Abstract

A macroscopic angular Goos–Hänchen effect at total reflection on curved interfaces is studied experimentally. The results are compared with the complex-angular-momentum model of quasi-critical scattering. An extremum in angular deflection, which has not yet been predicted by any theory other than exact Mie scattering computations, is identified at low size parameters.

© 1995 Optical Society of America

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References

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  1. H. K. V. Lotsch, Optik 32, 116 (1970); H. K. V. Lotsch, Optik 32, 189 (1970).
    [PubMed]
  2. F. Goos, H. Hänchen, Ann. Phys. (Leipzig) 1, 333 (1947); F. Goos, H. Lindberg-Hänchen, Ann. Phys. (Leipzig) 2, 87 (1949).
    [CrossRef]
  3. H. K. V. Lotsch, Optik 32, 299 (1971).
  4. F. Bretenaker, L. Dutriaux, A. Le Floch, Phys. Rev. Lett. 68, 931 (1992).
    [CrossRef] [PubMed]
  5. E. Pfleghaar, A. Marseille, A. Weis, Phys. Rev. Lett. 70, 2281 (1993).
    [CrossRef] [PubMed]
  6. H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge U. Press, Cambridge, 1992), Chap. 12, p. 156.
  7. N. Fiedler-Ferrari, H. M. Nussenzveig, W. J. Wiscombe, Phys. Rev. A 43, 1005 (1991).
    [CrossRef] [PubMed]
  8. P. L. Marston, J. L. Johnson, S. P. Love, B. L. Brim, J. Opt. Soc. Am. 73, 1658 (1983); D. S. Langley, P. L. Marston, Appl. Opt. 23, 1044 (1984).
    [CrossRef] [PubMed]
  9. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 15, p. 300.
  10. D. Q. Chowdhury, D. H. Leach, R. K. Chang, J. Opt. Soc. Am. A 11, 1110 (1994).
    [CrossRef]
  11. J. C. Knight, H. S. T. Driver, G. N. Robertson, J. Opt. Soc. Am. B 11, 2046 (1994).
    [CrossRef]

1994 (2)

1993 (1)

E. Pfleghaar, A. Marseille, A. Weis, Phys. Rev. Lett. 70, 2281 (1993).
[CrossRef] [PubMed]

1992 (1)

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

1991 (1)

N. Fiedler-Ferrari, H. M. Nussenzveig, W. J. Wiscombe, Phys. Rev. A 43, 1005 (1991).
[CrossRef] [PubMed]

1983 (1)

1971 (1)

H. K. V. Lotsch, Optik 32, 299 (1971).

1970 (1)

H. K. V. Lotsch, Optik 32, 116 (1970); H. K. V. Lotsch, Optik 32, 189 (1970).
[PubMed]

1947 (1)

F. Goos, H. Hänchen, Ann. Phys. (Leipzig) 1, 333 (1947); F. Goos, H. Lindberg-Hänchen, Ann. Phys. (Leipzig) 2, 87 (1949).
[CrossRef]

Bretenaker, F.

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

Brim, B. L.

Chang, R. K.

Chowdhury, D. Q.

Driver, H. S. T.

Dutriaux, L.

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

Fiedler-Ferrari, N.

N. Fiedler-Ferrari, H. M. Nussenzveig, W. J. Wiscombe, Phys. Rev. A 43, 1005 (1991).
[CrossRef] [PubMed]

Goos, F.

F. Goos, H. Hänchen, Ann. Phys. (Leipzig) 1, 333 (1947); F. Goos, H. Lindberg-Hänchen, Ann. Phys. (Leipzig) 2, 87 (1949).
[CrossRef]

Hänchen, H.

F. Goos, H. Hänchen, Ann. Phys. (Leipzig) 1, 333 (1947); F. Goos, H. Lindberg-Hänchen, Ann. Phys. (Leipzig) 2, 87 (1949).
[CrossRef]

Johnson, J. L.

Knight, J. C.

Le Floch, A.

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

Leach, D. H.

Lotsch, H. K. V.

H. K. V. Lotsch, Optik 32, 299 (1971).

H. K. V. Lotsch, Optik 32, 116 (1970); H. K. V. Lotsch, Optik 32, 189 (1970).
[PubMed]

Love, S. P.

Marseille, A.

E. Pfleghaar, A. Marseille, A. Weis, Phys. Rev. Lett. 70, 2281 (1993).
[CrossRef] [PubMed]

Marston, P. L.

Nussenzveig, H. M.

N. Fiedler-Ferrari, H. M. Nussenzveig, W. J. Wiscombe, Phys. Rev. A 43, 1005 (1991).
[CrossRef] [PubMed]

H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge U. Press, Cambridge, 1992), Chap. 12, p. 156.

Pfleghaar, E.

E. Pfleghaar, A. Marseille, A. Weis, Phys. Rev. Lett. 70, 2281 (1993).
[CrossRef] [PubMed]

Robertson, G. N.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 15, p. 300.

Weis, A.

E. Pfleghaar, A. Marseille, A. Weis, Phys. Rev. Lett. 70, 2281 (1993).
[CrossRef] [PubMed]

Wiscombe, W. J.

N. Fiedler-Ferrari, H. M. Nussenzveig, W. J. Wiscombe, Phys. Rev. A 43, 1005 (1991).
[CrossRef] [PubMed]

Ann. Phys. (1)

F. Goos, H. Hänchen, Ann. Phys. (Leipzig) 1, 333 (1947); F. Goos, H. Lindberg-Hänchen, Ann. Phys. (Leipzig) 2, 87 (1949).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Optik (2)

H. K. V. Lotsch, Optik 32, 299 (1971).

H. K. V. Lotsch, Optik 32, 116 (1970); H. K. V. Lotsch, Optik 32, 189 (1970).
[PubMed]

Phys. Rev. A (1)

N. Fiedler-Ferrari, H. M. Nussenzveig, W. J. Wiscombe, Phys. Rev. A 43, 1005 (1991).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

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

E. Pfleghaar, A. Marseille, A. Weis, Phys. Rev. Lett. 70, 2281 (1993).
[CrossRef] [PubMed]

Other (2)

H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge U. Press, Cambridge, 1992), Chap. 12, p. 156.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 15, p. 300.

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Figures (3)

Fig. 1
Fig. 1

Geometry of the experiment. The scattering of an incident wave by a cylindrical air bubble is shown. The axis of the cylinder is perpendicular to the plane of the figure. Two typical TE and TM rays are shown tunneling through the low-index medium and thus experiencing an angular Goos–Hänchen deflection. θTE and θTM are the scattering angles.

Fig. 2
Fig. 2

Experimental (left column) and theoretical (right column) TE and TM scattering spectra for three values of β: (a) β = 220, (b) β = 140, and (c) β = 50. The values of β used to compute the theoretical spectra are adjusted to fit the experimental spectra: (a) β = 205, (b) β = 145, and (c) β = 48. The arrows indicate the positions of the extrema, showing the shift between the two polarizations. The critical scattering angle is θt = 94.5°

Fig. 3
Fig. 3

Evolution of the angular shift δθGH versus 1/(β∊1/2). Solid line, CAM theory [Eq. (4)]. Open triangles and circles, shifts measured on the experimental spectra for the positions of the first valley and the second peak, respectively (see the arrows in Fig. 2). Filled triangles and circles, shifts observed on the spectra computed from Eqs. (1)(3) for the positions of the first valley and the second peak, respectively. The dashed curves are guides to the eye.

Equations (5)

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I j = ( 4 / π β ) T j ( m , β , θ ) 2 ,
T j = p = 0 p a j , p cos ( p θ ) ,
a TE , p = m J p ( m β ) J p ( β ) - J p ( m β ) J p ( β ) m J p ( m β ) H p ( β ) - J p ( m β ) H p ( β ) ,
a TM , p = J p ( m β ) J p ( β ) - m J p ( m β ) J p ( β ) J p ( m β ) H p ( β ) - m J p ( m β ) H p ( β ) .
δ θ GH = ( 2 M ) 1 / 2 m 3 / 2 1 β 1 / 2 ,

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