Abstract

Spin is an intrinsic property of the photon. A method for using an externally applied dc electric field to manipulate the transfer of spin angular momentum of light in an optically active medium is presented. To discuss this, we first develop a wave coupling theory of the mutual action of natural optical activity and the linear electro-optic effect. Besides being used for analyzing the electrically controlled transfer of spin angular momentum of light, the theory can also be used to describe the propagation of light traveling along an arbitrary direction in any optically active medium with an external dc electric field along an arbitrary direction.

© 2006 Optical Society of America

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References

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  1. J. H. Poynting, Proc. R. Soc. London, Ser. A 82, 560 (1909).
    [CrossRef]
  2. R. A. Beth, Phys. Rev. 50, 115 (1936).
    [CrossRef]
  3. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef] [PubMed]
  4. S. M. Barnett and L. Allen, Opt. Commun. 110, 670 (1994).
    [CrossRef]
  5. S. M. Barnett, J. Opt. B 4, S7 (2002).
    [CrossRef]
  6. B. Piccirillo, C. Toscano, F. Vetrano, and E. Santamato, Phys. Rev. Lett. 86, 2285 (2001).
    [CrossRef] [PubMed]
  7. W. G. Driscoll and W. Vaughan, Handbook of Optics (Kingsport, 1978), Sec. 10, p. 146.
  8. X. Yin, S. Zhang, and J. Wang, J. Opt. Soc. Am. B 22, 394 (2005).
    [CrossRef]
  9. A. Yariv, Quantum Electronics (Wiley, 1988).
  10. T. A. Maldonado and T. K. Gaylord, Appl. Opt. 27, 5051 (1988).
    [CrossRef] [PubMed]
  11. W. She and W. Lee, Opt. Commun. 195, 303 (2001).
    [CrossRef]
  12. D. Wu, H. Chen, and W. She, J. Opt. Soc. Am. B 22, 2366 (2005).
    [CrossRef]
  13. G. Zheng and W. She, Opt. Commun. (to be published), doi:10.1016/j.optcom.2006.07.068.
  14. G. Zheng, H. Wang, and W. She, Opt. Express 14, 5535 (2006).
    [CrossRef] [PubMed]
  15. L. D. Laudau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, 1984).
  16. S. Guo, Nonlinear Optics (Xidian U. Press, 1986).
  17. M. J. Padgett and L. Allen, Opt. Quantum Electron. 31, 1 (1999).
    [CrossRef]
  18. N. B. Simpson, L. Allen, and M. J. Padgett, presented at the Inaugural Meeting of the Scottish Chapter of LEOS (Glasgow University, Glasgow, 1996).

2006 (1)

2005 (2)

2002 (1)

S. M. Barnett, J. Opt. B 4, S7 (2002).
[CrossRef]

2001 (2)

B. Piccirillo, C. Toscano, F. Vetrano, and E. Santamato, Phys. Rev. Lett. 86, 2285 (2001).
[CrossRef] [PubMed]

W. She and W. Lee, Opt. Commun. 195, 303 (2001).
[CrossRef]

1999 (1)

M. J. Padgett and L. Allen, Opt. Quantum Electron. 31, 1 (1999).
[CrossRef]

1994 (1)

S. M. Barnett and L. Allen, Opt. Commun. 110, 670 (1994).
[CrossRef]

1992 (1)

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

1988 (1)

1936 (1)

R. A. Beth, Phys. Rev. 50, 115 (1936).
[CrossRef]

1909 (1)

J. H. Poynting, Proc. R. Soc. London, Ser. A 82, 560 (1909).
[CrossRef]

Allen, L.

M. J. Padgett and L. Allen, Opt. Quantum Electron. 31, 1 (1999).
[CrossRef]

S. M. Barnett and L. Allen, Opt. Commun. 110, 670 (1994).
[CrossRef]

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

N. B. Simpson, L. Allen, and M. J. Padgett, presented at the Inaugural Meeting of the Scottish Chapter of LEOS (Glasgow University, Glasgow, 1996).

Barnett, S. M.

S. M. Barnett, J. Opt. B 4, S7 (2002).
[CrossRef]

S. M. Barnett and L. Allen, Opt. Commun. 110, 670 (1994).
[CrossRef]

Beijersbergen, M. W.

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

Beth, R. A.

R. A. Beth, Phys. Rev. 50, 115 (1936).
[CrossRef]

Chen, H.

Driscoll, W. G.

W. G. Driscoll and W. Vaughan, Handbook of Optics (Kingsport, 1978), Sec. 10, p. 146.

Gaylord, T. K.

Guo, S.

S. Guo, Nonlinear Optics (Xidian U. Press, 1986).

Laudau, L. D.

L. D. Laudau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, 1984).

Lee, W.

W. She and W. Lee, Opt. Commun. 195, 303 (2001).
[CrossRef]

Lifshitz, E. M.

L. D. Laudau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, 1984).

Maldonado, T. A.

Padgett, M. J.

M. J. Padgett and L. Allen, Opt. Quantum Electron. 31, 1 (1999).
[CrossRef]

N. B. Simpson, L. Allen, and M. J. Padgett, presented at the Inaugural Meeting of the Scottish Chapter of LEOS (Glasgow University, Glasgow, 1996).

Piccirillo, B.

B. Piccirillo, C. Toscano, F. Vetrano, and E. Santamato, Phys. Rev. Lett. 86, 2285 (2001).
[CrossRef] [PubMed]

Poynting, J. H.

J. H. Poynting, Proc. R. Soc. London, Ser. A 82, 560 (1909).
[CrossRef]

Santamato, E.

B. Piccirillo, C. Toscano, F. Vetrano, and E. Santamato, Phys. Rev. Lett. 86, 2285 (2001).
[CrossRef] [PubMed]

She, W.

G. Zheng, H. Wang, and W. She, Opt. Express 14, 5535 (2006).
[CrossRef] [PubMed]

D. Wu, H. Chen, and W. She, J. Opt. Soc. Am. B 22, 2366 (2005).
[CrossRef]

W. She and W. Lee, Opt. Commun. 195, 303 (2001).
[CrossRef]

G. Zheng and W. She, Opt. Commun. (to be published), doi:10.1016/j.optcom.2006.07.068.

Simpson, N. B.

N. B. Simpson, L. Allen, and M. J. Padgett, presented at the Inaugural Meeting of the Scottish Chapter of LEOS (Glasgow University, Glasgow, 1996).

Spreeuw, R. J. C.

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

Toscano, C.

B. Piccirillo, C. Toscano, F. Vetrano, and E. Santamato, Phys. Rev. Lett. 86, 2285 (2001).
[CrossRef] [PubMed]

Vaughan, W.

W. G. Driscoll and W. Vaughan, Handbook of Optics (Kingsport, 1978), Sec. 10, p. 146.

Vetrano, F.

B. Piccirillo, C. Toscano, F. Vetrano, and E. Santamato, Phys. Rev. Lett. 86, 2285 (2001).
[CrossRef] [PubMed]

Wang, H.

Wang, J.

Woerdman, J. P.

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

Wu, D.

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, 1988).

Yin, X.

Zhang, S.

Zheng, G.

G. Zheng, H. Wang, and W. She, Opt. Express 14, 5535 (2006).
[CrossRef] [PubMed]

G. Zheng and W. She, Opt. Commun. (to be published), doi:10.1016/j.optcom.2006.07.068.

Appl. Opt. (1)

J. Opt. B (1)

S. M. Barnett, J. Opt. B 4, S7 (2002).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (2)

W. She and W. Lee, Opt. Commun. 195, 303 (2001).
[CrossRef]

S. M. Barnett and L. Allen, Opt. Commun. 110, 670 (1994).
[CrossRef]

Opt. Express (1)

Opt. Quantum Electron. (1)

M. J. Padgett and L. Allen, Opt. Quantum Electron. 31, 1 (1999).
[CrossRef]

Phys. Rev. (1)

R. A. Beth, Phys. Rev. 50, 115 (1936).
[CrossRef]

Phys. Rev. A (1)

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

Phys. Rev. Lett. (1)

B. Piccirillo, C. Toscano, F. Vetrano, and E. Santamato, Phys. Rev. Lett. 86, 2285 (2001).
[CrossRef] [PubMed]

Proc. R. Soc. London, Ser. A (1)

J. H. Poynting, Proc. R. Soc. London, Ser. A 82, 560 (1909).
[CrossRef]

Other (6)

W. G. Driscoll and W. Vaughan, Handbook of Optics (Kingsport, 1978), Sec. 10, p. 146.

A. Yariv, Quantum Electronics (Wiley, 1988).

N. B. Simpson, L. Allen, and M. J. Padgett, presented at the Inaugural Meeting of the Scottish Chapter of LEOS (Glasgow University, Glasgow, 1996).

L. D. Laudau and E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, 1984).

S. Guo, Nonlinear Optics (Xidian U. Press, 1986).

G. Zheng and W. She, Opt. Commun. (to be published), doi:10.1016/j.optcom.2006.07.068.

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Figures (1)

Fig. 1
Fig. 1

(a) Left- or right-handed circularly polarized photon number normalized, and (b) the total spin angular momentum normalized of light controlled by an external dc electric field.

Equations (16)

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P μ ω = ϵ 0 χ μ α β β E α ω = i ϵ 0 χ μ α β E α ω k β .
E ( ω ) = E 1 ( ω ) + E 2 ( ω ) = E 1 ( r ) exp ( i k 1 r ) + E 2 ( r ) exp ( i k 2 r ) ,
P 1 ( 2 ) ( ω ) = i 2 ϵ 0 κ 1 ( 2 ) : E 1 ( r ) k 1 exp ( i k 1 r ) + i 2 ϵ 0 κ 2 ( 2 ) : E 2 ( r ) k 2 exp ( i k 2 r ) ,
P 2 ( 2 ) ( ω ) = 2 ϵ 0 χ ( 2 ) ( ω , 0 ) : E 1 ( r ) E ( 0 ) exp ( i k 1 r ) + 2 ϵ 0 χ ( 2 ) ( ω , 0 ) : E 2 ( r ) E ( 0 ) exp ( i k 2 r ) .
P ( 2 ) ( ω ) = i 2 ϵ 0 κ 1 ( 2 ) : E 1 ( r ) k 1 exp ( i k 1 r ) + i 2 ϵ 0 κ 2 ( 2 ) : E 2 ( r ) k 2 exp ( i k 2 r ) + 2 ϵ 0 χ ( 2 ) ( ω , 0 ) : E 1 ( r ) E ( 0 ) exp ( i k 1 r ) + 2 ϵ 0 χ ( 2 ) ( ω , 0 ) : E 2 ( r ) E ( 0 ) exp ( i k 2 r ) .
d E 1 ( r ) d r = ( 1 n 1 f 0 i d 1 ) E 2 ( r ) exp ( i Δ k r ) i d 2 E 1 ( r ) ,
d E 2 ( r ) d r = ( 1 n 2 f 0 i d 3 ) E 1 ( r ) exp ( i Δ k r ) i d 4 E 2 ( r ) ,
d E 1 ( r ) d r = ( f i d ) E 2 ( r ) ,
d E 2 ( r ) d r = ( f i d ) E 1 ( r ) ,
E 1 ( r ) = E in cos ( f 2 + d 2 r ) ,
E 2 ( r ) = E in sin ( f 2 + d 2 r ) exp ( i θ ) ,
E ( r ) = [ E 1 ( r ) E 2 ( r ) ] = E in { α L [ 1 2 i 2 ] + α R [ 1 2 i 2 ] } ,
α L = 1 2 [ cos ( f 2 + d 2 r ) i sin ( f 2 + d 2 r ) exp ( i θ ) ] ,
α R = 1 2 [ cos ( f 2 + d 2 r ) + i sin ( f 2 + d 2 r ) exp ( i θ ) ] .
N L = c ϵ 0 α L E in 2 2 ω , N R = c ϵ 0 α R E in 2 2 ω .
M = c ϵ 0 E in 2 2 ω ( α R 2 α L 2 ) = c ϵ 0 E in 2 2 ω sin θ sin ( 2 f 2 + d 2 r ) .

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