Abstract

We present a scheme for the determination of the vector nature of an electric field by optical second-harmonic generation. We demonstrate the technique by mapping the two-dimensional electric-field vector of a biased transmission line structure on silicon with a spatial resolution of 10 µm.

© 1999 Optical Society of America

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  1. A. Nahata, T. F. Heinz, and J. A. Misewich, Appl. Phys. Lett. 69, 746 (1996).
    [CrossRef]
  2. C. Ohlhoff, C. Meyer, G. Lüpke, T. Löffler, T. Pfeifer, H. G. Roskos, and H. Kurz, Appl. Phys. Lett. 68, 1 (1996).
    [CrossRef]
  3. A. Nahata and T. F. Heinz, Opt. Lett. 23, 67 (1998).
    [CrossRef]
  4. D. H. Auston, in Ultrashort Laser Pulses:?Generation and Applications, 2nd ed., W. Kaiser, ed. (Springer-Verlag, Berlin, 1993), pp. 183 and 445.
  5. C. H. Lee, R. K. Chang, and N. Bloembergen, Phys. Rev. Lett. 18, 167 (1967); O. A. Aktsipetrov, A. A. Fedyanin, V. N. Golovkina, and T. V. Murzina, Opt. Lett. 19, 1450 (1994); J. I. Dadap, X. F. Hu, M. H. Anderson, M. C. Downer, J. K. Lowell, and O. A. Aktsipetrov, Phys. Rev. B 53, R7607 (1996); J. Bloch, J. G. Mihaychuk, and H. M. van Driel, Phys. Rev. Lett. 77, 920 (1996); P. Godefroy, W. de Jong, C. W. van Hasselt, M. A. C. Devillers, and Th. Rasing, Appl. Phys. Lett. 68, 1982 (1996).
    [CrossRef] [PubMed]
  6. G. L. Richmond, J. M. Robinson, and V. L. Shannon, Prog. Surf. Sci. 28, 1 (1988); R. M. Corn and D. A. Higgins, Chem. Rev. 94, 107 (1994); K. B. Eisenthal, Chem. Rev. 96, 1343 (1996).
    [CrossRef] [PubMed]
  7. T. F. Heinz, in Nonlinear Surface Electromagnetic Phenomena, H.-E. Ponath and G. I. Stegeman, eds. (North-Holland, Amsterdam, 1991), p. 353; G. A. Reider and T. F. Heinz, in Photonic Probes of Surfaces, P. Halevi, ed. (Elsevier, Amsterdam, 1995), p. 413.
  8. Y. Uesu, S. Kurimura, and Y. Yamamoto, Appl. Phys. Lett. 66, 2165 (1995); V. Kirilyuk, A. Kirilyuk, and Th. Rasing, Appl. Phys. Lett. 70, 2306 (1997).
    [CrossRef]
  9. T. Itatani, T. Nakagawa, F. Kano, K. Ohta, and Y. Sugiyama, IEICE Trans. Electron. E78-C, 73 (1995).
  10. R. Stolle, G. Marowsky, E. Schwarzberg, and G. Berkovic, Appl. Phys. B 63, 491 (1996), and references therein; P. Wilson, Y. Jiang, O. A. Aktsipetrov, E. D. Mishina, and M. C. Downer, Opt. Lett. 24, 496 (1999).
    [CrossRef]
  11. J. I. Dadap, J. Shan, A. S. Weling, J. A. Misewich, and T. F. Heinz, Appl. Phys. B 68, 333 (1999).
    [CrossRef]
  12. J. I. Dadap, P. T. Wilson, M. H. Anderson, M. C. Downer, and M. ter Beek, Opt. Lett. 22, 901 (1997).
    [CrossRef] [PubMed]

1999 (1)

J. I. Dadap, J. Shan, A. S. Weling, J. A. Misewich, and T. F. Heinz, Appl. Phys. B 68, 333 (1999).
[CrossRef]

1998 (1)

1997 (1)

1996 (3)

R. Stolle, G. Marowsky, E. Schwarzberg, and G. Berkovic, Appl. Phys. B 63, 491 (1996), and references therein; P. Wilson, Y. Jiang, O. A. Aktsipetrov, E. D. Mishina, and M. C. Downer, Opt. Lett. 24, 496 (1999).
[CrossRef]

A. Nahata, T. F. Heinz, and J. A. Misewich, Appl. Phys. Lett. 69, 746 (1996).
[CrossRef]

C. Ohlhoff, C. Meyer, G. Lüpke, T. Löffler, T. Pfeifer, H. G. Roskos, and H. Kurz, Appl. Phys. Lett. 68, 1 (1996).
[CrossRef]

1995 (2)

Y. Uesu, S. Kurimura, and Y. Yamamoto, Appl. Phys. Lett. 66, 2165 (1995); V. Kirilyuk, A. Kirilyuk, and Th. Rasing, Appl. Phys. Lett. 70, 2306 (1997).
[CrossRef]

T. Itatani, T. Nakagawa, F. Kano, K. Ohta, and Y. Sugiyama, IEICE Trans. Electron. E78-C, 73 (1995).

1988 (1)

G. L. Richmond, J. M. Robinson, and V. L. Shannon, Prog. Surf. Sci. 28, 1 (1988); R. M. Corn and D. A. Higgins, Chem. Rev. 94, 107 (1994); K. B. Eisenthal, Chem. Rev. 96, 1343 (1996).
[CrossRef] [PubMed]

1967 (1)

C. H. Lee, R. K. Chang, and N. Bloembergen, Phys. Rev. Lett. 18, 167 (1967); O. A. Aktsipetrov, A. A. Fedyanin, V. N. Golovkina, and T. V. Murzina, Opt. Lett. 19, 1450 (1994); J. I. Dadap, X. F. Hu, M. H. Anderson, M. C. Downer, J. K. Lowell, and O. A. Aktsipetrov, Phys. Rev. B 53, R7607 (1996); J. Bloch, J. G. Mihaychuk, and H. M. van Driel, Phys. Rev. Lett. 77, 920 (1996); P. Godefroy, W. de Jong, C. W. van Hasselt, M. A. C. Devillers, and Th. Rasing, Appl. Phys. Lett. 68, 1982 (1996).
[CrossRef] [PubMed]

Anderson, M. H.

Auston, D. H.

D. H. Auston, in Ultrashort Laser Pulses:?Generation and Applications, 2nd ed., W. Kaiser, ed. (Springer-Verlag, Berlin, 1993), pp. 183 and 445.

Berkovic, G.

R. Stolle, G. Marowsky, E. Schwarzberg, and G. Berkovic, Appl. Phys. B 63, 491 (1996), and references therein; P. Wilson, Y. Jiang, O. A. Aktsipetrov, E. D. Mishina, and M. C. Downer, Opt. Lett. 24, 496 (1999).
[CrossRef]

Bloembergen, N.

C. H. Lee, R. K. Chang, and N. Bloembergen, Phys. Rev. Lett. 18, 167 (1967); O. A. Aktsipetrov, A. A. Fedyanin, V. N. Golovkina, and T. V. Murzina, Opt. Lett. 19, 1450 (1994); J. I. Dadap, X. F. Hu, M. H. Anderson, M. C. Downer, J. K. Lowell, and O. A. Aktsipetrov, Phys. Rev. B 53, R7607 (1996); J. Bloch, J. G. Mihaychuk, and H. M. van Driel, Phys. Rev. Lett. 77, 920 (1996); P. Godefroy, W. de Jong, C. W. van Hasselt, M. A. C. Devillers, and Th. Rasing, Appl. Phys. Lett. 68, 1982 (1996).
[CrossRef] [PubMed]

Chang, R. K.

C. H. Lee, R. K. Chang, and N. Bloembergen, Phys. Rev. Lett. 18, 167 (1967); O. A. Aktsipetrov, A. A. Fedyanin, V. N. Golovkina, and T. V. Murzina, Opt. Lett. 19, 1450 (1994); J. I. Dadap, X. F. Hu, M. H. Anderson, M. C. Downer, J. K. Lowell, and O. A. Aktsipetrov, Phys. Rev. B 53, R7607 (1996); J. Bloch, J. G. Mihaychuk, and H. M. van Driel, Phys. Rev. Lett. 77, 920 (1996); P. Godefroy, W. de Jong, C. W. van Hasselt, M. A. C. Devillers, and Th. Rasing, Appl. Phys. Lett. 68, 1982 (1996).
[CrossRef] [PubMed]

Dadap, J. I.

J. I. Dadap, J. Shan, A. S. Weling, J. A. Misewich, and T. F. Heinz, Appl. Phys. B 68, 333 (1999).
[CrossRef]

J. I. Dadap, P. T. Wilson, M. H. Anderson, M. C. Downer, and M. ter Beek, Opt. Lett. 22, 901 (1997).
[CrossRef] [PubMed]

Downer, M. C.

Heinz, T. F.

J. I. Dadap, J. Shan, A. S. Weling, J. A. Misewich, and T. F. Heinz, Appl. Phys. B 68, 333 (1999).
[CrossRef]

A. Nahata and T. F. Heinz, Opt. Lett. 23, 67 (1998).
[CrossRef]

A. Nahata, T. F. Heinz, and J. A. Misewich, Appl. Phys. Lett. 69, 746 (1996).
[CrossRef]

T. F. Heinz, in Nonlinear Surface Electromagnetic Phenomena, H.-E. Ponath and G. I. Stegeman, eds. (North-Holland, Amsterdam, 1991), p. 353; G. A. Reider and T. F. Heinz, in Photonic Probes of Surfaces, P. Halevi, ed. (Elsevier, Amsterdam, 1995), p. 413.

Itatani, T.

T. Itatani, T. Nakagawa, F. Kano, K. Ohta, and Y. Sugiyama, IEICE Trans. Electron. E78-C, 73 (1995).

Kano, F.

T. Itatani, T. Nakagawa, F. Kano, K. Ohta, and Y. Sugiyama, IEICE Trans. Electron. E78-C, 73 (1995).

Kurimura, S.

Y. Uesu, S. Kurimura, and Y. Yamamoto, Appl. Phys. Lett. 66, 2165 (1995); V. Kirilyuk, A. Kirilyuk, and Th. Rasing, Appl. Phys. Lett. 70, 2306 (1997).
[CrossRef]

Kurz, H.

C. Ohlhoff, C. Meyer, G. Lüpke, T. Löffler, T. Pfeifer, H. G. Roskos, and H. Kurz, Appl. Phys. Lett. 68, 1 (1996).
[CrossRef]

Lee, C. H.

C. H. Lee, R. K. Chang, and N. Bloembergen, Phys. Rev. Lett. 18, 167 (1967); O. A. Aktsipetrov, A. A. Fedyanin, V. N. Golovkina, and T. V. Murzina, Opt. Lett. 19, 1450 (1994); J. I. Dadap, X. F. Hu, M. H. Anderson, M. C. Downer, J. K. Lowell, and O. A. Aktsipetrov, Phys. Rev. B 53, R7607 (1996); J. Bloch, J. G. Mihaychuk, and H. M. van Driel, Phys. Rev. Lett. 77, 920 (1996); P. Godefroy, W. de Jong, C. W. van Hasselt, M. A. C. Devillers, and Th. Rasing, Appl. Phys. Lett. 68, 1982 (1996).
[CrossRef] [PubMed]

Löffler, T.

C. Ohlhoff, C. Meyer, G. Lüpke, T. Löffler, T. Pfeifer, H. G. Roskos, and H. Kurz, Appl. Phys. Lett. 68, 1 (1996).
[CrossRef]

Lüpke, G.

C. Ohlhoff, C. Meyer, G. Lüpke, T. Löffler, T. Pfeifer, H. G. Roskos, and H. Kurz, Appl. Phys. Lett. 68, 1 (1996).
[CrossRef]

Marowsky, G.

R. Stolle, G. Marowsky, E. Schwarzberg, and G. Berkovic, Appl. Phys. B 63, 491 (1996), and references therein; P. Wilson, Y. Jiang, O. A. Aktsipetrov, E. D. Mishina, and M. C. Downer, Opt. Lett. 24, 496 (1999).
[CrossRef]

Meyer, C.

C. Ohlhoff, C. Meyer, G. Lüpke, T. Löffler, T. Pfeifer, H. G. Roskos, and H. Kurz, Appl. Phys. Lett. 68, 1 (1996).
[CrossRef]

Misewich, J. A.

J. I. Dadap, J. Shan, A. S. Weling, J. A. Misewich, and T. F. Heinz, Appl. Phys. B 68, 333 (1999).
[CrossRef]

A. Nahata, T. F. Heinz, and J. A. Misewich, Appl. Phys. Lett. 69, 746 (1996).
[CrossRef]

Nahata, A.

A. Nahata and T. F. Heinz, Opt. Lett. 23, 67 (1998).
[CrossRef]

A. Nahata, T. F. Heinz, and J. A. Misewich, Appl. Phys. Lett. 69, 746 (1996).
[CrossRef]

Nakagawa, T.

T. Itatani, T. Nakagawa, F. Kano, K. Ohta, and Y. Sugiyama, IEICE Trans. Electron. E78-C, 73 (1995).

Ohlhoff, C.

C. Ohlhoff, C. Meyer, G. Lüpke, T. Löffler, T. Pfeifer, H. G. Roskos, and H. Kurz, Appl. Phys. Lett. 68, 1 (1996).
[CrossRef]

Ohta, K.

T. Itatani, T. Nakagawa, F. Kano, K. Ohta, and Y. Sugiyama, IEICE Trans. Electron. E78-C, 73 (1995).

Pfeifer, T.

C. Ohlhoff, C. Meyer, G. Lüpke, T. Löffler, T. Pfeifer, H. G. Roskos, and H. Kurz, Appl. Phys. Lett. 68, 1 (1996).
[CrossRef]

Richmond, G. L.

G. L. Richmond, J. M. Robinson, and V. L. Shannon, Prog. Surf. Sci. 28, 1 (1988); R. M. Corn and D. A. Higgins, Chem. Rev. 94, 107 (1994); K. B. Eisenthal, Chem. Rev. 96, 1343 (1996).
[CrossRef] [PubMed]

Robinson, J. M.

G. L. Richmond, J. M. Robinson, and V. L. Shannon, Prog. Surf. Sci. 28, 1 (1988); R. M. Corn and D. A. Higgins, Chem. Rev. 94, 107 (1994); K. B. Eisenthal, Chem. Rev. 96, 1343 (1996).
[CrossRef] [PubMed]

Roskos, H. G.

C. Ohlhoff, C. Meyer, G. Lüpke, T. Löffler, T. Pfeifer, H. G. Roskos, and H. Kurz, Appl. Phys. Lett. 68, 1 (1996).
[CrossRef]

Schwarzberg, E.

R. Stolle, G. Marowsky, E. Schwarzberg, and G. Berkovic, Appl. Phys. B 63, 491 (1996), and references therein; P. Wilson, Y. Jiang, O. A. Aktsipetrov, E. D. Mishina, and M. C. Downer, Opt. Lett. 24, 496 (1999).
[CrossRef]

Shan, J.

J. I. Dadap, J. Shan, A. S. Weling, J. A. Misewich, and T. F. Heinz, Appl. Phys. B 68, 333 (1999).
[CrossRef]

Shannon, V. L.

G. L. Richmond, J. M. Robinson, and V. L. Shannon, Prog. Surf. Sci. 28, 1 (1988); R. M. Corn and D. A. Higgins, Chem. Rev. 94, 107 (1994); K. B. Eisenthal, Chem. Rev. 96, 1343 (1996).
[CrossRef] [PubMed]

Stolle, R.

R. Stolle, G. Marowsky, E. Schwarzberg, and G. Berkovic, Appl. Phys. B 63, 491 (1996), and references therein; P. Wilson, Y. Jiang, O. A. Aktsipetrov, E. D. Mishina, and M. C. Downer, Opt. Lett. 24, 496 (1999).
[CrossRef]

Sugiyama, Y.

T. Itatani, T. Nakagawa, F. Kano, K. Ohta, and Y. Sugiyama, IEICE Trans. Electron. E78-C, 73 (1995).

ter Beek, M.

Uesu, Y.

Y. Uesu, S. Kurimura, and Y. Yamamoto, Appl. Phys. Lett. 66, 2165 (1995); V. Kirilyuk, A. Kirilyuk, and Th. Rasing, Appl. Phys. Lett. 70, 2306 (1997).
[CrossRef]

Weling, A. S.

J. I. Dadap, J. Shan, A. S. Weling, J. A. Misewich, and T. F. Heinz, Appl. Phys. B 68, 333 (1999).
[CrossRef]

Wilson, P. T.

Yamamoto, Y.

Y. Uesu, S. Kurimura, and Y. Yamamoto, Appl. Phys. Lett. 66, 2165 (1995); V. Kirilyuk, A. Kirilyuk, and Th. Rasing, Appl. Phys. Lett. 70, 2306 (1997).
[CrossRef]

Appl. Phys. B (2)

R. Stolle, G. Marowsky, E. Schwarzberg, and G. Berkovic, Appl. Phys. B 63, 491 (1996), and references therein; P. Wilson, Y. Jiang, O. A. Aktsipetrov, E. D. Mishina, and M. C. Downer, Opt. Lett. 24, 496 (1999).
[CrossRef]

J. I. Dadap, J. Shan, A. S. Weling, J. A. Misewich, and T. F. Heinz, Appl. Phys. B 68, 333 (1999).
[CrossRef]

Appl. Phys. Lett. (3)

A. Nahata, T. F. Heinz, and J. A. Misewich, Appl. Phys. Lett. 69, 746 (1996).
[CrossRef]

C. Ohlhoff, C. Meyer, G. Lüpke, T. Löffler, T. Pfeifer, H. G. Roskos, and H. Kurz, Appl. Phys. Lett. 68, 1 (1996).
[CrossRef]

Y. Uesu, S. Kurimura, and Y. Yamamoto, Appl. Phys. Lett. 66, 2165 (1995); V. Kirilyuk, A. Kirilyuk, and Th. Rasing, Appl. Phys. Lett. 70, 2306 (1997).
[CrossRef]

IEICE Trans. Electron. (1)

T. Itatani, T. Nakagawa, F. Kano, K. Ohta, and Y. Sugiyama, IEICE Trans. Electron. E78-C, 73 (1995).

Opt. Lett. (2)

Phys. Rev. Lett. (1)

C. H. Lee, R. K. Chang, and N. Bloembergen, Phys. Rev. Lett. 18, 167 (1967); O. A. Aktsipetrov, A. A. Fedyanin, V. N. Golovkina, and T. V. Murzina, Opt. Lett. 19, 1450 (1994); J. I. Dadap, X. F. Hu, M. H. Anderson, M. C. Downer, J. K. Lowell, and O. A. Aktsipetrov, Phys. Rev. B 53, R7607 (1996); J. Bloch, J. G. Mihaychuk, and H. M. van Driel, Phys. Rev. Lett. 77, 920 (1996); P. Godefroy, W. de Jong, C. W. van Hasselt, M. A. C. Devillers, and Th. Rasing, Appl. Phys. Lett. 68, 1982 (1996).
[CrossRef] [PubMed]

Prog. Surf. Sci. (1)

G. L. Richmond, J. M. Robinson, and V. L. Shannon, Prog. Surf. Sci. 28, 1 (1988); R. M. Corn and D. A. Higgins, Chem. Rev. 94, 107 (1994); K. B. Eisenthal, Chem. Rev. 96, 1343 (1996).
[CrossRef] [PubMed]

Other (2)

T. F. Heinz, in Nonlinear Surface Electromagnetic Phenomena, H.-E. Ponath and G. I. Stegeman, eds. (North-Holland, Amsterdam, 1991), p. 353; G. A. Reider and T. F. Heinz, in Photonic Probes of Surfaces, P. Halevi, ed. (Elsevier, Amsterdam, 1995), p. 413.

D. H. Auston, in Ultrashort Laser Pulses:?Generation and Applications, 2nd ed., W. Kaiser, ed. (Springer-Verlag, Berlin, 1993), pp. 183 and 445.

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Figures (2)

Fig. 1
Fig. 1

Experimental setup for vector electric-field measurements by SHG. Inset, details of probing area and electrode structure.

Fig. 2
Fig. 2

Experimental results: vector map of the electric field E0.

Equations (9)

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

Pi2ω=jklχijkl3EjωEkωEl0.
χiii2,eff=χiiii3Ei0,
χjii2,eff=χjiij3Ej0.
χxyy2,eff=χxyyx3Ex0,
χyyy2,eff=χyyyy3Ey0,
χzyy2,eff=χzyyz3Ez0.
EFD,x2ω=fχxyyx3Eyω2Ex0,
EFD,y2ω=fχyyyy3Eyω2Ey0,
I2ω,iEref,i2ω+EFD,i2ω2Eref,i2ω2+2Eref,i2ωEFD,i2ω.

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