phys. 71, 66 (1993).
[CrossRef]

Davydov, A. V.

N. A. Sanford, A. V. Davydov, D. V. Tsvetkov, A. V. Dmitriev, S. Keller, U. K. Mishra, S. P. DenBaars, S. S. Park, J. Y. Han, and R. J. Molnar, J. Appl. Phys. 97, 053512 (2005).
[CrossRef]

Denariez-Roberge, M. M.

P. Provencher, C. Y. Côté, and M. M. Denariez-Roberge, Can. J. Phys. 71, 66 (1993).
[CrossRef]

DenBaars, S. P.

N. A. Sanford, A. V. Davydov, D. V. Tsvetkov, A. V. Dmitriev, S. Keller, U. K. Mishra, S. P. DenBaars, S. S. Park, J. Y. Han, and R. J. Molnar, J. Appl. Phys. 97, 053512 (2005).
[CrossRef]

Dmitriev, A. V.

N. A. Sanford, A. V. Davydov, D. V. Tsvetkov, A. V. Dmitriev, S. Keller, U. K. Mishra, S. P. DenBaars, S. S. Park, J. Y. Han, and R. J. Molnar, J. Appl. Phys. 97, 053512 (2005).
[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] [PubMed]

Faccio, D.

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] [PubMed]

Franken, P. A.

P. A. Franken and J. F. Ward, Rev. Mod. Phys. 35, 23 (1963).
[CrossRef]

Han, J. Y.

N. A. Sanford, A. V. Davydov, D. V. Tsvetkov, A. V. Dmitriev, S. Keller, U. K. Mishra, S. P. DenBaars, S. S. Park, J. Y. Han, and R. J. Molnar, J. Appl. Phys. 97, 053512 (2005).
[CrossRef]

Jerphagnon, J.

J. Jerphagnon and S. K. Kurtz, J. Appl. Phys. 41, 1667 (1970).
[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] [PubMed]

Kauranen, M.

S. Cattaneo and M. Kauranen, Phys. Rev. B 72, 033412 (2005).
[CrossRef]

S. Cattaneo, E. Vuorimaa, H. Lemmetyinen, and M. Kauranen, J. Chem. Phys. 120, 9245 (2004).
[CrossRef] [PubMed]

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

Kazansky, P. G.

Keller, R. A.

Keller, S.

N. A. Sanford, A. V. Davydov, D. V. Tsvetkov, A. V. Dmitriev, S. Keller, U. K. Mishra, S. P. DenBaars, S. S. Park, J. Y. Han, and R. J. Molnar, J. Appl. Phys. 97, 053512 (2005).
[CrossRef]

Kistenmacher, T. J.

Kurtz, S. K.

J. Jerphagnon and S. K. Kurtz, J. Appl. Phys. 41, 1667 (1970).
[CrossRef]

Larciprete, M. C.

M. C. Larciprete, M. Centini, A. Belardini, L. Sciscione, M. Bertolotti, C. Sibilia, M. Scalora, A. Passaseo, and B. Potì, Appl. Phys. Lett. 89, 131105 (2006).
[CrossRef]

Lemmetyinen, H.

S. Cattaneo, E. Vuorimaa, H. Lemmetyinen, and M. Kauranen, J. Chem. Phys. 120, 9245 (2004).
[CrossRef] [PubMed]

Levine, B. F.

B. F. Levine, Phys. Rev. B 55, 13630 (1997).
[CrossRef]

Levine, Z. H.

J. Chen, Z. H. Levine, and J. W. Wilkins, Appl. Phys. Lett. 66, 1129 (1995).
[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] [PubMed]

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] [PubMed]

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] [PubMed]

Miragliotta, J.

Mishra, U. K.

N. A. Sanford, A. V. Davydov, D. V. Tsvetkov, A. V. Dmitriev, S. Keller, U. K. Mishra, S. P. DenBaars, S. S. Park, J. Y. Han, and R. J. Molnar, J. Appl. Phys. 97, 053512 (2005).
[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] [PubMed]

Molnar, R. J.

N. A. Sanford, A. V. Davydov, D. V. Tsvetkov, A. V. Dmitriev, S. Keller, U. K. Mishra, S. P. DenBaars, S. S. Park, J. Y. Han, and R. J. Molnar, J. Appl. Phys. 97, 053512 (2005).
[CrossRef]

Muenchausen, R. E.

Nogar, N. S.

Park, S. S.

N. A. Sanford, A. V. Davydov, D. V. Tsvetkov, A. V. Dmitriev, S. Keller, U. K. Mishra, S. P. DenBaars, S. S. Park, J. Y. Han, and R. J. Molnar, J. Appl. Phys. 97, 053512 (2005).
[CrossRef]

Passaseo, A.

M. C. Larciprete, M. Centini, A. Belardini, L. Sciscione, M. Bertolotti, C. Sibilia, M. Scalora, A. Passaseo, and B. Potì, Appl. Phys. Lett. 89, 131105 (2006).
[CrossRef]

Potì, B.

M. C. Larciprete, M. Centini, A. Belardini, L. Sciscione, M. Bertolotti, C. Sibilia, M. Scalora, A. Passaseo, and B. Potì, Appl. Phys. Lett. 89, 131105 (2006).
[CrossRef]

Provencher, P.

P. Provencher, C. Y. Côté, and M. M. Denariez-Roberge, Can. J. Phys. 71, 66 (1993).
[CrossRef]

Pruneri, V.

Sanford, N. A.

N. A. Sanford, A. V. Davydov, D. V. Tsvetkov, A. V. Dmitriev, S. Keller, U. K. Mishra, S. P. DenBaars, S. S. Park, J. Y. Han, and R. J. Molnar, J. Appl. Phys. 97, 053512 (2005).
[CrossRef]

Scalora, M.

M. C. Larciprete, M. Centini, A. Belardini, L. Sciscione, M. Bertolotti, C. Sibilia, M. Scalora, A. Passaseo, and B. Potì, Appl. Phys. Lett. 89, 131105 (2006).
[CrossRef]

Sciscione, L.

M. C. Larciprete, M. Centini, A. Belardini, L. Sciscione, M. Bertolotti, C. Sibilia, M. Scalora, A. Passaseo, and B. Potì, Appl. Phys. Lett. 89, 131105 (2006).
[CrossRef]

Sibilia, C.

M. C. Larciprete, M. Centini, A. Belardini, L. Sciscione, M. Bertolotti, C. Sibilia, M. Scalora, A. Passaseo, and B. Potì, Appl. Phys. Lett. 89, 131105 (2006).
[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] [PubMed]

Tsvetkov, D. V.

N. A. Sanford, A. V. Davydov, D. V. Tsvetkov, A. V. Dmitriev, S. Keller, U. K. Mishra, S. P. DenBaars, S. S. Park, J. Y. Han, and R. J. Molnar, J. Appl. Phys. 97, 053512 (2005).
[CrossRef]

Vuorimaa, E.

S. Cattaneo, E. Vuorimaa, H. Lemmetyinen, and M. Kauranen, J. Chem. Phys. 120, 9245 (2004).
[CrossRef] [PubMed]

Ward, J. F.

P. A. Franken and J. F. Ward, Rev. Mod. Phys. 35, 23 (1963).
[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] [PubMed]

Wickenden, D. K.

Wilkins, J. W.

J. Chen, Z. H. Levine, and J. W. Wilkins, Appl. Phys. Lett. 66, 1129 (1995).
[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] [PubMed]

Yariv, A.

A. Yariv, Optical Electronics, 4th ed. (Saunders College Publishing, 1991).

Appl. Phys. Lett. (2)

M. C. Larciprete, M. Centini, A. Belardini, L. Sciscione, M. Bertolotti, C. Sibilia, M. Scalora, A. Passaseo, and B. Potì, Appl. Phys. Lett. 89, 131105 (2006).
[CrossRef]

J. Chen, Z. H. Levine, and J. W. Wilkins, Appl. Phys. Lett. 66, 1129 (1995).
[CrossRef]

Can. J. Phys. (1)

P. Provencher, C. Y. Côté, and M. M. Denariez-Roberge, Can. J. Phys. 71, 66 (1993).
[CrossRef]

J. Appl. Phys. (2)

N. A. Sanford, A. V. Davydov, D. V. Tsvetkov, A. V. Dmitriev, S. Keller, U. K. Mishra, S. P. DenBaars, S. S. Park, J. Y. Han, and R. J. Molnar, J. Appl. Phys. 97, 053512 (2005).
[CrossRef]

J. Jerphagnon and S. K. Kurtz, J. Appl. Phys. 41, 1667 (1970).
[CrossRef]

J. Chem. Phys. (1)

S. Cattaneo, E. Vuorimaa, H. Lemmetyinen, and M. Kauranen, J. Chem. Phys. 120, 9245 (2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B (2)

Opt. Lett. (2)

Phys. Rev. B (2)

S. Cattaneo and M. Kauranen, Phys. Rev. B 72, 033412 (2005).
[CrossRef]

B. F. Levine, Phys. Rev. B 55, 13630 (1997).
[CrossRef]

Phys. Rev. Lett. (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] [PubMed]

Rev. Mod. Phys. (1)

P. A. Franken and J. F. Ward, Rev. Mod. Phys. 35, 23 (1963).
[CrossRef]

Other (1)

A. Yariv, Optical Electronics, 4th ed. (Saunders College Publishing, 1991).

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Figures (3)

Fig. 1
Fig. 1

Details of the experimental geometry used for noncollinear SHG. For a given rotation angle α, the corresponding incidence angles of the two pump beams result to be α 1 = α β and α 2 = α γ . Black arrows indicate the crystalline axes.

Fig. 2
Fig. 2

Second-harmonic signal as a function of the polarization state of the first pump beam ( ϕ 1 ) and the second pump beam ( ϕ 2 ) , (a) experimentally measured and (b) theoretically calculated. Sample rotation angle was fixed to α = 35 ° . Polarization state of the analyzer is set to p ̑ , i.e., ϕ = 0 ° . The inset is a schematic representation of the polarization of pump beams at the absolute maxima, i.e., when both pump beams are p ̑ polarized.

Fig. 3
Fig. 3

Second-harmonic signal as a function of the polarization state of the first pump beam ( ϕ 1 ) and the second pump beam ( ϕ 2 ) , (a) experimentally measured and (b) theoretically calculated. Sample rotation angle was fixed to α = 35 ° . Polarization state of the analyzer is set to s ̑ , i.e., ϕ = 90 ° . The inset shows the polarization of pump beams at the absolute maxima, i.e., when the first pump is s ̑ polarized and the second pump is p ̑ polarized.

Equations (2)

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

d eff S = d 15 [ sin ( ϕ 1 ) cos ( ϕ 2 ) sin ( α 2 ) + cos ( ϕ 1 ) sin ( ϕ 2 ) sin ( α 1 ) ]
d eff P = d 24 cos ( α 3 ) [ cos ( α 1 ) sin ( α 2 ) + sin ( α 1 ) cos ( α 2 ) ] cos ( ϕ 1 ) cos ( ϕ 2 ) sin ( α 3 ) { d 31 sin ( ϕ 1 ) sin ( ϕ 2 ) + cos ( ϕ 1 ) cos ( ϕ 2 ) [ d 32 cos ( α 1 ) cos ( α 2 ) + d 33 sin ( α 1 ) sin ( α 2 ) ] } ,

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