Abstract

In second-harmonic scanning imaging of interface structures, interference from constant-background contributions can lead to severe distortions of the second-harmonic image compared with the true interface morphology. Similar phenomena can appear in time-dependent second-harmonic measurements. We present an analysis of these effects and demonstrate a simple but powerful technique to eliminate these coherence artifacts.

© 1998 Optical Society of America

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1998 (1)

M. Cernusca, R. Heer, and G. A. Reider, “Photoinduced trap generation at the Si–SiO2 interface,” Appl. Phys. B 66, 367–370 (1998).
[CrossRef]

1997 (5)

M. Florsheimer, M. Bosch, C. Brillert, M. Wierschem, and H. Fuchs, “Interface imaging by second harmonic microscopy,” J. Vac. Sci. Technol. B 15, 1564–1568 (1997).
[CrossRef]

L. Smilowitz, Q. X. Jia, X. Yang, D. Q. Li, D. McBranch, S. J. Buelow, and J. M. Robinson, “Imaging nanometer-thick patterned self-assembled monolayers via second harmonic generation microscopy,” J. Appl. Phys. 81, 2051–2054 (1997).
[CrossRef]

Y. Yamamoto, T. Ashida, S. Kurimura, and Y. Uesu, “Two-dimensional observation of the Maker fringe and its application to the poling state evaluation of ferroelectric domains,” Appl. Opt. 36, 602–605 (1997).
[CrossRef] [PubMed]

V. Kirilyuk, A. Kirilyuk, and T. Rasing, “New mode of domain imaging: second harmonic generation microscopy,” J. Appl. Phys. 81, 5014 (1997).
[CrossRef]

C. E. Allen, R. Ditchfield, and E. G. Seebauer, “Surface diffusion of Ge on Si(111): experiment and simulation,” Phys. Rev. B 55, 13304–13313 (1997).
[CrossRef]

1996 (1)

H. Tanaka, H. Kurokawa, E. Kobayashi, H. Sano, G. Mizutani, and S. Ushioda, “Optical second harmonic intensity image of multi-layered metal film patterns,” Prog. Cryst. Growth Characteriz. Mater. 33, 129–132 (1996).
[CrossRef]

1994 (1)

M. Florsheimer, H. Looser, M. Kupfer, and P. Gunter, “In situ imaging of Langmuir monolayers by second harmonic microscopy,” Thin Solid Films 244, 1001–1006 (1994).
[CrossRef]

1993 (1)

1992 (1)

K. A. Schultz and E. G. Seebauer, “Surface diffusion of Sb on Ge(111) monitored quantitatively with optical second harmonic microscopy,” J. Chem. Phys. 97, 6958–6967 (1992).
[CrossRef]

1991 (1)

1990 (2)

R. W. J. Hollering, Q. H. F. Vrehen, and G. Marowsky, “Angular dependence of optical second harmonic generation from a monolayer grating,” Opt. Commun. 78, 387–392 (1990).
[CrossRef]

R. Superfine, J. Y. Huang, and Y. R. Shen, “Phase measurement for surface infrared-visible sum-frequency generation,” Opt. Lett. 15, 1276–1278 (1990).
[CrossRef] [PubMed]

1989 (3)

1988 (1)

G. A. Reider, M. Huemer, and A. J. Schmidt, “Surface second harmonic generation spectroscopy without interference of substrate contributions,” Opt. Commun. 68, 149–152 (1988).
[CrossRef]

1986 (3)

G. T. Boyd, Y. R. Shen, and T. W. Hänsch, “Continuous-wave second harmonic generation as a surface microprobe,” Opt. Lett. 11, 97–99 (1986).
[CrossRef]

H. W. K. Tom, X. D. Zhu, Y. R. Shen, and G. A. Somorjai, “Investigation of Si(111)–(7×7) surface by second harmonic generation: oxidation and the effects of surface phosphorus,” Surf. Sci. 167, 167–176 (1986).
[CrossRef]

K. Kemnitz, K. Bhattacharyya, J. M. Hicks, G. R. Pinto, K. B. Eisenthal, and T. F. Heinz, “The phase of second harmonic light generated at an interface and its relation to absolute molecular orientation,” Chem. Phys. Lett. 131, 285–290 (1986).
[CrossRef]

1965 (1)

R. K. Chang, J. Ducuing, and N. Bloembergen, “Relative phase measurement between fundamental and second harmonic light,” Phys. Rev. Lett. 15, 6–8 (1965).
[CrossRef]

Allen, C. E.

C. E. Allen, R. Ditchfield, and E. G. Seebauer, “Surface diffusion of Ge on Si(111): experiment and simulation,” Phys. Rev. B 55, 13304–13313 (1997).
[CrossRef]

Ashida, T.

Berkovic, G.

Bhattacharyya, K.

K. Kemnitz, K. Bhattacharyya, J. M. Hicks, G. R. Pinto, K. B. Eisenthal, and T. F. Heinz, “The phase of second harmonic light generated at an interface and its relation to absolute molecular orientation,” Chem. Phys. Lett. 131, 285–290 (1986).
[CrossRef]

Bloembergen, N.

R. K. Chang, J. Ducuing, and N. Bloembergen, “Relative phase measurement between fundamental and second harmonic light,” Phys. Rev. Lett. 15, 6–8 (1965).
[CrossRef]

Bosch, M.

M. Florsheimer, M. Bosch, C. Brillert, M. Wierschem, and H. Fuchs, “Interface imaging by second harmonic microscopy,” J. Vac. Sci. Technol. B 15, 1564–1568 (1997).
[CrossRef]

Boyd, G. T.

Brillert, C.

M. Florsheimer, M. Bosch, C. Brillert, M. Wierschem, and H. Fuchs, “Interface imaging by second harmonic microscopy,” J. Vac. Sci. Technol. B 15, 1564–1568 (1997).
[CrossRef]

Buelow, S. J.

L. Smilowitz, Q. X. Jia, X. Yang, D. Q. Li, D. McBranch, S. J. Buelow, and J. M. Robinson, “Imaging nanometer-thick patterned self-assembled monolayers via second harmonic generation microscopy,” J. Appl. Phys. 81, 2051–2054 (1997).
[CrossRef]

Cernusca, M.

M. Cernusca, R. Heer, and G. A. Reider, “Photoinduced trap generation at the Si–SiO2 interface,” Appl. Phys. B 66, 367–370 (1998).
[CrossRef]

Chang, R. K.

R. K. Chang, J. Ducuing, and N. Bloembergen, “Relative phase measurement between fundamental and second harmonic light,” Phys. Rev. Lett. 15, 6–8 (1965).
[CrossRef]

Chen, Z.

Ditchfield, R.

C. E. Allen, R. Ditchfield, and E. G. Seebauer, “Surface diffusion of Ge on Si(111): experiment and simulation,” Phys. Rev. B 55, 13304–13313 (1997).
[CrossRef]

Ducuing, J.

R. K. Chang, J. Ducuing, and N. Bloembergen, “Relative phase measurement between fundamental and second harmonic light,” Phys. Rev. Lett. 15, 6–8 (1965).
[CrossRef]

Eisenthal, K. B.

K. Kemnitz, K. Bhattacharyya, J. M. Hicks, G. R. Pinto, K. B. Eisenthal, and T. F. Heinz, “The phase of second harmonic light generated at an interface and its relation to absolute molecular orientation,” Chem. Phys. Lett. 131, 285–290 (1986).
[CrossRef]

Florsheimer, M.

M. Florsheimer, M. Bosch, C. Brillert, M. Wierschem, and H. Fuchs, “Interface imaging by second harmonic microscopy,” J. Vac. Sci. Technol. B 15, 1564–1568 (1997).
[CrossRef]

M. Florsheimer, H. Looser, M. Kupfer, and P. Gunter, “In situ imaging of Langmuir monolayers by second harmonic microscopy,” Thin Solid Films 244, 1001–1006 (1994).
[CrossRef]

Fuchs, H.

M. Florsheimer, M. Bosch, C. Brillert, M. Wierschem, and H. Fuchs, “Interface imaging by second harmonic microscopy,” J. Vac. Sci. Technol. B 15, 1564–1568 (1997).
[CrossRef]

Gunter, P.

M. Florsheimer, H. Looser, M. Kupfer, and P. Gunter, “In situ imaging of Langmuir monolayers by second harmonic microscopy,” Thin Solid Films 244, 1001–1006 (1994).
[CrossRef]

Hänsch, T. W.

Heer, R.

M. Cernusca, R. Heer, and G. A. Reider, “Photoinduced trap generation at the Si–SiO2 interface,” Appl. Phys. B 66, 367–370 (1998).
[CrossRef]

Heinz, T. F.

T. Suzuki and T. F. Heinz, “Second harmonic diffraction from a monolayer grating,” Opt. Lett. 14, 1201–1203 (1989).
[CrossRef] [PubMed]

K. Kemnitz, K. Bhattacharyya, J. M. Hicks, G. R. Pinto, K. B. Eisenthal, and T. F. Heinz, “The phase of second harmonic light generated at an interface and its relation to absolute molecular orientation,” Chem. Phys. Lett. 131, 285–290 (1986).
[CrossRef]

Hicks, J. M.

K. Kemnitz, K. Bhattacharyya, J. M. Hicks, G. R. Pinto, K. B. Eisenthal, and T. F. Heinz, “The phase of second harmonic light generated at an interface and its relation to absolute molecular orientation,” Chem. Phys. Lett. 131, 285–290 (1986).
[CrossRef]

Hollering, R. W. J.

R. W. J. Hollering, Q. H. F. Vrehen, and G. Marowsky, “Angular dependence of optical second harmonic generation from a monolayer grating,” Opt. Commun. 78, 387–392 (1990).
[CrossRef]

Huang, J. Y.

Huemer, M.

G. A. Reider, M. Huemer, and A. J. Schmidt, “Surface second harmonic generation spectroscopy without interference of substrate contributions,” Opt. Commun. 68, 149–152 (1988).
[CrossRef]

Jia, Q. X.

L. Smilowitz, Q. X. Jia, X. Yang, D. Q. Li, D. McBranch, S. J. Buelow, and J. M. Robinson, “Imaging nanometer-thick patterned self-assembled monolayers via second harmonic generation microscopy,” J. Appl. Phys. 81, 2051–2054 (1997).
[CrossRef]

Kemnitz, K.

K. Kemnitz, K. Bhattacharyya, J. M. Hicks, G. R. Pinto, K. B. Eisenthal, and T. F. Heinz, “The phase of second harmonic light generated at an interface and its relation to absolute molecular orientation,” Chem. Phys. Lett. 131, 285–290 (1986).
[CrossRef]

Kirilyuk, A.

V. Kirilyuk, A. Kirilyuk, and T. Rasing, “New mode of domain imaging: second harmonic generation microscopy,” J. Appl. Phys. 81, 5014 (1997).
[CrossRef]

Kirilyuk, V.

V. Kirilyuk, A. Kirilyuk, and T. Rasing, “New mode of domain imaging: second harmonic generation microscopy,” J. Appl. Phys. 81, 5014 (1997).
[CrossRef]

Kobayashi, E.

H. Tanaka, H. Kurokawa, E. Kobayashi, H. Sano, G. Mizutani, and S. Ushioda, “Optical second harmonic intensity image of multi-layered metal film patterns,” Prog. Cryst. Growth Characteriz. Mater. 33, 129–132 (1996).
[CrossRef]

Kupfer, M.

M. Florsheimer, H. Looser, M. Kupfer, and P. Gunter, “In situ imaging of Langmuir monolayers by second harmonic microscopy,” Thin Solid Films 244, 1001–1006 (1994).
[CrossRef]

Kurimura, S.

Kurokawa, H.

H. Tanaka, H. Kurokawa, E. Kobayashi, H. Sano, G. Mizutani, and S. Ushioda, “Optical second harmonic intensity image of multi-layered metal film patterns,” Prog. Cryst. Growth Characteriz. Mater. 33, 129–132 (1996).
[CrossRef]

Lewis, A.

Li, D. Q.

L. Smilowitz, Q. X. Jia, X. Yang, D. Q. Li, D. McBranch, S. J. Buelow, and J. M. Robinson, “Imaging nanometer-thick patterned self-assembled monolayers via second harmonic generation microscopy,” J. Appl. Phys. 81, 2051–2054 (1997).
[CrossRef]

Looser, H.

M. Florsheimer, H. Looser, M. Kupfer, and P. Gunter, “In situ imaging of Langmuir monolayers by second harmonic microscopy,” Thin Solid Films 244, 1001–1006 (1994).
[CrossRef]

Marowsky, G.

R. W. J. Hollering, Q. H. F. Vrehen, and G. Marowsky, “Angular dependence of optical second harmonic generation from a monolayer grating,” Opt. Commun. 78, 387–392 (1990).
[CrossRef]

G. Berkovic, Y. R. Shen, G. Marowsky, and R. Steinhoff, “Interference between second-harmonic generation from a substrate and from an adsorbate layer,” J. Opt. Soc. Am. B 6, 205–208 (1989).
[CrossRef]

McBranch, D.

L. Smilowitz, Q. X. Jia, X. Yang, D. Q. Li, D. McBranch, S. J. Buelow, and J. M. Robinson, “Imaging nanometer-thick patterned self-assembled monolayers via second harmonic generation microscopy,” J. Appl. Phys. 81, 2051–2054 (1997).
[CrossRef]

Mizutani, G.

H. Tanaka, H. Kurokawa, E. Kobayashi, H. Sano, G. Mizutani, and S. Ushioda, “Optical second harmonic intensity image of multi-layered metal film patterns,” Prog. Cryst. Growth Characteriz. Mater. 33, 129–132 (1996).
[CrossRef]

Nebenzahl, I.

Pinto, G. R.

K. Kemnitz, K. Bhattacharyya, J. M. Hicks, G. R. Pinto, K. B. Eisenthal, and T. F. Heinz, “The phase of second harmonic light generated at an interface and its relation to absolute molecular orientation,” Chem. Phys. Lett. 131, 285–290 (1986).
[CrossRef]

Rasing, T.

V. Kirilyuk, A. Kirilyuk, and T. Rasing, “New mode of domain imaging: second harmonic generation microscopy,” J. Appl. Phys. 81, 5014 (1997).
[CrossRef]

Reider, G. A.

M. Cernusca, R. Heer, and G. A. Reider, “Photoinduced trap generation at the Si–SiO2 interface,” Appl. Phys. B 66, 367–370 (1998).
[CrossRef]

G. A. Reider, M. Huemer, and A. J. Schmidt, “Surface second harmonic generation spectroscopy without interference of substrate contributions,” Opt. Commun. 68, 149–152 (1988).
[CrossRef]

Robinson, J. M.

L. Smilowitz, Q. X. Jia, X. Yang, D. Q. Li, D. McBranch, S. J. Buelow, and J. M. Robinson, “Imaging nanometer-thick patterned self-assembled monolayers via second harmonic generation microscopy,” J. Appl. Phys. 81, 2051–2054 (1997).
[CrossRef]

Sano, H.

H. Tanaka, H. Kurokawa, E. Kobayashi, H. Sano, G. Mizutani, and S. Ushioda, “Optical second harmonic intensity image of multi-layered metal film patterns,” Prog. Cryst. Growth Characteriz. Mater. 33, 129–132 (1996).
[CrossRef]

Schmidt, A. J.

G. A. Reider, M. Huemer, and A. J. Schmidt, “Surface second harmonic generation spectroscopy without interference of substrate contributions,” Opt. Commun. 68, 149–152 (1988).
[CrossRef]

Schultz, K. A.

K. A. Schultz, I. I. Suni, and E. G. Seebauer, “Microscopy of adsorbates by surface second harmonic generation,” J. Opt. Soc. Am. B 10, 546–550 (1993).
[CrossRef]

K. A. Schultz and E. G. Seebauer, “Surface diffusion of Sb on Ge(111) monitored quantitatively with optical second harmonic microscopy,” J. Chem. Phys. 97, 6958–6967 (1992).
[CrossRef]

Seebauer, E. G.

C. E. Allen, R. Ditchfield, and E. G. Seebauer, “Surface diffusion of Ge on Si(111): experiment and simulation,” Phys. Rev. B 55, 13304–13313 (1997).
[CrossRef]

K. A. Schultz, I. I. Suni, and E. G. Seebauer, “Microscopy of adsorbates by surface second harmonic generation,” J. Opt. Soc. Am. B 10, 546–550 (1993).
[CrossRef]

K. A. Schultz and E. G. Seebauer, “Surface diffusion of Sb on Ge(111) monitored quantitatively with optical second harmonic microscopy,” J. Chem. Phys. 97, 6958–6967 (1992).
[CrossRef]

Shen, Y. R.

Smilowitz, L.

L. Smilowitz, Q. X. Jia, X. Yang, D. Q. Li, D. McBranch, S. J. Buelow, and J. M. Robinson, “Imaging nanometer-thick patterned self-assembled monolayers via second harmonic generation microscopy,” J. Appl. Phys. 81, 2051–2054 (1997).
[CrossRef]

Somorjai, G. A.

H. W. K. Tom, X. D. Zhu, Y. R. Shen, and G. A. Somorjai, “Investigation of Si(111)–(7×7) surface by second harmonic generation: oxidation and the effects of surface phosphorus,” Surf. Sci. 167, 167–176 (1986).
[CrossRef]

Steinhoff, R.

Suni, I. I.

Superfine, R.

Suzuki, T.

Takei, H.

Tanaka, H.

H. Tanaka, H. Kurokawa, E. Kobayashi, H. Sano, G. Mizutani, and S. Ushioda, “Optical second harmonic intensity image of multi-layered metal film patterns,” Prog. Cryst. Growth Characteriz. Mater. 33, 129–132 (1996).
[CrossRef]

Tom, H. W. K.

H. W. K. Tom, X. D. Zhu, Y. R. Shen, and G. A. Somorjai, “Investigation of Si(111)–(7×7) surface by second harmonic generation: oxidation and the effects of surface phosphorus,” Surf. Sci. 167, 167–176 (1986).
[CrossRef]

Uesu, Y.

Ushioda, S.

H. Tanaka, H. Kurokawa, E. Kobayashi, H. Sano, G. Mizutani, and S. Ushioda, “Optical second harmonic intensity image of multi-layered metal film patterns,” Prog. Cryst. Growth Characteriz. Mater. 33, 129–132 (1996).
[CrossRef]

Vrehen, Q. H. F.

R. W. J. Hollering, Q. H. F. Vrehen, and G. Marowsky, “Angular dependence of optical second harmonic generation from a monolayer grating,” Opt. Commun. 78, 387–392 (1990).
[CrossRef]

Wierschem, M.

M. Florsheimer, M. Bosch, C. Brillert, M. Wierschem, and H. Fuchs, “Interface imaging by second harmonic microscopy,” J. Vac. Sci. Technol. B 15, 1564–1568 (1997).
[CrossRef]

Yamamoto, Y.

Yang, X.

L. Smilowitz, Q. X. Jia, X. Yang, D. Q. Li, D. McBranch, S. J. Buelow, and J. M. Robinson, “Imaging nanometer-thick patterned self-assembled monolayers via second harmonic generation microscopy,” J. Appl. Phys. 81, 2051–2054 (1997).
[CrossRef]

Zhu, X. D.

X. D. Zhu and Y. R. Shen, “Generation and detection of a monolayer grating by laser desorption and second-harmonic generation: CO on Ni(111),” Opt. Lett. 14, 503–505 (1989).
[CrossRef] [PubMed]

H. W. K. Tom, X. D. Zhu, Y. R. Shen, and G. A. Somorjai, “Investigation of Si(111)–(7×7) surface by second harmonic generation: oxidation and the effects of surface phosphorus,” Surf. Sci. 167, 167–176 (1986).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B (1)

M. Cernusca, R. Heer, and G. A. Reider, “Photoinduced trap generation at the Si–SiO2 interface,” Appl. Phys. B 66, 367–370 (1998).
[CrossRef]

Chem. Phys. Lett. (1)

K. Kemnitz, K. Bhattacharyya, J. M. Hicks, G. R. Pinto, K. B. Eisenthal, and T. F. Heinz, “The phase of second harmonic light generated at an interface and its relation to absolute molecular orientation,” Chem. Phys. Lett. 131, 285–290 (1986).
[CrossRef]

J. Appl. Phys. (2)

V. Kirilyuk, A. Kirilyuk, and T. Rasing, “New mode of domain imaging: second harmonic generation microscopy,” J. Appl. Phys. 81, 5014 (1997).
[CrossRef]

L. Smilowitz, Q. X. Jia, X. Yang, D. Q. Li, D. McBranch, S. J. Buelow, and J. M. Robinson, “Imaging nanometer-thick patterned self-assembled monolayers via second harmonic generation microscopy,” J. Appl. Phys. 81, 2051–2054 (1997).
[CrossRef]

J. Chem. Phys. (1)

K. A. Schultz and E. G. Seebauer, “Surface diffusion of Sb on Ge(111) monitored quantitatively with optical second harmonic microscopy,” J. Chem. Phys. 97, 6958–6967 (1992).
[CrossRef]

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

J. Vac. Sci. Technol. B (1)

M. Florsheimer, M. Bosch, C. Brillert, M. Wierschem, and H. Fuchs, “Interface imaging by second harmonic microscopy,” J. Vac. Sci. Technol. B 15, 1564–1568 (1997).
[CrossRef]

Opt. Commun. (2)

G. A. Reider, M. Huemer, and A. J. Schmidt, “Surface second harmonic generation spectroscopy without interference of substrate contributions,” Opt. Commun. 68, 149–152 (1988).
[CrossRef]

R. W. J. Hollering, Q. H. F. Vrehen, and G. Marowsky, “Angular dependence of optical second harmonic generation from a monolayer grating,” Opt. Commun. 78, 387–392 (1990).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. B (1)

C. E. Allen, R. Ditchfield, and E. G. Seebauer, “Surface diffusion of Ge on Si(111): experiment and simulation,” Phys. Rev. B 55, 13304–13313 (1997).
[CrossRef]

Phys. Rev. Lett. (1)

R. K. Chang, J. Ducuing, and N. Bloembergen, “Relative phase measurement between fundamental and second harmonic light,” Phys. Rev. Lett. 15, 6–8 (1965).
[CrossRef]

Prog. Cryst. Growth Characteriz. Mater. (1)

H. Tanaka, H. Kurokawa, E. Kobayashi, H. Sano, G. Mizutani, and S. Ushioda, “Optical second harmonic intensity image of multi-layered metal film patterns,” Prog. Cryst. Growth Characteriz. Mater. 33, 129–132 (1996).
[CrossRef]

Surf. Sci. (1)

H. W. K. Tom, X. D. Zhu, Y. R. Shen, and G. A. Somorjai, “Investigation of Si(111)–(7×7) surface by second harmonic generation: oxidation and the effects of surface phosphorus,” Surf. Sci. 167, 167–176 (1986).
[CrossRef]

Thin Solid Films (1)

M. Florsheimer, H. Looser, M. Kupfer, and P. Gunter, “In situ imaging of Langmuir monolayers by second harmonic microscopy,” Thin Solid Films 244, 1001–1006 (1994).
[CrossRef]

Other (3)

A. Yariv, Optical Electronics (Holt, Rinehart and Winston, New York, 1985).

T. F. Heinz, “Second-order nonlinear optical effects at surfaces and interfaces,” in Nonlinear Surface Electromagnetic Phenomena, H. Ponath and G. Stegeman, eds. (Elsevier, Amsterdam, 1991), pp. 353–417; G. A. Reider and T. F. Heinz, “Second-order nonlinear optical effects at surfaces and interfaces: recent advances,” in Electromagnetic Waves: Recent Developments in Research Vol. 2. Photonic Probes of Surfaces, P. Halevi, ed. (Elsevier, Amsterdam, 1995), pp. 413–478.

J. G. Mihaychuk, J. Bloch, Y. Liu, and H. M. van Driel, “Time-dependent second-harmonic generation from the Si–SiO2 interface induced by charge transfer,” Opt. Lett. 20, 2063–2065 (1995); J. Bloch, J. G. Mihaychuk, Y. Liu, and H. M. van Driel, “UV-photoinduced charge trapping at the Si–SiO2 interface observed with second harmonic generation,” Phys. Rev. Lett. 77, 920–923 (1996).
[CrossRef] [PubMed]

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Figures (8)

Fig. 1
Fig. 1

Linearly increasing nonlinear susceptibility χsig(2)(x, t) superimposed upon phase-shifted constant background χbkg(2); the total susceptibility χsys(2)(x, t) is displayed in the inset.

Fig. 2
Fig. 2

Simulated SH scans from spatial Gaussian-shaped nonlinear susceptibility distribution χsig(2)(x), superimposed upon a background with phase ϕ as a parameter.

Fig. 3
Fig. 3

Experimental setup for the background-free measurements. Eiω and Erω are the incident and reflected fundamental fields, respectively. Esys2ω and Eaux2ω are the SH fields generated by the sample and the nonlinear crystal (NL X-TAL). Filter F blocks the fundamental light. POL, polarizer; DET, detector.

Fig. 4
Fig. 4

Various complex SH field amplitudes relevant for the indirect background-elimination procedure; field vectors that originate from the center of the coordinate system are accessible to direct measurements.

Fig. 5
Fig. 5

Original experimental data of the time evolution of the SH response from an oxidized silicon surface.

Fig. 6
Fig. 6

Time evolution of photoinduced susceptibility |χsig(2)(t)| yielded by the direct and by the indirect background-elimination methods; solid curve, difference between the two results.

Fig. 7
Fig. 7

SH scanning image of a damaged sample spot; original data.

Fig. 8
Fig. 8

Directly background-compensated SH scanning image of the damaged sample spot shown in Fig. 7.

Equations (8)

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Eω(z)exp-rwω(z)2exp-jkωr22Rω(z),
E2ω(z)[Eω(z)]2exp-2rwω(z)2exp-j2kωr22Rω(z).
E2ω[e2ωχ(2):eωeω]EiωEiω=:χ(2)EiωEiω,
P2ωE2ωE2ω*|χ(2)|2(Pω)2.
χsys(2)(x, t)=χbkg(2) exp(jϕ)+χsig(2)(x, t).
P2ω(x, t)|χbkg(2)|2+|χsig(2)(x, t)|2+2|χbkg(2)||χsig(2)(x, t)|cos ϕ.
|Esig2ω|2=|Ebkg2ω|2+|Esys2ω|2-2|Ebkg2ω||Esys2ω|cos(α-β),
cos ϕ=(|Esys2ω|2-|Ebkg2ω|2-|Esig2ω|2)/(2|Ebkg2ω||Esig2ω|).

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