Abstract

Stokes polarimetry measurements are carried out to calculate the spatial and angular Goos–Hänchen and Imbert–Fedorov shifts of a Gaussian beam reflected at glass–air interface, by measuring the phase difference between the TE and TM components and the amplitude of reflection. Variation of the beam shifts as a function of input beam polarization is also measured. The results obtained here are in good agreement with the theoretical predictions and the results obtained using a position sensitive detector. The polarimetric measurement method is accurate, independent of the intensity distribution of the beam, and opens up a new method to study the beam shift problem.

© 2014 Optical Society of America

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2014 (1)

2013 (4)

2012 (5)

A. Aiello, New J. Phys. 14, 013058 (2012).
[CrossRef]

S. A. Taya, E. J. El-Farram, and T. M. El-Agez, Int. J. Electon. Commun. (AEÜ) 66, 204 (2012).

J. B. Götte and M. R. Dennis, New J. Phys. 14, 073016 (2012).
[CrossRef]

C. Prajapati and D. Ranganathan, J. Opt. Soc. Am. A 29, 1377 (2012).
[CrossRef]

S. Pidishety, V. Kumar, and N. K. Viswanathan, Opt. Lett. 37, 4233 (2012).
[CrossRef]

2010 (1)

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, Phys. Rev. A 82, 023817 (2010).
[CrossRef]

2009 (2)

A. Aiello, M. Merano, and J. P. Woerdman, Opt. Lett. 34, 1207 (2009).
[CrossRef]

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photonics 3, 337 (2009).
[CrossRef]

2008 (1)

2007 (1)

H. W. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

2006 (2)

X. Yin and L. Hesselink, Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

K. Yu. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef]

2004 (1)

2001 (1)

W. Nasalski, Opt. Commun. 197, 217 (2001).
[CrossRef]

2000 (1)

1986 (1)

1985 (1)

1974 (1)

Y. M. Antar and W. M. Boerner, Can. J. Phys. 52, 962 (1974).

1973 (1)

J. W. Ra, H. L. Bertoni, and L. B. Felsen, SIAM J. Appl. Math. 24, 396 (1973).
[CrossRef]

1972 (1)

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

1971 (1)

1955 (1)

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

1948 (1)

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

1947 (1)

F. Goos and H. Hanchen, Ann. Phys. 436, 333 (1947).
[CrossRef]

Aiello, A.

K. Y. Bliokh and A. Aiello, J. Opt. 15, 014001 (2013).
[CrossRef]

A. Aiello, New J. Phys. 14, 013058 (2012).
[CrossRef]

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, Phys. Rev. A 82, 023817 (2010).
[CrossRef]

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photonics 3, 337 (2009).
[CrossRef]

A. Aiello, M. Merano, and J. P. Woerdman, Opt. Lett. 34, 1207 (2009).
[CrossRef]

A. Aiello and J. P. Woerdman, Opt. Lett. 33, 1437 (2008).
[CrossRef]

Antar, Y. M.

Y. M. Antar and W. M. Boerner, Can. J. Phys. 52, 962 (1974).

Artmann, K.

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

Baida, F. I.

Bertoni, H. L.

J. W. Ra, H. L. Bertoni, and L. B. Felsen, SIAM J. Appl. Math. 24, 396 (1973).
[CrossRef]

Bliokh, K. Y.

K. Y. Bliokh and A. Aiello, J. Opt. 15, 014001 (2013).
[CrossRef]

Bliokh, K. Yu.

K. Yu. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef]

Bliokh, Y. P.

K. Yu. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef]

Boerner, W. M.

Y. M. Antar and W. M. Boerner, Can. J. Phys. 52, 962 (1974).

Chan, C. C.

Cheng, F. C.

Dennis, M. R.

J. B. Götte and M. R. Dennis, New J. Phys. 14, 073016 (2012).
[CrossRef]

El-Agez, T. M.

S. A. Taya, E. J. El-Farram, and T. M. El-Agez, Int. J. Electon. Commun. (AEÜ) 66, 204 (2012).

El-Farram, E. J.

S. A. Taya, E. J. El-Farram, and T. M. El-Agez, Int. J. Electon. Commun. (AEÜ) 66, 204 (2012).

Fedorov, F. I.

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

Felsen, L. B.

J. W. Ra, H. L. Bertoni, and L. B. Felsen, SIAM J. Appl. Math. 24, 396 (1973).
[CrossRef]

Gilles, H.

Girard, S.

Goldstein, D. H.

D. H. Goldstein, Polarized Light, (CRC Press, 2011).

Goos, F.

F. Goos and H. Hanchen, Ann. Phys. 436, 333 (1947).
[CrossRef]

Götte, J. B.

J. B. Götte and M. R. Dennis, New J. Phys. 14, 073016 (2012).
[CrossRef]

Hanchen, H.

F. Goos and H. Hanchen, Ann. Phys. 436, 333 (1947).
[CrossRef]

Hermosa, N.

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, Phys. Rev. A 82, 023817 (2010).
[CrossRef]

Hesselink, L.

X. Yin and L. Hesselink, Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

Horowitz, B. R.

Imbert, C.

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

Jayaswal, G.

Joseph, J.

Kumar, V.

Labeke, D. V.

Lai, H. M.

Lee, H.

H. W. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

Liu, H. W.

H. W. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

Merano, M.

G. Jayaswal, G. Mistura, and M. Merano, Opt. Lett. 39, 2266 (2014).
[CrossRef]

G. Jayaswal, G. Mistura, and M. Merano, Opt. Lett. 38, 1232 (2013).
[CrossRef]

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, Phys. Rev. A 82, 023817 (2010).
[CrossRef]

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photonics 3, 337 (2009).
[CrossRef]

A. Aiello, M. Merano, and J. P. Woerdman, Opt. Lett. 34, 1207 (2009).
[CrossRef]

Mistura, G.

Nasalski, W.

W. Nasalski, Opt. Commun. 197, 217 (2001).
[CrossRef]

Pidishety, S.

Pillon, F.

Prajapati, C.

Ra, J. W.

J. W. Ra, H. L. Bertoni, and L. B. Felsen, SIAM J. Appl. Math. 24, 396 (1973).
[CrossRef]

Ranganathan, D.

Sun, C.

H. W. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

Tamir, C.

Tamir, T.

Tang, W. K.

Taya, S. A.

S. A. Taya, E. J. El-Farram, and T. M. El-Agez, Int. J. Electon. Commun. (AEÜ) 66, 204 (2012).

van Exter, M. P.

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photonics 3, 337 (2009).
[CrossRef]

Vigoureux, J.-M.

Viswanathan, N. K.

Woerdman, J. P.

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, Phys. Rev. A 82, 023817 (2010).
[CrossRef]

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photonics 3, 337 (2009).
[CrossRef]

A. Aiello, M. Merano, and J. P. Woerdman, Opt. Lett. 34, 1207 (2009).
[CrossRef]

A. Aiello and J. P. Woerdman, Opt. Lett. 33, 1437 (2008).
[CrossRef]

Xiong, Y.

H. W. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

Yin, X.

X. Yin and L. Hesselink, Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

Zhang, X.

H. W. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

Ann. Phys. (2)

F. Goos and H. Hanchen, Ann. Phys. 436, 333 (1947).
[CrossRef]

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

Appl. Opt. (1)

Appl. Phys. Lett. (1)

X. Yin and L. Hesselink, Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

Can. J. Phys. (1)

Y. M. Antar and W. M. Boerner, Can. J. Phys. 52, 962 (1974).

Dokl. Akad. Nauk SSSR (1)

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

Int. J. Electon. Commun. (AEÜ) (1)

S. A. Taya, E. J. El-Farram, and T. M. El-Agez, Int. J. Electon. Commun. (AEÜ) 66, 204 (2012).

J. Opt. (1)

K. Y. Bliokh and A. Aiello, J. Opt. 15, 014001 (2013).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Nat. Photonics (1)

M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, Nat. Photonics 3, 337 (2009).
[CrossRef]

New J. Phys. (2)

A. Aiello, New J. Phys. 14, 013058 (2012).
[CrossRef]

J. B. Götte and M. R. Dennis, New J. Phys. 14, 073016 (2012).
[CrossRef]

Opt. Commun. (1)

W. Nasalski, Opt. Commun. 197, 217 (2001).
[CrossRef]

Opt. Lett. (7)

Phys. Rev. A (1)

M. Merano, N. Hermosa, J. P. Woerdman, and A. Aiello, Phys. Rev. A 82, 023817 (2010).
[CrossRef]

Phys. Rev. D (1)

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

Phys. Rev. Lett. (1)

K. Yu. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
[CrossRef]

Science (1)

H. W. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[CrossRef]

SIAM J. Appl. Math. (1)

J. W. Ra, H. L. Bertoni, and L. B. Felsen, SIAM J. Appl. Math. 24, 396 (1973).
[CrossRef]

Other (1)

D. H. Goldstein, Polarized Light, (CRC Press, 2011).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the experimental setup. WP, half/quarter wave plate; QWP, quarter-wave-plate; P1 and P2, Glan–Thompson polarizer; D, detector; and P, BK7 prism.

Fig. 2.
Fig. 2.

Plot of angular GH shift for the TM-polarized beam obtained from theory (blue line) and from experimental measurement (red symbol).

Fig. 3.
Fig. 3.

(a) Experimental measurement and (c) theory simulation of the angular GH shift for TE (magenta); ±45° (black, red); RC/LC (blue, green) polarized beams. (b) Experimental measurement and (d) theory simulation of angular IF shift for TE and TM (magenta, orange) and ±45° (black, red) polarized beams.

Fig. 4.
Fig. 4.

Experimental measurement of (a) spatial GH shift and (b) spatial IF shift for TE and TM (magenta, orange), ±45° (black, red), and RC/LC (blue, green) polarized beams. Theory simulation of (c) spatial GH shift and (d) spatial IF shift.

Fig. 5.
Fig. 5.

Experimental measurement of (a) spatial GH shift and (b) spatial IF shift with varying input beam polarization from TE to TM passing through linear states (red) and through elliptical/circular states (black).

Equations (4)

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ϕsϕp=arctan(S3S2)η.
|rs|=S0+S12E0x2and|rp|=S0S12E0y2.
GH=λ2π|rs|2as2I(lnrsθi)+|rp|2ap2I(lnrpθi)|rs|2as2+|rp|2ap2+Zrk2L2|rs|2as2R(lnrsθi)+|rp|2ap2R(lnrpθi)|rs|2as2+|rp|2ap2
IF=λ2πapascotθi|rs|2as2+|rp|2ap2{(|rs|2+|rp|2)sinη+2|rs||rp|sin(η+ϕsϕp)}Zrk2L2asap(|rs|2|rp|2)cotθi|rs|2as2+|rp|2ap2cosη,

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