Abstract

A new method for the determination of spatially resolved phase differences of nonlinear susceptibilities is presented. The technique is based on the interference of the signal field with a reference field. A phase-shifting element that directly changes the phase difference between the two second-harmonic fields is introduced. The reliability of the method is tested by an experiment with two quartz crystals. As a first application, a measurement of the phase difference between domains in antiferromagnetic YMnO3 is presented.

© 1999 Optical Society of America

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  1. R. K. Chang, J. Ducuing, and N. Bloembergen, Phys. Rev. Lett. 15, 6 (1965).
    [CrossRef]
  2. K. Kemnitz, K. Bhattacharyya, J. M. Hicks, G. R. Pinto, K. B. Eisenthal, and T. F. Heinz, Chem. Phys. Lett. 131, 285 (1986).
  3. R. Stolle, G. Marowsky, E. Schwarzberg, and G. Berkovic, Appl. Phys. B 63, 491 (1996).
    [CrossRef]
  4. K. J. Veenstra, A. V. Petukhov, A. P. de Boer, and Th. Rasing, Phys. Rev. B 58, R16020 (1998).
    [CrossRef]
  5. J. Chen, S. Machida, and Y. Yamanoto, Opt. Lett. 23, 676 (1998).
    [CrossRef]
  6. M. Fiebig, D. Fröhlich, B. B. Krichevtsov, and R. V. Pisarev, Phys. Rev. Lett. 73, 2127 (1994).
    [CrossRef] [PubMed]
  7. M. Fiebig, D. Fröhlich, G. Sluyterman v. L., and R. V. Pisarev, Appl. Phys. Lett. 66, 2906 (1995).
    [CrossRef]
  8. M. Fiebig, D. Fröhlich, St. Leute, and R. V. Pisarev, Appl. Phys. B 66, 265 (1998).
    [CrossRef]
  9. Y. Tanabe, M. Muto, M. Fiebig, and E. Hanamura, Phys. Rev. B 58, 8654 (1998).
    [CrossRef]
  10. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).
  11. D. Fröhlich, Th. Kiefer, St. Leute, and Th. Lottermoser, Appl. Phys. B 68, 465 (1999).
    [CrossRef]
  12. D. Fröhlich, St. Leute, V. V. Pavlov, and R. V. Pisarev, Phys. Rev. Lett. 81, 3239 (1998).
    [CrossRef]

1999

D. Fröhlich, Th. Kiefer, St. Leute, and Th. Lottermoser, Appl. Phys. B 68, 465 (1999).
[CrossRef]

1998

D. Fröhlich, St. Leute, V. V. Pavlov, and R. V. Pisarev, Phys. Rev. Lett. 81, 3239 (1998).
[CrossRef]

K. J. Veenstra, A. V. Petukhov, A. P. de Boer, and Th. Rasing, Phys. Rev. B 58, R16020 (1998).
[CrossRef]

J. Chen, S. Machida, and Y. Yamanoto, Opt. Lett. 23, 676 (1998).
[CrossRef]

M. Fiebig, D. Fröhlich, St. Leute, and R. V. Pisarev, Appl. Phys. B 66, 265 (1998).
[CrossRef]

Y. Tanabe, M. Muto, M. Fiebig, and E. Hanamura, Phys. Rev. B 58, 8654 (1998).
[CrossRef]

1996

R. Stolle, G. Marowsky, E. Schwarzberg, and G. Berkovic, Appl. Phys. B 63, 491 (1996).
[CrossRef]

1995

M. Fiebig, D. Fröhlich, G. Sluyterman v. L., and R. V. Pisarev, Appl. Phys. Lett. 66, 2906 (1995).
[CrossRef]

1994

M. Fiebig, D. Fröhlich, B. B. Krichevtsov, and R. V. Pisarev, Phys. Rev. Lett. 73, 2127 (1994).
[CrossRef] [PubMed]

1986

K. Kemnitz, K. Bhattacharyya, J. M. Hicks, G. R. Pinto, K. B. Eisenthal, and T. F. Heinz, Chem. Phys. Lett. 131, 285 (1986).

1965

R. K. Chang, J. Ducuing, and N. Bloembergen, Phys. Rev. Lett. 15, 6 (1965).
[CrossRef]

Berkovic, G.

R. Stolle, G. Marowsky, E. Schwarzberg, and G. Berkovic, Appl. Phys. B 63, 491 (1996).
[CrossRef]

Bhattacharyya, K.

K. Kemnitz, K. Bhattacharyya, J. M. Hicks, G. R. Pinto, K. B. Eisenthal, and T. F. Heinz, Chem. Phys. Lett. 131, 285 (1986).

Bloembergen, N.

R. K. Chang, J. Ducuing, and N. Bloembergen, Phys. Rev. Lett. 15, 6 (1965).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

Chang, R. K.

R. K. Chang, J. Ducuing, and N. Bloembergen, Phys. Rev. Lett. 15, 6 (1965).
[CrossRef]

Chen, J.

de Boer, A. P.

K. J. Veenstra, A. V. Petukhov, A. P. de Boer, and Th. Rasing, Phys. Rev. B 58, R16020 (1998).
[CrossRef]

Ducuing, J.

R. K. Chang, J. Ducuing, and N. Bloembergen, Phys. Rev. Lett. 15, 6 (1965).
[CrossRef]

Eisenthal, K. B.

K. Kemnitz, K. Bhattacharyya, J. M. Hicks, G. R. Pinto, K. B. Eisenthal, and T. F. Heinz, Chem. Phys. Lett. 131, 285 (1986).

Fiebig, M.

Y. Tanabe, M. Muto, M. Fiebig, and E. Hanamura, Phys. Rev. B 58, 8654 (1998).
[CrossRef]

M. Fiebig, D. Fröhlich, St. Leute, and R. V. Pisarev, Appl. Phys. B 66, 265 (1998).
[CrossRef]

M. Fiebig, D. Fröhlich, G. Sluyterman v. L., and R. V. Pisarev, Appl. Phys. Lett. 66, 2906 (1995).
[CrossRef]

M. Fiebig, D. Fröhlich, B. B. Krichevtsov, and R. V. Pisarev, Phys. Rev. Lett. 73, 2127 (1994).
[CrossRef] [PubMed]

Fröhlich, D.

D. Fröhlich, Th. Kiefer, St. Leute, and Th. Lottermoser, Appl. Phys. B 68, 465 (1999).
[CrossRef]

D. Fröhlich, St. Leute, V. V. Pavlov, and R. V. Pisarev, Phys. Rev. Lett. 81, 3239 (1998).
[CrossRef]

M. Fiebig, D. Fröhlich, St. Leute, and R. V. Pisarev, Appl. Phys. B 66, 265 (1998).
[CrossRef]

M. Fiebig, D. Fröhlich, G. Sluyterman v. L., and R. V. Pisarev, Appl. Phys. Lett. 66, 2906 (1995).
[CrossRef]

M. Fiebig, D. Fröhlich, B. B. Krichevtsov, and R. V. Pisarev, Phys. Rev. Lett. 73, 2127 (1994).
[CrossRef] [PubMed]

Hanamura, E.

Y. Tanabe, M. Muto, M. Fiebig, and E. Hanamura, Phys. Rev. B 58, 8654 (1998).
[CrossRef]

Heinz, T. F.

K. Kemnitz, K. Bhattacharyya, J. M. Hicks, G. R. Pinto, K. B. Eisenthal, and T. F. Heinz, Chem. Phys. Lett. 131, 285 (1986).

Hicks, J. M.

K. Kemnitz, K. Bhattacharyya, J. M. Hicks, G. R. Pinto, K. B. Eisenthal, and T. F. Heinz, Chem. Phys. Lett. 131, 285 (1986).

Kemnitz, K.

K. Kemnitz, K. Bhattacharyya, J. M. Hicks, G. R. Pinto, K. B. Eisenthal, and T. F. Heinz, Chem. Phys. Lett. 131, 285 (1986).

Kiefer, Th.

D. Fröhlich, Th. Kiefer, St. Leute, and Th. Lottermoser, Appl. Phys. B 68, 465 (1999).
[CrossRef]

Krichevtsov, B. B.

M. Fiebig, D. Fröhlich, B. B. Krichevtsov, and R. V. Pisarev, Phys. Rev. Lett. 73, 2127 (1994).
[CrossRef] [PubMed]

Leute, St.

D. Fröhlich, Th. Kiefer, St. Leute, and Th. Lottermoser, Appl. Phys. B 68, 465 (1999).
[CrossRef]

D. Fröhlich, St. Leute, V. V. Pavlov, and R. V. Pisarev, Phys. Rev. Lett. 81, 3239 (1998).
[CrossRef]

M. Fiebig, D. Fröhlich, St. Leute, and R. V. Pisarev, Appl. Phys. B 66, 265 (1998).
[CrossRef]

Lottermoser, Th.

D. Fröhlich, Th. Kiefer, St. Leute, and Th. Lottermoser, Appl. Phys. B 68, 465 (1999).
[CrossRef]

Machida, S.

Marowsky, G.

R. Stolle, G. Marowsky, E. Schwarzberg, and G. Berkovic, Appl. Phys. B 63, 491 (1996).
[CrossRef]

Muto, M.

Y. Tanabe, M. Muto, M. Fiebig, and E. Hanamura, Phys. Rev. B 58, 8654 (1998).
[CrossRef]

Pavlov, V. V.

D. Fröhlich, St. Leute, V. V. Pavlov, and R. V. Pisarev, Phys. Rev. Lett. 81, 3239 (1998).
[CrossRef]

Petukhov, A. V.

K. J. Veenstra, A. V. Petukhov, A. P. de Boer, and Th. Rasing, Phys. Rev. B 58, R16020 (1998).
[CrossRef]

Pinto, G. R.

K. Kemnitz, K. Bhattacharyya, J. M. Hicks, G. R. Pinto, K. B. Eisenthal, and T. F. Heinz, Chem. Phys. Lett. 131, 285 (1986).

Pisarev, R. V.

M. Fiebig, D. Fröhlich, St. Leute, and R. V. Pisarev, Appl. Phys. B 66, 265 (1998).
[CrossRef]

D. Fröhlich, St. Leute, V. V. Pavlov, and R. V. Pisarev, Phys. Rev. Lett. 81, 3239 (1998).
[CrossRef]

M. Fiebig, D. Fröhlich, G. Sluyterman v. L., and R. V. Pisarev, Appl. Phys. Lett. 66, 2906 (1995).
[CrossRef]

M. Fiebig, D. Fröhlich, B. B. Krichevtsov, and R. V. Pisarev, Phys. Rev. Lett. 73, 2127 (1994).
[CrossRef] [PubMed]

Rasing, Th.

K. J. Veenstra, A. V. Petukhov, A. P. de Boer, and Th. Rasing, Phys. Rev. B 58, R16020 (1998).
[CrossRef]

Schwarzberg, E.

R. Stolle, G. Marowsky, E. Schwarzberg, and G. Berkovic, Appl. Phys. B 63, 491 (1996).
[CrossRef]

Sluyterman v. L., G.

M. Fiebig, D. Fröhlich, G. Sluyterman v. L., and R. V. Pisarev, Appl. Phys. Lett. 66, 2906 (1995).
[CrossRef]

Stolle, R.

R. Stolle, G. Marowsky, E. Schwarzberg, and G. Berkovic, Appl. Phys. B 63, 491 (1996).
[CrossRef]

Tanabe, Y.

Y. Tanabe, M. Muto, M. Fiebig, and E. Hanamura, Phys. Rev. B 58, 8654 (1998).
[CrossRef]

Veenstra, K. J.

K. J. Veenstra, A. V. Petukhov, A. P. de Boer, and Th. Rasing, Phys. Rev. B 58, R16020 (1998).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

Yamanoto, Y.

Appl. Phys. B

R. Stolle, G. Marowsky, E. Schwarzberg, and G. Berkovic, Appl. Phys. B 63, 491 (1996).
[CrossRef]

M. Fiebig, D. Fröhlich, St. Leute, and R. V. Pisarev, Appl. Phys. B 66, 265 (1998).
[CrossRef]

D. Fröhlich, Th. Kiefer, St. Leute, and Th. Lottermoser, Appl. Phys. B 68, 465 (1999).
[CrossRef]

Appl. Phys. Lett.

M. Fiebig, D. Fröhlich, G. Sluyterman v. L., and R. V. Pisarev, Appl. Phys. Lett. 66, 2906 (1995).
[CrossRef]

Chem. Phys. Lett.

K. Kemnitz, K. Bhattacharyya, J. M. Hicks, G. R. Pinto, K. B. Eisenthal, and T. F. Heinz, Chem. Phys. Lett. 131, 285 (1986).

Opt. Lett.

Phys. Rev. B

Y. Tanabe, M. Muto, M. Fiebig, and E. Hanamura, Phys. Rev. B 58, 8654 (1998).
[CrossRef]

K. J. Veenstra, A. V. Petukhov, A. P. de Boer, and Th. Rasing, Phys. Rev. B 58, R16020 (1998).
[CrossRef]

Phys. Rev. Lett.

R. K. Chang, J. Ducuing, and N. Bloembergen, Phys. Rev. Lett. 15, 6 (1965).
[CrossRef]

M. Fiebig, D. Fröhlich, B. B. Krichevtsov, and R. V. Pisarev, Phys. Rev. Lett. 73, 2127 (1994).
[CrossRef] [PubMed]

D. Fröhlich, St. Leute, V. V. Pavlov, and R. V. Pisarev, Phys. Rev. Lett. 81, 3239 (1998).
[CrossRef]

Other

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of an interferogram according to relation (1) for ES=ER. ΔψSBC at the first maximum is equal to -δψr=ψR-ψSr.

Fig. 2
Fig. 2

Experimental setup: A, analyzer; CCD, CCD camera; L, lens; LPF, long-pass filter; OPO, optical parametric oscillator; SPF, short-pass filter; THG, third-harmonic generation; WP, half-wave plate; REF, reference.

Fig. 3
Fig. 3

Experimental result of phase measurements with a 100µm z-cut quartz crystal as the sample and a 500µm y-cut quartz crystal as reference. In (a) and (b) three interferograms measured simultaneously on different regions on the sample are shown. In (a) the distance between the two quartz crystals was 1 mm; in (b) it was 13 mm. Filled circles, experimental points; solid curves, fits to relation (1).

Fig. 4
Fig. 4

(a), (b) Domain pattern and (c) interference signal of YMnO3 at 6 K. In (a) and (b) the domain pattern is shown for ΔψSBC settings of -28° and +157°, respectively, as marked in the interferograms (c). The interferograms were taken at the positions outlined by squares in (a) and (b). Open squares and filled circles in (c) refer to the upper and lower outlined squares, respectively, in (a) and (b).

Fig. 5
Fig. 5

Experimental result for phase difference ΔψS=ψSr-ψSr between two different antiferromagnetic domains as a function of the SH energy. Filled circles, phase difference ΔψS between the domains. Dashed line, the expected phase difference of 180°. Solid curve, the χc spectrum of YMnO3.

Equations (1)

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ITotalrES2+ER2+2ESER×cosψSr-ψR+ΔψSBC.

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