Abstract

It is known that orbital angular momentum (OAM) couples the Goos–Hänchen and Imbert–Fedorov shifts. Here, we present the first study of these shifts when the OAM-endowed LG,p beams have higher-order radial mode index (p>0). We show theoretically and experimentally that the angular shifts are enhanced by p while the positional shifts are not.

© 2012 Optical Society of America

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References

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  1. A. Aiello and J. P. Woerdman, Opt. Lett. 33, 1437 (2008).
    [CrossRef]
  2. C.-F. Li, Phys. Rev. A 76, 15 (2006).
  3. F. Goos and H. Hanchen, Ann. Phys. 436, 1 (1947).
  4. F. I. Fedorov, Dokl. Akad. Nauk SSSR 105, 465 (1955).
  5. C. Imbert, Phys. Rev. D 5, 787 (1972).
    [CrossRef]
  6. M. Merano, A. Aiello, G. W. ’t Hooft, M. P. Van Exter, E. R. Eliel, and J. P. Woerdman, Opt. Express 15, 15928 (2007).
    [CrossRef]
  7. N. Hermosa, A. M. Nugrowati, A. Aiello, and J. P. Woerdman, Opt. Lett. 36, 3200 (2011).
    [CrossRef]
  8. J.-M. Ménard, A. Mattacchione, H. Van Driel, C. Hautmann, and M. Betz, Phys. Rev. B 82, 1 (2010).
  9. P. R. Berman, Phys. Rev. E 66 (2002).
  10. A. Aiello, M. Merano, and J. P. Woerdman, Phys. Rev. A 80, 4 (2009).
    [CrossRef]
  11. M. Merano, A. Aiello, M. P. Van Exter, and J. P. Woerdman, Nat. Photon. 3, 337 (2009).
  12. K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, Opt. Lett. 34, 389 (2009).
    [CrossRef]
  13. M. Merano, N. Hermosa, J. Woerdman, and A. Aiello, Phys. Rev. A 82, 023817 (2010).
    [CrossRef]
  14. A. Aiello and J. Woerdman, Opt. Lett. 36, 543 (2011).
    [CrossRef]
  15. R. Dasgupta and P. Gupta, Opt. Commun. 257, 91 (2006).
    [CrossRef]
  16. D. Golla and S. D. Gupta, Pramana J. Phys. 76, 603 (2011).
  17. N. Hermosa, M. Merano, A. Aiello, and J. P. Woerdman, in Proc. SPIE 7950, 79500F (2011).
  18. A. Siegman, Lasers (University Science Books, 1986).
  19. S. Kennedy, M. Szabo, H. Teslow, J. Porterfield, and E. Abraham, Phys. Rev. A 66, 1 (2002).
    [CrossRef]
  20. N. Matsumoto, T. Ando, T. Inoue, Y. Ohtake, N. Fukuchi, and T. Hara, J. Opt. Soc. Am. A 25, 1642 (2008).
    [CrossRef]
  21. V. Garces-Chavez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, Phys. Rev. Lett. 91, 093602 (2003).
    [CrossRef]
  22. J. Tempere, J. T. Devreese, and E. R. I. Abraham, Phys. Rev. A 64, 23603 (2001).
    [CrossRef]
  23. S. Chelkowski, S. Hild, and A. Freise, Phys. Rev. D 79, 12 (2009).
    [CrossRef]
  24. P. Fulda, K. Kokeyama, S. Chelkowski, and A. Freise, Phys. Rev. D 82, 1 (2010).
    [CrossRef]
  25. M. Granata, C. Buy, R. Ward, and M. Barsuglia, Phys. Rev. Lett. 105, 231102 (2010).
    [CrossRef]
  26. N. Hermosa, A. Aiello, and J. P. Woerdman, Opt. Lett. 36, 409 (2011).
    [CrossRef]
  27. If a centroid detector is used instead of a median detector, 2ℓ⟶ℓ and ξ(ℓ,p)=2p+|ℓ|+1.
  28. M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
  29. L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef]
  30. M. Merano, N. Hermosa, A. Aiello, and J. P. Woerdman, Opt. Lett. 35, 3562 (2010).
    [CrossRef]

2011 (5)

2010 (5)

M. Merano, N. Hermosa, A. Aiello, and J. P. Woerdman, Opt. Lett. 35, 3562 (2010).
[CrossRef]

P. Fulda, K. Kokeyama, S. Chelkowski, and A. Freise, Phys. Rev. D 82, 1 (2010).
[CrossRef]

M. Granata, C. Buy, R. Ward, and M. Barsuglia, Phys. Rev. Lett. 105, 231102 (2010).
[CrossRef]

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

J.-M. Ménard, A. Mattacchione, H. Van Driel, C. Hautmann, and M. Betz, Phys. Rev. B 82, 1 (2010).

2009 (4)

A. Aiello, M. Merano, and J. P. Woerdman, Phys. Rev. A 80, 4 (2009).
[CrossRef]

M. Merano, A. Aiello, M. P. Van Exter, and J. P. Woerdman, Nat. Photon. 3, 337 (2009).

K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, Opt. Lett. 34, 389 (2009).
[CrossRef]

S. Chelkowski, S. Hild, and A. Freise, Phys. Rev. D 79, 12 (2009).
[CrossRef]

2008 (2)

2007 (1)

2006 (2)

R. Dasgupta and P. Gupta, Opt. Commun. 257, 91 (2006).
[CrossRef]

C.-F. Li, Phys. Rev. A 76, 15 (2006).

2003 (1)

V. Garces-Chavez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

2002 (2)

S. Kennedy, M. Szabo, H. Teslow, J. Porterfield, and E. Abraham, Phys. Rev. A 66, 1 (2002).
[CrossRef]

P. R. Berman, Phys. Rev. E 66 (2002).

2001 (1)

J. Tempere, J. T. Devreese, and E. R. I. Abraham, Phys. Rev. A 64, 23603 (2001).
[CrossRef]

1993 (1)

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).

1992 (1)

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

1972 (1)

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

1955 (1)

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

1947 (1)

F. Goos and H. Hanchen, Ann. Phys. 436, 1 (1947).

Abraham, E.

S. Kennedy, M. Szabo, H. Teslow, J. Porterfield, and E. Abraham, Phys. Rev. A 66, 1 (2002).
[CrossRef]

Abraham, E. R. I.

J. Tempere, J. T. Devreese, and E. R. I. Abraham, Phys. Rev. A 64, 23603 (2001).
[CrossRef]

Aiello, A.

Allen, L.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Ando, T.

Barsuglia, M.

M. Granata, C. Buy, R. Ward, and M. Barsuglia, Phys. Rev. Lett. 105, 231102 (2010).
[CrossRef]

Beijersbergen, M.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Beijersbergen, M. W.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).

Berman, P. R.

P. R. Berman, Phys. Rev. E 66 (2002).

Betz, M.

J.-M. Ménard, A. Mattacchione, H. Van Driel, C. Hautmann, and M. Betz, Phys. Rev. B 82, 1 (2010).

Bliokh, K. Y.

Buy, C.

M. Granata, C. Buy, R. Ward, and M. Barsuglia, Phys. Rev. Lett. 105, 231102 (2010).
[CrossRef]

Chelkowski, S.

P. Fulda, K. Kokeyama, S. Chelkowski, and A. Freise, Phys. Rev. D 82, 1 (2010).
[CrossRef]

S. Chelkowski, S. Hild, and A. Freise, Phys. Rev. D 79, 12 (2009).
[CrossRef]

Dasgupta, R.

R. Dasgupta and P. Gupta, Opt. Commun. 257, 91 (2006).
[CrossRef]

Devreese, J. T.

J. Tempere, J. T. Devreese, and E. R. I. Abraham, Phys. Rev. A 64, 23603 (2001).
[CrossRef]

Dholakia, K.

V. Garces-Chavez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

Dultz, W.

V. Garces-Chavez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

Eliel, E. R.

Fedorov, F. I.

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

Freise, A.

P. Fulda, K. Kokeyama, S. Chelkowski, and A. Freise, Phys. Rev. D 82, 1 (2010).
[CrossRef]

S. Chelkowski, S. Hild, and A. Freise, Phys. Rev. D 79, 12 (2009).
[CrossRef]

Fukuchi, N.

Fulda, P.

P. Fulda, K. Kokeyama, S. Chelkowski, and A. Freise, Phys. Rev. D 82, 1 (2010).
[CrossRef]

Garces-Chavez, V.

V. Garces-Chavez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

Golla, D.

D. Golla and S. D. Gupta, Pramana J. Phys. 76, 603 (2011).

Goos, F.

F. Goos and H. Hanchen, Ann. Phys. 436, 1 (1947).

Granata, M.

M. Granata, C. Buy, R. Ward, and M. Barsuglia, Phys. Rev. Lett. 105, 231102 (2010).
[CrossRef]

Gupta, P.

R. Dasgupta and P. Gupta, Opt. Commun. 257, 91 (2006).
[CrossRef]

Gupta, S. D.

D. Golla and S. D. Gupta, Pramana J. Phys. 76, 603 (2011).

Hanchen, H.

F. Goos and H. Hanchen, Ann. Phys. 436, 1 (1947).

Hara, T.

Hautmann, C.

J.-M. Ménard, A. Mattacchione, H. Van Driel, C. Hautmann, and M. Betz, Phys. Rev. B 82, 1 (2010).

Hermosa, N.

Hild, S.

S. Chelkowski, S. Hild, and A. Freise, Phys. Rev. D 79, 12 (2009).
[CrossRef]

Hooft, G. W. ’t

Imbert, C.

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

Inoue, T.

Kennedy, S.

S. Kennedy, M. Szabo, H. Teslow, J. Porterfield, and E. Abraham, Phys. Rev. A 66, 1 (2002).
[CrossRef]

Kivshar, Y. S.

Kokeyama, K.

P. Fulda, K. Kokeyama, S. Chelkowski, and A. Freise, Phys. Rev. D 82, 1 (2010).
[CrossRef]

Li, C.-F.

C.-F. Li, Phys. Rev. A 76, 15 (2006).

Matsumoto, N.

Mattacchione, A.

J.-M. Ménard, A. Mattacchione, H. Van Driel, C. Hautmann, and M. Betz, Phys. Rev. B 82, 1 (2010).

McGloin, D.

V. Garces-Chavez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

Ménard, J.-M.

J.-M. Ménard, A. Mattacchione, H. Van Driel, C. Hautmann, and M. Betz, Phys. Rev. B 82, 1 (2010).

Merano, M.

N. Hermosa, M. Merano, A. Aiello, and J. P. Woerdman, in Proc. SPIE 7950, 79500F (2011).

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

M. Merano, N. Hermosa, A. Aiello, and J. P. Woerdman, Opt. Lett. 35, 3562 (2010).
[CrossRef]

M. Merano, A. Aiello, M. P. Van Exter, and J. P. Woerdman, Nat. Photon. 3, 337 (2009).

A. Aiello, M. Merano, and J. P. Woerdman, Phys. Rev. A 80, 4 (2009).
[CrossRef]

M. Merano, A. Aiello, G. W. ’t Hooft, M. P. Van Exter, E. R. Eliel, and J. P. Woerdman, Opt. Express 15, 15928 (2007).
[CrossRef]

Nugrowati, A. M.

Ohtake, Y.

Padgett, M. J.

V. Garces-Chavez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

Porterfield, J.

S. Kennedy, M. Szabo, H. Teslow, J. Porterfield, and E. Abraham, Phys. Rev. A 66, 1 (2002).
[CrossRef]

Schmitzer, H.

V. Garces-Chavez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

Shadrivov, I. V.

Siegman, A.

A. Siegman, Lasers (University Science Books, 1986).

Spreeuw, R.

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Szabo, M.

S. Kennedy, M. Szabo, H. Teslow, J. Porterfield, and E. Abraham, Phys. Rev. A 66, 1 (2002).
[CrossRef]

Tempere, J.

J. Tempere, J. T. Devreese, and E. R. I. Abraham, Phys. Rev. A 64, 23603 (2001).
[CrossRef]

Teslow, H.

S. Kennedy, M. Szabo, H. Teslow, J. Porterfield, and E. Abraham, Phys. Rev. A 66, 1 (2002).
[CrossRef]

van der Veen, H. E. L. O.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).

Van Driel, H.

J.-M. Ménard, A. Mattacchione, H. Van Driel, C. Hautmann, and M. Betz, Phys. Rev. B 82, 1 (2010).

Van Exter, M. P.

M. Merano, A. Aiello, M. P. Van Exter, and J. P. Woerdman, Nat. Photon. 3, 337 (2009).

M. Merano, A. Aiello, G. W. ’t Hooft, M. P. Van Exter, E. R. Eliel, and J. P. Woerdman, Opt. Express 15, 15928 (2007).
[CrossRef]

Ward, R.

M. Granata, C. Buy, R. Ward, and M. Barsuglia, Phys. Rev. Lett. 105, 231102 (2010).
[CrossRef]

Woerdman, J.

A. Aiello and J. Woerdman, Opt. Lett. 36, 543 (2011).
[CrossRef]

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

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

Woerdman, J. P.

N. Hermosa, A. M. Nugrowati, A. Aiello, and J. P. Woerdman, Opt. Lett. 36, 3200 (2011).
[CrossRef]

N. Hermosa, A. Aiello, and J. P. Woerdman, Opt. Lett. 36, 409 (2011).
[CrossRef]

N. Hermosa, M. Merano, A. Aiello, and J. P. Woerdman, in Proc. SPIE 7950, 79500F (2011).

M. Merano, N. Hermosa, A. Aiello, and J. P. Woerdman, Opt. Lett. 35, 3562 (2010).
[CrossRef]

M. Merano, A. Aiello, M. P. Van Exter, and J. P. Woerdman, Nat. Photon. 3, 337 (2009).

A. Aiello, M. Merano, and J. P. Woerdman, Phys. Rev. A 80, 4 (2009).
[CrossRef]

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

M. Merano, A. Aiello, G. W. ’t Hooft, M. P. Van Exter, E. R. Eliel, and J. P. Woerdman, Opt. Express 15, 15928 (2007).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).

Ann. Phys. (1)

F. Goos and H. Hanchen, Ann. Phys. 436, 1 (1947).

Dokl. Akad. Nauk SSSR (1)

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

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

Nat. Photon. (1)

M. Merano, A. Aiello, M. P. Van Exter, and J. P. Woerdman, Nat. Photon. 3, 337 (2009).

Opt. Commun. (2)

R. Dasgupta and P. Gupta, Opt. Commun. 257, 91 (2006).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).

Opt. Express (1)

Opt. Lett. (6)

Phys. Rev. A (6)

J. Tempere, J. T. Devreese, and E. R. I. Abraham, Phys. Rev. A 64, 23603 (2001).
[CrossRef]

S. Kennedy, M. Szabo, H. Teslow, J. Porterfield, and E. Abraham, Phys. Rev. A 66, 1 (2002).
[CrossRef]

L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef]

A. Aiello, M. Merano, and J. P. Woerdman, Phys. Rev. A 80, 4 (2009).
[CrossRef]

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

C.-F. Li, Phys. Rev. A 76, 15 (2006).

Phys. Rev. B (1)

J.-M. Ménard, A. Mattacchione, H. Van Driel, C. Hautmann, and M. Betz, Phys. Rev. B 82, 1 (2010).

Phys. Rev. D (3)

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

S. Chelkowski, S. Hild, and A. Freise, Phys. Rev. D 79, 12 (2009).
[CrossRef]

P. Fulda, K. Kokeyama, S. Chelkowski, and A. Freise, Phys. Rev. D 82, 1 (2010).
[CrossRef]

Phys. Rev. E (1)

P. R. Berman, Phys. Rev. E 66 (2002).

Phys. Rev. Lett. (2)

M. Granata, C. Buy, R. Ward, and M. Barsuglia, Phys. Rev. Lett. 105, 231102 (2010).
[CrossRef]

V. Garces-Chavez, D. McGloin, M. J. Padgett, W. Dultz, H. Schmitzer, and K. Dholakia, Phys. Rev. Lett. 91, 093602 (2003).
[CrossRef]

Pramana J. Phys. (1)

D. Golla and S. D. Gupta, Pramana J. Phys. 76, 603 (2011).

Proc. SPIE (1)

N. Hermosa, M. Merano, A. Aiello, and J. P. Woerdman, in Proc. SPIE 7950, 79500F (2011).

Other (2)

A. Siegman, Lasers (University Science Books, 1986).

If a centroid detector is used instead of a median detector, 2ℓ⟶ℓ and ξ(ℓ,p)=2p+|ℓ|+1.

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Figures (3)

Fig. 1.
Fig. 1.

Experimental setup used to measure the polarization differential beam shifts as a function of the incident angle. LCVR is the variable retarder. SWG is the square wave generator. QD is the quadrant detector. L1, L2, and L3 are lenses. More details are in the text.

Fig. 2.
Fig. 2.

Matrix element for different values of and p. The solid line is M12=2.

Fig. 3.
Fig. 3.

Matrix element M22 for different values of and p. The solid line is ξ(,p). A discussion of ξ(,p) is in the text.

Equations (7)

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

up(r,ϕ)=[2p!π(p+||)]1/2exp(iϕ)exp(i2r2ziL)×exp[i(2p+||+1)arctan(zL)]×1w(z)Lp(2r2w2(z))(2rw(z))||,
[ΔGHΘIFΔIFΘGH]=[12000ξ(,p)000012000ξ(,p)][ΔGHΘIFΔIFΘGH],
ΔGH0=wpIm(lnrpθ)+wsIm(lnrsθ),
ΘGH0=wpRe(lnrpθ)+wsRe(lnrsθ),
ΔIF0=apascotθRp2ap2+Rs2as2×[(Rp2+Rs2)sinη+2RpRssin(ηφp+φs)],
ΘIF0=apascotθRp2ap2+Rs2as2[(Rp2Rs2)cosη],
I±(,p)=a=0pb=0p(1)a+ba!b!(p+||pa)(p+||pb)×Γ(a+b+||+1±12).

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