Abstract

The Goos–Hänchen shift for a light beam totally reflected on the external interface of a dielectric thin film deposited on a high-index substrate can be strongly enhanced through some specific incidence angles corresponding to the leaky guided modes into the layer. Because the resonant eigenstates are polarization dependent, it has been possible to observe such resonance with an experimental setup based on a periodic modulation of the polarization state combined with position-sensitive detection. Classical models usually used for a single interface (Artmann’s model based on phase argument and Renard’s model based on an energetic interpretation) have been re-adapted to describe the behavior of the entire layer. Good agreement is obtained between theory and experimental results.

© 2005 Optical Society of America

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  1. F. Goos and H. Hänchen, "Ein neuer und fundamentaler Versuch zur Totalreflexion," Ann. Phys. 1, 333-346 (1947).
  2. F. Goos and H. Hänchen, "Neumessung des Strahlversetzungeffktes bei Totalreflexion," Ann. Phys. 2, 87-102 (1949).
  3. C. Imbert, "L'effet inertial de spin du photon: théorie et preuve expérimentale," Nouv. Rev. Opt. Appl. 3, 199-208 (1972).
    [CrossRef]
  4. F. Bretenaker, A. Le Floch, and L. Dutriaux, "Direct measurement of the optical Goos-Hänchen effect in lasers," Phys. Rev. Lett. 68, 931-933 (1992).
    [CrossRef]
  5. H. Gilles, S. Girard, and 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]
  6. F. I. Fedorov, "K Teopnn IIOJIHOrO OTpaxehnr," Dokl. Akad. Nauk SSSR 105, 465-468 (1955).
  7. F. Pillon, H. Gilles, and S. Girard, "Experimental observation of the Imbert-Fedorov transverse displacement after a single total reflection," Appl. Opt. 43, 1863-1869 (2004).
    [CrossRef] [PubMed]
  8. Y. Levy and C. Imbert, "Amplification des déplacements à la réflexion totale," Opt. Commun. 13, 43-47 (1975).
    [CrossRef]
  9. O. Costa de Beauregard, C. Imbert, and Y. Lévy, "Observation of shifts in total reflection of a light beam by a multilayered structure," Phys. Rev. D 15, 3553-3562 (1977).
    [CrossRef]
  10. R. Kaiser, Y. Levy, J. Fleming, S. Muniz, and V. S. Bagnato, "Resonances in a single thin dielectric layer: enhancement of the Goos-Hanchen shift," Pure Appl. Opt. 5, 891-898 (1996).
    [CrossRef]
  11. R. Kaiser, Y. Lévy, N. Vansteenkiste, A. Aspect, W. Seifert, D. Leipold, and J. Mlynek, "Resonant enhancement of evanescent waves with a thin dielectric waveguide," Opt. Commun. 104, 234-240 (1994).
    [CrossRef]
  12. K. Artmann, "Berechnung der Seitenversetzung des totalreflektieren Strahles," Ann. Phys. 2, 87-102 (1948).
  13. R. H. Renard, "Total reflection: A new evaluation of the Goos-Hänchen shift," J. Opt. Soc. Am. 54, 1190-1197 (1964).
    [CrossRef]
  14. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).
    [CrossRef]
  15. P. R. Berman, "Goos-Hänchen shift in negatively refractive media," Phys. Rev. E 66, 067603-1/3 (2002).
    [CrossRef]
  16. I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, "Giant Goos-Hänchen effect at the reflection from left-handed metamaterials," Appl. Phys. Lett. 83, 2713-2715 (2003).
    [CrossRef]

2004

2003

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, "Giant Goos-Hänchen effect at the reflection from left-handed metamaterials," Appl. Phys. Lett. 83, 2713-2715 (2003).
[CrossRef]

2002

1996

R. Kaiser, Y. Levy, J. Fleming, S. Muniz, and V. S. Bagnato, "Resonances in a single thin dielectric layer: enhancement of the Goos-Hanchen shift," Pure Appl. Opt. 5, 891-898 (1996).
[CrossRef]

1994

R. Kaiser, Y. Lévy, N. Vansteenkiste, A. Aspect, W. Seifert, D. Leipold, and J. Mlynek, "Resonant enhancement of evanescent waves with a thin dielectric waveguide," Opt. Commun. 104, 234-240 (1994).
[CrossRef]

1992

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

1977

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

1975

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

1972

C. Imbert, "L'effet inertial de spin du photon: théorie et preuve expérimentale," Nouv. Rev. Opt. Appl. 3, 199-208 (1972).
[CrossRef]

1964

1955

F. I. Fedorov, "K Teopnn IIOJIHOrO OTpaxehnr," Dokl. Akad. Nauk SSSR 105, 465-468 (1955).

1949

F. Goos and H. Hänchen, "Neumessung des Strahlversetzungeffktes bei Totalreflexion," Ann. Phys. 2, 87-102 (1949).

1948

K. Artmann, "Berechnung der Seitenversetzung des totalreflektieren Strahles," Ann. Phys. 2, 87-102 (1948).

1947

F. Goos and H. Hänchen, "Ein neuer und fundamentaler Versuch zur Totalreflexion," Ann. Phys. 1, 333-346 (1947).

Artmann, K.

K. Artmann, "Berechnung der Seitenversetzung des totalreflektieren Strahles," Ann. Phys. 2, 87-102 (1948).

Aspect, A.

R. Kaiser, Y. Lévy, N. Vansteenkiste, A. Aspect, W. Seifert, D. Leipold, and J. Mlynek, "Resonant enhancement of evanescent waves with a thin dielectric waveguide," Opt. Commun. 104, 234-240 (1994).
[CrossRef]

Bagnato, V. S.

R. Kaiser, Y. Levy, J. Fleming, S. Muniz, and V. S. Bagnato, "Resonances in a single thin dielectric layer: enhancement of the Goos-Hanchen shift," Pure Appl. Opt. 5, 891-898 (1996).
[CrossRef]

Berman, P. R.

P. R. Berman, "Goos-Hänchen shift in negatively refractive media," Phys. Rev. E 66, 067603-1/3 (2002).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).
[CrossRef]

Bretenaker, F.

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

Costa de Beauregard, O.

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

Dutriaux, L.

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

Fedorov, F. I.

F. I. Fedorov, "K Teopnn IIOJIHOrO OTpaxehnr," Dokl. Akad. Nauk SSSR 105, 465-468 (1955).

Fleming, J.

R. Kaiser, Y. Levy, J. Fleming, S. Muniz, and V. S. Bagnato, "Resonances in a single thin dielectric layer: enhancement of the Goos-Hanchen shift," Pure Appl. Opt. 5, 891-898 (1996).
[CrossRef]

Gilles, H.

Girard, S.

Goos, F.

F. Goos and H. Hänchen, "Neumessung des Strahlversetzungeffktes bei Totalreflexion," Ann. Phys. 2, 87-102 (1949).

F. Goos and H. Hänchen, "Ein neuer und fundamentaler Versuch zur Totalreflexion," Ann. Phys. 1, 333-346 (1947).

Hamel, J.

Hänchen, H.

F. Goos and H. Hänchen, "Neumessung des Strahlversetzungeffktes bei Totalreflexion," Ann. Phys. 2, 87-102 (1949).

F. Goos and H. Hänchen, "Ein neuer und fundamentaler Versuch zur Totalreflexion," Ann. Phys. 1, 333-346 (1947).

Imbert, C.

O. Costa de Beauregard, C. Imbert, and 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 and C. Imbert, "Amplification des déplacements à la réflexion totale," Opt. Commun. 13, 43-47 (1975).
[CrossRef]

C. Imbert, "L'effet inertial de spin du photon: théorie et preuve expérimentale," Nouv. Rev. Opt. Appl. 3, 199-208 (1972).
[CrossRef]

Kaiser, R.

R. Kaiser, Y. Levy, J. Fleming, S. Muniz, and V. S. Bagnato, "Resonances in a single thin dielectric layer: enhancement of the Goos-Hanchen shift," Pure Appl. Opt. 5, 891-898 (1996).
[CrossRef]

R. Kaiser, Y. Lévy, N. Vansteenkiste, A. Aspect, W. Seifert, D. Leipold, and J. Mlynek, "Resonant enhancement of evanescent waves with a thin dielectric waveguide," Opt. Commun. 104, 234-240 (1994).
[CrossRef]

Kivshar, Y. S.

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, "Giant Goos-Hänchen effect at the reflection from left-handed metamaterials," Appl. Phys. Lett. 83, 2713-2715 (2003).
[CrossRef]

Le Floch, A.

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

Leipold, D.

R. Kaiser, Y. Lévy, N. Vansteenkiste, A. Aspect, W. Seifert, D. Leipold, and J. Mlynek, "Resonant enhancement of evanescent waves with a thin dielectric waveguide," Opt. Commun. 104, 234-240 (1994).
[CrossRef]

Levy, Y.

R. Kaiser, Y. Levy, J. Fleming, S. Muniz, and V. S. Bagnato, "Resonances in a single thin dielectric layer: enhancement of the Goos-Hanchen shift," Pure Appl. Opt. 5, 891-898 (1996).
[CrossRef]

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

Lévy, Y.

R. Kaiser, Y. Lévy, N. Vansteenkiste, A. Aspect, W. Seifert, D. Leipold, and J. Mlynek, "Resonant enhancement of evanescent waves with a thin dielectric waveguide," Opt. Commun. 104, 234-240 (1994).
[CrossRef]

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

Mlynek, J.

R. Kaiser, Y. Lévy, N. Vansteenkiste, A. Aspect, W. Seifert, D. Leipold, and J. Mlynek, "Resonant enhancement of evanescent waves with a thin dielectric waveguide," Opt. Commun. 104, 234-240 (1994).
[CrossRef]

Muniz, S.

R. Kaiser, Y. Levy, J. Fleming, S. Muniz, and V. S. Bagnato, "Resonances in a single thin dielectric layer: enhancement of the Goos-Hanchen shift," Pure Appl. Opt. 5, 891-898 (1996).
[CrossRef]

Pillon, F.

Renard, R. H.

Seifert, W.

R. Kaiser, Y. Lévy, N. Vansteenkiste, A. Aspect, W. Seifert, D. Leipold, and J. Mlynek, "Resonant enhancement of evanescent waves with a thin dielectric waveguide," Opt. Commun. 104, 234-240 (1994).
[CrossRef]

Shadrivov, I. V.

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, "Giant Goos-Hänchen effect at the reflection from left-handed metamaterials," Appl. Phys. Lett. 83, 2713-2715 (2003).
[CrossRef]

Vansteenkiste, N.

R. Kaiser, Y. Lévy, N. Vansteenkiste, A. Aspect, W. Seifert, D. Leipold, and J. Mlynek, "Resonant enhancement of evanescent waves with a thin dielectric waveguide," Opt. Commun. 104, 234-240 (1994).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).
[CrossRef]

Zharov, A. A.

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, "Giant Goos-Hänchen effect at the reflection from left-handed metamaterials," Appl. Phys. Lett. 83, 2713-2715 (2003).
[CrossRef]

Ann. Phys.

F. Goos and H. Hänchen, "Ein neuer und fundamentaler Versuch zur Totalreflexion," Ann. Phys. 1, 333-346 (1947).

F. Goos and H. Hänchen, "Neumessung des Strahlversetzungeffktes bei Totalreflexion," Ann. Phys. 2, 87-102 (1949).

K. Artmann, "Berechnung der Seitenversetzung des totalreflektieren Strahles," Ann. Phys. 2, 87-102 (1948).

Appl. Opt.

Appl. Phys. Lett.

I. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, "Giant Goos-Hänchen effect at the reflection from left-handed metamaterials," Appl. Phys. Lett. 83, 2713-2715 (2003).
[CrossRef]

Dokl. Akad. Nauk SSSR

F. I. Fedorov, "K Teopnn IIOJIHOrO OTpaxehnr," Dokl. Akad. Nauk SSSR 105, 465-468 (1955).

J. Opt. Soc. Am.

Nouv. Rev. Opt. Appl.

C. Imbert, "L'effet inertial de spin du photon: théorie et preuve expérimentale," Nouv. Rev. Opt. Appl. 3, 199-208 (1972).
[CrossRef]

Opt. Commun.

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

R. Kaiser, Y. Lévy, N. Vansteenkiste, A. Aspect, W. Seifert, D. Leipold, and J. Mlynek, "Resonant enhancement of evanescent waves with a thin dielectric waveguide," Opt. Commun. 104, 234-240 (1994).
[CrossRef]

Opt. Lett.

Phys. Rev. D

O. Costa de Beauregard, C. Imbert, and 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. E

P. R. Berman, "Goos-Hänchen shift in negatively refractive media," Phys. Rev. E 66, 067603-1/3 (2002).
[CrossRef]

Phys. Rev. Lett.

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

Pure Appl. Opt.

R. Kaiser, Y. Levy, J. Fleming, S. Muniz, and V. S. Bagnato, "Resonances in a single thin dielectric layer: enhancement of the Goos-Hanchen shift," Pure Appl. Opt. 5, 891-898 (1996).
[CrossRef]

Other

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Schematic representation of the Goos–Hänchen effect as a pure spatial shift for the reflected light beam. This simplified representation is correct when the incident beam has low divergence.

Fig. 2
Fig. 2

Size of the incident beam d adjusted exactly such that the spatial shift corresponds to an incident beam that completely penetrates into the lower-refractive-index medium as an evanescent wave (Renard’s model).

Fig. 3
Fig. 3

Schematic representation of the thin layer deposited on a substrate: (a) the prismatic structure of the substrate, (b) the reflected wave that can be calculated with an approach similar to the one usually used in Fabry-Perot interferometer with the multiple reflections into the thin film.

Fig. 4
Fig. 4

Calculated electric field distribution inside the guiding structure for TE 0 and TE 1 modes.

Fig. 5
Fig. 5

Calculated GH shift by Artmann’s or Renard’s models versus the incidence angle for two polarization eigenstates: TE mode, TM mode.

Fig. 6
Fig. 6

Experimental setup used to measure the GH and IF shifts on a thin dielectric layer.

Fig. 7
Fig. 7

Difference between the GH shifts for TE and TM polarization states versus the incidence angle on the thin film: comparison between theory (solid curve) and experiment (filled squares).

Fig. 8
Fig. 8

Longitudinal shift measured versus the angular orientation of the QWP located in front of the LCV; measured for i 1 = 48.5 ° corresponding to the first resonance peak.

Fig. 9
Fig. 9

Difference between the IF shift for σ + and σ polarization states versus the incidence angle on the thin film: comparison between theory (solid curve) and experiment (filled squares).

Fig. 10
Fig. 10

The two contributions for the Imbert-Fedorov shift attributed, respectively, to (a) the multiple reflections inside the thin film (dashed curve), (b) the evanescent wave along the film–air interface (dotted curve). The solid curve represents the sum of the two contributions and should be compared with the experimental results.

Equations (28)

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L GH = λ 2 π n 1 cos i 1 ( d Φ d i 1 ) ,
L GH = 1 Σ rx 0 Σ tz d x ,
r tot = r 12 + t 12 t 21 r 23 exp ( j φ ) 1 r 21 r 23 exp ( j φ ) = r tot exp ( j Φ ) ,
φ = 2 π n 2 λ 2 h cos i 2 .
Δ L GH = λ 2 π n 1 cos i 1 [ ( d Φ TE d i 1 ) ( d Φ TM d i 1 ) ] ,
L GH = 1 Σ rx ( h 0 Σ 2 z d x + h Σ 3 z d x ) ,
Δ L GH = L GH TE L GH TM ,
L GH TE = tan i 1 h 0 U cos α x + V sin α x 2 d x + t eva 2 δ 2 r tot 2 ,
L GH TM = tan i 1 h 0 U cos α x + V sin α x 2 d x + t eva 2 δ 2 r tot 2 .
L IF = 1 Σ rx ( h 0 Σ 2 y d x + h Σ 3 y d x ) .
Σ r = n 1 E 0 2 2 μ 0 c r tot 2 ( cos i 1 0 sin i 1 ) ,
Σ 3 = n 3 E 0 2 2 μ 0 c t eva 2 exp [ 2 ( x + h ) δ ] ( 0 0 n 1 n 3 sin i 1 ) ,
k 2 d = ( α 0 β ) ,
k 2 a = ( α 0 β ) ,
E 2 = E 0 ( U cos α x + V sin α x ) × exp [ j ( ω t β z ) ] × ( 0 1 0 ) .
B 2 = { E 0 c n 2 sin i 2 ( U cos α x + V sin α x ) × exp [ j ( ω t β z ) ] 0 j E 0 c n 2 cos i 2 ( U cos α x + V sin α x ) × exp [ j ( ω t β z ) ] } .
E 2 y ( h ) = E 3 y ( h ) ,
B 2 z ( h ) = B 3 z ( h ) ,
U = t eva { cos α h + n 3 n 2 cos i 2 [ ( n 1 n 3 sin i 1 ) 2 1 ] 1 2 × sin α h } ,
V = t eva { sin α h + n 3 n 2 cos i 2 [ ( n 1 n 3 sin i 1 ) 2 1 ] 1 2 × cos α h } .
Σ 2 = E 0 2 2 μ 0 c n 1 sin i 1 ( U cos α z + V sin α z ) 2 × ( 0 0 1 ) .
B 2 = n 2 E 0 c ( U cos α x + V sin α x ) × exp [ j ( ω t β z ) ] × ( 0 1 0 ) .
E 2 = { E 0 ( U cos α x + V sin α x ) n 1 n 2 sin i 1 × exp [ j ( ω t β z ) ] 0 j E 0 cos i 2 ( U cos α x + V sin α x ) × exp [ j ( ω t β z ) ] } .
E 2 z ( h ) = E 3 z ( h ) ,
B 2 y ( h ) = B 3 y ( h ) ,
U = t eva { n 3 n 2 cos α h + 1 cos i 2 [ ( n 1 n 3 sin i 1 ) 2 1 ] 1 2 × sin α h } ,
V = t eva { n 3 n 2 sin α h + 1 cos i 2 [ ( n 1 n 3 sin i 1 ) 1 ] 1 2 × cos α h } .
Σ 2 = E 0 2 2 μ 0 c n 1 sin i 1 ( U cos α z + V sin α z ) 2 × ( 0 0 1 ) .

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