Abstract

An original approach to directly measuring the Goos–Hänchen longitudinal shift between TE and TM polarization states during a total internal reflection is introduced. The technique is based on the modulation of the polarization state of a laser by an electro-optic modulator combined with a precise measurement of the resulting spatial displacement with a position-sensitive detector. This method presents many advantages over other techniques and allows measurements at different wavelengths over a broad range for the incident angle.

© 2002 Optical Society of America

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References

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  1. F. Goos and H. Hänchen, Ann. Phys. (Leipzig) 1, 333 (1947).
    [CrossRef]
  2. F. Goos and H. Hänchen, Ann. Phys. (Leipzig) 2, 87 (1949).
  3. K. Artmann, Ann. Phys. (Leipzig) 2, 87 (1948).
    [CrossRef]
  4. R. H. Renard, J. Opt. Soc. Am. 54, 1190 (1964).
  5. Y. Levy and C. Imbert, Opt. Commun. 13, 43 (1975).
    [CrossRef]
  6. J. P. Hugonin and R. Petit, J. Opt. 8, 73 (1977).
    [CrossRef]
  7. F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
    [CrossRef] [PubMed]
  8. B. Chéron, J. Hamel, and H. Gilles, Bull. Union Physiciens 93, 37 (1999).
  9. H. Gilles, B. Chéron, and J. Hamel, Opt. Commun. 190, 179 (2001).
    [CrossRef]
  10. Optical Components Guide (Melles-Griot, Irvine, Calif., 1999).
  11. F. I. Fedorov, Dokl. Akad. Nauk SSR 105, 465 (1955).
  12. C. Imbert, Phys. Rev. D 5, 787 (1972).
    [CrossRef]

2001

H. Gilles, B. Chéron, and J. Hamel, Opt. Commun. 190, 179 (2001).
[CrossRef]

1999

B. Chéron, J. Hamel, and H. Gilles, Bull. Union Physiciens 93, 37 (1999).

1992

F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef] [PubMed]

1977

J. P. Hugonin and R. Petit, J. Opt. 8, 73 (1977).
[CrossRef]

1975

Y. Levy and C. Imbert, Opt. Commun. 13, 43 (1975).
[CrossRef]

1972

C. Imbert, Phys. Rev. D 5, 787 (1972).
[CrossRef]

1964

1955

F. I. Fedorov, Dokl. Akad. Nauk SSR 105, 465 (1955).

1949

F. Goos and H. Hänchen, Ann. Phys. (Leipzig) 2, 87 (1949).

1948

K. Artmann, Ann. Phys. (Leipzig) 2, 87 (1948).
[CrossRef]

1947

F. Goos and H. Hänchen, Ann. Phys. (Leipzig) 1, 333 (1947).
[CrossRef]

Artmann, K.

K. Artmann, Ann. Phys. (Leipzig) 2, 87 (1948).
[CrossRef]

Bretenaker, F.

F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef] [PubMed]

Chéron, B.

H. Gilles, B. Chéron, and J. Hamel, Opt. Commun. 190, 179 (2001).
[CrossRef]

B. Chéron, J. Hamel, and H. Gilles, Bull. Union Physiciens 93, 37 (1999).

Dutriaux, L.

F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef] [PubMed]

Fedorov, F. I.

F. I. Fedorov, Dokl. Akad. Nauk SSR 105, 465 (1955).

Gilles, H.

H. Gilles, B. Chéron, and J. Hamel, Opt. Commun. 190, 179 (2001).
[CrossRef]

B. Chéron, J. Hamel, and H. Gilles, Bull. Union Physiciens 93, 37 (1999).

Goos, F.

F. Goos and H. Hänchen, Ann. Phys. (Leipzig) 2, 87 (1949).

F. Goos and H. Hänchen, Ann. Phys. (Leipzig) 1, 333 (1947).
[CrossRef]

Hamel, J.

H. Gilles, B. Chéron, and J. Hamel, Opt. Commun. 190, 179 (2001).
[CrossRef]

B. Chéron, J. Hamel, and H. Gilles, Bull. Union Physiciens 93, 37 (1999).

Hänchen, H.

F. Goos and H. Hänchen, Ann. Phys. (Leipzig) 2, 87 (1949).

F. Goos and H. Hänchen, Ann. Phys. (Leipzig) 1, 333 (1947).
[CrossRef]

Hugonin, J. P.

J. P. Hugonin and R. Petit, J. Opt. 8, 73 (1977).
[CrossRef]

Imbert, C.

Y. Levy and C. Imbert, Opt. Commun. 13, 43 (1975).
[CrossRef]

C. Imbert, Phys. Rev. D 5, 787 (1972).
[CrossRef]

Le Floch, A.

F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef] [PubMed]

Levy, Y.

Y. Levy and C. Imbert, Opt. Commun. 13, 43 (1975).
[CrossRef]

Petit, R.

J. P. Hugonin and R. Petit, J. Opt. 8, 73 (1977).
[CrossRef]

Renard, R. H.

Ann. Phys. (Leipzig)

F. Goos and H. Hänchen, Ann. Phys. (Leipzig) 1, 333 (1947).
[CrossRef]

F. Goos and H. Hänchen, Ann. Phys. (Leipzig) 2, 87 (1949).

K. Artmann, Ann. Phys. (Leipzig) 2, 87 (1948).
[CrossRef]

Bull. Union Physiciens

B. Chéron, J. Hamel, and H. Gilles, Bull. Union Physiciens 93, 37 (1999).

Dokl. Akad. Nauk SSR

F. I. Fedorov, Dokl. Akad. Nauk SSR 105, 465 (1955).

J. Opt.

J. P. Hugonin and R. Petit, J. Opt. 8, 73 (1977).
[CrossRef]

J. Opt. Soc. Am.

Opt. Commun.

Y. Levy and C. Imbert, Opt. Commun. 13, 43 (1975).
[CrossRef]

H. Gilles, B. Chéron, and J. Hamel, Opt. Commun. 190, 179 (2001).
[CrossRef]

Phys. Rev. D

C. Imbert, Phys. Rev. D 5, 787 (1972).
[CrossRef]

Phys. Rev. Lett.

F. Bretenaker, A. Le Floch, and L. Dutriaux, Phys. Rev. Lett. 68, 931 (1992).
[CrossRef] [PubMed]

Other

Optical Components Guide (Melles-Griot, Irvine, Calif., 1999).

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Figures (4)

Fig. 1
Fig. 1

Structure of a PSD.

Fig. 2
Fig. 2

Experimental setup: LD, laser diode (λ=0.67 µm or 1.083 µm); L, collimating lens; M, plane mirror; EOM, electro-optic modulator; P, total reflexion prism.

Fig. 3
Fig. 3

Typical intensity modulation signals obtained on the PSD for i just above the critical angle i=41.5° and λ=0.67 µm.

Fig. 4
Fig. 4

Difference between the TM and TE longitudinal GH shift versus the angle of incidence.

Equations (3)

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

x=l2×I1-I2I1+I2,
V1=V01+vGH2 Rect2πft, V2=V02-vGH2 Rect2πft,
dTE=λπsinin2 sin2i-11/2, dTM=dTE1+n2sin2i-11/2,

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