Abstract

We describe a simple experimental setup with which to observe the transverse shift—also known as the Imbert-Fedorov effect—that circularly or elliptically polarized optical beams undergo after a single total internal reflection on a dielectric plane. A comparison between a theoretical model based on the conservation of energy and experimental measurements shows good agreement simultaneously for longitudinal (Goos-Hänchen) and transverse (Imbert-Fedorov) displacements.

© 2004 Optical Society of America

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References

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  1. H. K. Lotsch, “Reflection and refraction of a beam of light at a plane interface,” J. Opt. Soc. Am. 58, 551–561 (1968).
    [CrossRef]
  2. F. Goos, H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. (Leipzig) 1, 333–346 (1947).
  3. F. Goos, H. Hänchen, “Neumessung des Strahlversetzungeffktes bei Totalreflexion,” Ann. Phys. (Leipzig) 2, 87–102 (1949).
  4. See, for example, C. Imbert, “L’effet inertial de spin du photon: théorie et preuve expérimentale,” Nouv. Rev. Opt. Appl. 3, 199–208 (1972), and references therein.
  5. Y. Levy, C. Imbert, “Amplification des déplacements à la réflexion totale,” Opt. Commun. 13, 43–47 (1975).
    [CrossRef]
  6. O. Costa de Beauregard, C. Imbert, Y. Lévy, “Observation of shifts in total reflection of a light beam by a multilayered structure,” Phys. Rev. D 15, 3553–3562 (1977).
    [CrossRef]
  7. J. J. Cowan, B. Anicin, “Longitudinal and transverse displacements of a bounded microwave beam at total internal reflection,” J. Opt. Soc. Am. 67, 1307–1314 (1977).
    [CrossRef]
  8. F. Bretenaker, A. Le Floch, L. Dutriaux, “Direct measurement of the optical Goos-Hänchen effect in lasers,” Phys. Rev. Lett. 68, 931–933 (1992).
    [CrossRef] [PubMed]
  9. H. Gilles, S. Girard, J. Hamel, “A simple measurement technique of the Goos-Hänchen effect using polarization modulation and position sensitive detector,” Opt. Lett. 27, 1421–1423 (2002).
    [CrossRef]
  10. F. I. Fedorov, “Theory of total reflection,” Dokl. Akad. Nauk SSR 105, 465–468 (1955).
  11. M. Born, E. Wolf, Principles of Optics7th ed. (Cambridge U. Press, Cambridge, 1999).
  12. R. H. Renard, “Total reflection: a new evaluation of the Goos-Hänchen shift,” J. Opt. Soc. Am. 54, 1190–1197 (1964).
    [CrossRef]
  13. K. Artmann, “Berechnung der Seitenversetzung des totalreflektieren Strahles,” Ann. Phys. (Leipzig) 2, 87–102 (1948).

2002

1992

F. Bretenaker, A. Le Floch, L. Dutriaux, “Direct measurement of the optical Goos-Hänchen effect in lasers,” Phys. Rev. Lett. 68, 931–933 (1992).
[CrossRef] [PubMed]

1977

O. Costa de Beauregard, C. Imbert, Y. Lévy, “Observation of shifts in total reflection of a light beam by a multilayered structure,” Phys. Rev. D 15, 3553–3562 (1977).
[CrossRef]

J. J. Cowan, B. Anicin, “Longitudinal and transverse displacements of a bounded microwave beam at total internal reflection,” J. Opt. Soc. Am. 67, 1307–1314 (1977).
[CrossRef]

1975

Y. Levy, C. Imbert, “Amplification des déplacements à la réflexion totale,” Opt. Commun. 13, 43–47 (1975).
[CrossRef]

1972

See, for example, C. Imbert, “L’effet inertial de spin du photon: théorie et preuve expérimentale,” Nouv. Rev. Opt. Appl. 3, 199–208 (1972), and references therein.

1968

1964

1955

F. I. Fedorov, “Theory of total reflection,” Dokl. Akad. Nauk SSR 105, 465–468 (1955).

1949

F. Goos, H. Hänchen, “Neumessung des Strahlversetzungeffktes bei Totalreflexion,” Ann. Phys. (Leipzig) 2, 87–102 (1949).

1948

K. Artmann, “Berechnung der Seitenversetzung des totalreflektieren Strahles,” Ann. Phys. (Leipzig) 2, 87–102 (1948).

1947

F. Goos, H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. (Leipzig) 1, 333–346 (1947).

Anicin, B.

Artmann, K.

K. Artmann, “Berechnung der Seitenversetzung des totalreflektieren Strahles,” Ann. Phys. (Leipzig) 2, 87–102 (1948).

Born, M.

M. Born, E. Wolf, Principles of Optics7th ed. (Cambridge U. Press, Cambridge, 1999).

Bretenaker, F.

F. Bretenaker, A. Le Floch, L. Dutriaux, “Direct measurement of the optical Goos-Hänchen effect in lasers,” Phys. Rev. Lett. 68, 931–933 (1992).
[CrossRef] [PubMed]

Costa de Beauregard, O.

O. Costa de Beauregard, C. Imbert, Y. Lévy, “Observation of shifts in total reflection of a light beam by a multilayered structure,” Phys. Rev. D 15, 3553–3562 (1977).
[CrossRef]

Cowan, J. J.

Dutriaux, L.

F. Bretenaker, A. Le Floch, L. Dutriaux, “Direct measurement of the optical Goos-Hänchen effect in lasers,” Phys. Rev. Lett. 68, 931–933 (1992).
[CrossRef] [PubMed]

Fedorov, F. I.

F. I. Fedorov, “Theory of total reflection,” Dokl. Akad. Nauk SSR 105, 465–468 (1955).

Gilles, H.

Girard, S.

Goos, F.

F. Goos, H. Hänchen, “Neumessung des Strahlversetzungeffktes bei Totalreflexion,” Ann. Phys. (Leipzig) 2, 87–102 (1949).

F. Goos, H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. (Leipzig) 1, 333–346 (1947).

Hamel, J.

Hänchen, H.

F. Goos, H. Hänchen, “Neumessung des Strahlversetzungeffktes bei Totalreflexion,” Ann. Phys. (Leipzig) 2, 87–102 (1949).

F. Goos, H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. (Leipzig) 1, 333–346 (1947).

Imbert, C.

O. Costa de Beauregard, C. Imbert, Y. Lévy, “Observation of shifts in total reflection of a light beam by a multilayered structure,” Phys. Rev. D 15, 3553–3562 (1977).
[CrossRef]

Y. Levy, C. Imbert, “Amplification des déplacements à la réflexion totale,” Opt. Commun. 13, 43–47 (1975).
[CrossRef]

See, for example, C. Imbert, “L’effet inertial de spin du photon: théorie et preuve expérimentale,” Nouv. Rev. Opt. Appl. 3, 199–208 (1972), and references therein.

Le Floch, A.

F. Bretenaker, A. Le Floch, L. Dutriaux, “Direct measurement of the optical Goos-Hänchen effect in lasers,” Phys. Rev. Lett. 68, 931–933 (1992).
[CrossRef] [PubMed]

Levy, Y.

Y. Levy, C. Imbert, “Amplification des déplacements à la réflexion totale,” Opt. Commun. 13, 43–47 (1975).
[CrossRef]

Lévy, Y.

O. Costa de Beauregard, C. Imbert, Y. Lévy, “Observation of shifts in total reflection of a light beam by a multilayered structure,” Phys. Rev. D 15, 3553–3562 (1977).
[CrossRef]

Lotsch, H. K.

Renard, R. H.

Wolf, E.

M. Born, E. Wolf, Principles of Optics7th ed. (Cambridge U. Press, Cambridge, 1999).

Ann. Phys. (Leipzig)

F. Goos, H. Hänchen, “Ein neuer und fundamentaler Versuch zur Totalreflexion,” Ann. Phys. (Leipzig) 1, 333–346 (1947).

F. Goos, H. Hänchen, “Neumessung des Strahlversetzungeffktes bei Totalreflexion,” Ann. Phys. (Leipzig) 2, 87–102 (1949).

K. Artmann, “Berechnung der Seitenversetzung des totalreflektieren Strahles,” Ann. Phys. (Leipzig) 2, 87–102 (1948).

Dokl. Akad. Nauk SSR

F. I. Fedorov, “Theory of total reflection,” Dokl. Akad. Nauk SSR 105, 465–468 (1955).

J. Opt. Soc. Am.

Nouv. Rev. Opt. Appl.

See, for example, C. Imbert, “L’effet inertial de spin du photon: théorie et preuve expérimentale,” Nouv. Rev. Opt. Appl. 3, 199–208 (1972), and references therein.

Opt. Commun.

Y. Levy, C. Imbert, “Amplification des déplacements à la réflexion totale,” Opt. Commun. 13, 43–47 (1975).
[CrossRef]

Opt. Lett.

Phys. Rev. D

O. Costa de Beauregard, C. Imbert, Y. Lévy, “Observation of shifts in total reflection of a light beam by a multilayered structure,” Phys. Rev. D 15, 3553–3562 (1977).
[CrossRef]

Phys. Rev. Lett.

F. Bretenaker, A. Le Floch, L. Dutriaux, “Direct measurement of the optical Goos-Hänchen effect in lasers,” Phys. Rev. Lett. 68, 931–933 (1992).
[CrossRef] [PubMed]

Other

M. Born, E. Wolf, Principles of Optics7th ed. (Cambridge U. Press, Cambridge, 1999).

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Figures (6)

Fig. 1
Fig. 1

GH and IF spatial shifts at total reflection.

Fig. 2
Fig. 2

Orientation of the neutral axes o, ordinary; e, for extraordinary) of the retardation plate compared with the linear polarization states TE and TM.

Fig. 3
Fig. 3

Illustration of Renard’s model.

Fig. 4
Fig. 4

Schematic representation of the experimental setup: L, lens.

Fig. 5
Fig. 5

Longitudinal (filled squares, experimental measurements; darker solid curve, theory) and transverse (filled circles, experimental measurements; lighter solid curve, theory) shifts measured for incident angle i 1 = 41.65°.

Fig. 6
Fig. 6

Illustration of the beam displacement in the boundary plane versus the incident polarization states (A, TE-TM; B: σ+-; C, σ-+).

Equations (23)

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i1=arcsinn2/n1.
Etr, t=tE0 exp-x/δ×exp+jkt sin i2z-ωt,
δ=λ2πn12sini12-n221/2.
Σr=n1E022μ0c×-cosi1ux+sini1uz.
TE stateΣt=A×Buy+Cuz,
TM stateΣt=A×-Buy+Cuz,
A=n1E022μ0cexp-2xδsini1,B=2n2 sin2i1-11/2Rett*sin ϕ+jcos ϕ-1cos2 θ-sin2 θcos θ sin θ,C=2×cos2 θ sin2 θ×1-cos ϕ×|t|2-|t|2+|t|2,
Σr×d=-0 Σtzdx.
Lz=1Σrx-0 Σtzdx.
Ly=1Σrx-0 Σtydx,
LzTE=δ tani12|t|2+2cosθsinθ2×|t|2-|t|21-cosϕ,
LzTM=δ tani12|t|2+2cosθsinθ2×|t|2-|t|21-cosϕ,
LyTE=+δ tani1n2 sini12-11/2×sinθcosθRett*sin ϕ+jcos ϕ-1(cos2 θ-sin2 θ),
LyTM=-δ tani1(n2 sini12-11/2×sinθcosθRet×t*sin ϕ+jcos ϕ-1(cos2 θ-sin2 θ),
TE state:r=sini2-i1sini2+i1=n1 cos i1-n2 cos i2n1 cos i1+n2 cos i2,t=2 cos i1 sin i2sini1+i2,
TM state:r=tani2-i1tani2+i1=n1 cos i2-n2 cos i1n1 cos i2+n2 cos i1,t=2 cos i1 sin i2sini1+i2cosi1-i2.
Ei=E0 expjkicos i1x+sin i1z×cos θ sin θ1-expjϕsin i1sin2 θ+expjϕcos2 θ-cos θ sin θ1-expjϕcos i1,Bi=n1c E0 expjkicos i1x+sin i1z×-sin2 θ+expjϕcos2 θsin i1cos θ sin θ1-expjϕsin2 θ+expjϕcos2 θcos i1.
Er=E0 expjkr-cos i1x+sin i1z×r cos θ sin θ1-expjϕsin i1rsin2 θ+expjϕcos2 θr cos θ sin θ1-expjϕcos i1,Br=n1c E0 expjkr-cos i1x+sin i1z×-rsin2 θ+expjϕcos2 θsin i1r cos θ sin θ1-expjϕ-rsin2 θ+expjϕcos2 θcos i1.
Et=E0 exp-xδexpjktsin i2z×t cos θ sin θ1-expjϕsin i2tsin2 θ+expjϕcos2 θ-t cos θ sin θ1-expjϕcos i2,Bt=n2c E0 exp-xδexpjktsin i2z×-tsin2 θ+expjϕcos2 θsin i2t cos θ sin θ1-expjϕtsin2 θ+expjϕcos2 θcos i2.
Ei=E0 expjkicos i1x+sin i1z×cos2 θ+expjϕsin2 θsin i1cos θ sin θ1-expjϕ-cos2 θ+expjϕsin2 θcos i1,Bi=n1c E0 expjkicos i1x+sin i1z×-cos θ sin θ1-expjϕsin i1cos2 θ+expjϕsin2 θcos θ sin θ1-expjϕcos i1.
Er=E0 expjkr-cos i1x+sin i1z×rcos2 θ+expjϕsin2 θsin i1r cos θ sin θ1-expjϕrcos2 θ+expjϕsin2 θcos i1,Br=n1c E0 expjkr-cos i1x+sin i1z×-r cos θ sin θ1-expjϕsin i1rcos2 θ+expjϕsin2 θ-r cos θ sin θ1-expjϕcos i1.
Et=E0 exp-xδexpjktsin i2z×tcos2 θ+expjϕsin2 θsin i2t cos θ sin θ1-expjϕ-tcos2 θ+expjϕsin2 θcos i2,Bt=n2c E0 exp-xδexpjktsin i2z×-t cos θ sin θ1-expjϕsin i2tcos2 θ+expjϕsin2 θt cos θ sin θ1-expjϕcos i2.
Σ=12ReEB*μ0,

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