Abstract

We calculate the spin, intrinsic and extrinsic orbital angular momenta, as well as the barycenter of the focal field after a high-NA lens and find that, when the input beam is with nonuniform angular momentum (AM), the focal field carries both longitudinal and transverse parts of AM and the barycenter of the field has a transverse shift owing to the spin and orbital Hall effect of light. When one half of the input beam possesses spin and orbital AM, σ and l, and the other half with -σ and -l, a pure transverse AM is generated in the focal field, accompanying a shift of the field barycenter in the transverse plane that depends on σ and l.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Bekshaev, K. Bliokh, and M. Soskin, J. Opt. 13, 053001 (2011).
    [CrossRef]
  2. M. Mansuripur, Phys. Rev. A 84, 033838 (2011).
    [CrossRef]
  3. C.-F. Li, Phys. Rev. A 80, 063814 (2009).
    [CrossRef]
  4. A. M. Yao and M. J. Padgett, Adv. Opt. Photon. 3, 161 (2011).
    [CrossRef]
  5. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
    [CrossRef]
  6. N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Lett. 22, 52 (1997).
    [CrossRef]
  7. W. Zhu and W. She, Opt. Express 20, 25876 (2012).
    [CrossRef]
  8. P. Banzer, M. Neugebauer, A. Aiello, C. Marquardt, N. Lindlein, T. Bauer, and G. Leuchs, JEOS RP 8, 13032 (2013).
  9. W. Zhu and W. She, Opt. Express 21, 17265 (2013).
    [CrossRef]
  10. A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
    [CrossRef]
  11. J. Korger, A. Aiello, C. Gabriel, P. Banzer, T. Kolb, C. Marquardt, and G. Leuchs, Appl. Phys. B 102, 427 (2011).
    [CrossRef]
  12. L. Kong, S. Qian, Z.-C. Ren, X. Wang, and H. Wang, Phys. Rev. A 85, 035804 (2012).
    [CrossRef]
  13. K. Y. Bliokh and Y. P. Bliokh, Phys. Rev. Lett. 96, 073903 (2006).
    [CrossRef]
  14. H. L. Luo, S. C. Wen, W. X. Shu, Z. X. Tang, Y. H. Zou, and D. Y. Fan, Phys. Rev. A 80, 043810 (2009).
    [CrossRef]
  15. Y. Qin, Y. Li, H. Y. He, and Q. H. Gong, Opt. Lett. 34, 2551 (2009).
    [CrossRef]
  16. M. Merano, N. Hermosa, and J. P. Woerdman, Phys. Rev. A 82, 023817 (2010).
    [CrossRef]
  17. V. G. Fedoseyev, J. Opt. 13, 064025 (2011).
    [CrossRef]
  18. Z. Xiao, H. Luo, and S. Wen, Phys. Rev. A 85, 053822 (2012).
    [CrossRef]
  19. X. Zhou, Z. Xiao, H. Luo, and S. Wen, Phys. Rev. A 85, 043809 (2012).
    [CrossRef]
  20. Y. Qin, Y. Li, X. B. Feng, Z. P. Liu, H. Y. He, Y. F. Xiao, and Q. H. Gong, Opt. Express 18, 16832 (2010).
    [CrossRef]
  21. B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
    [CrossRef]
  22. K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, Phys. Rev. A 82, 063825 (2010).
    [CrossRef]
  23. T. A. Nieminen, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 10, 115005 (2008).
    [CrossRef]
  24. Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, Phys. Rev. Lett. 99, 073901 (2007).
    [CrossRef]
  25. P. Banzer, U. Peschel, S. Quabis, and G. Leuchs, Opt. Express 18, 10905 (2010).
    [CrossRef]
  26. R. Dasgupta, S. Ahlawat, R. S. Verma, and P. K. Gupta, Opt. Express 19, 7680 (2011).
    [CrossRef]
  27. H. Shpaisman, D. B. Ruffner, and D. G. Grier, Appl. Phys. Lett. 102, 071103 (2013).
    [CrossRef]

2013 (3)

P. Banzer, M. Neugebauer, A. Aiello, C. Marquardt, N. Lindlein, T. Bauer, and G. Leuchs, JEOS RP 8, 13032 (2013).

W. Zhu and W. She, Opt. Express 21, 17265 (2013).
[CrossRef]

H. Shpaisman, D. B. Ruffner, and D. G. Grier, Appl. Phys. Lett. 102, 071103 (2013).
[CrossRef]

2012 (4)

W. Zhu and W. She, Opt. Express 20, 25876 (2012).
[CrossRef]

L. Kong, S. Qian, Z.-C. Ren, X. Wang, and H. Wang, Phys. Rev. A 85, 035804 (2012).
[CrossRef]

Z. Xiao, H. Luo, and S. Wen, Phys. Rev. A 85, 053822 (2012).
[CrossRef]

X. Zhou, Z. Xiao, H. Luo, and S. Wen, Phys. Rev. A 85, 043809 (2012).
[CrossRef]

2011 (6)

J. Korger, A. Aiello, C. Gabriel, P. Banzer, T. Kolb, C. Marquardt, and G. Leuchs, Appl. Phys. B 102, 427 (2011).
[CrossRef]

A. Bekshaev, K. Bliokh, and M. Soskin, J. Opt. 13, 053001 (2011).
[CrossRef]

M. Mansuripur, Phys. Rev. A 84, 033838 (2011).
[CrossRef]

A. M. Yao and M. J. Padgett, Adv. Opt. Photon. 3, 161 (2011).
[CrossRef]

R. Dasgupta, S. Ahlawat, R. S. Verma, and P. K. Gupta, Opt. Express 19, 7680 (2011).
[CrossRef]

V. G. Fedoseyev, J. Opt. 13, 064025 (2011).
[CrossRef]

2010 (4)

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

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, Phys. Rev. A 82, 063825 (2010).
[CrossRef]

P. Banzer, U. Peschel, S. Quabis, and G. Leuchs, Opt. Express 18, 10905 (2010).
[CrossRef]

Y. Qin, Y. Li, X. B. Feng, Z. P. Liu, H. Y. He, Y. F. Xiao, and Q. H. Gong, Opt. Express 18, 16832 (2010).
[CrossRef]

2009 (4)

H. L. Luo, S. C. Wen, W. X. Shu, Z. X. Tang, Y. H. Zou, and D. Y. Fan, Phys. Rev. A 80, 043810 (2009).
[CrossRef]

Y. Qin, Y. Li, H. Y. He, and Q. H. Gong, Opt. Lett. 34, 2551 (2009).
[CrossRef]

C.-F. Li, Phys. Rev. A 80, 063814 (2009).
[CrossRef]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
[CrossRef]

2008 (1)

T. A. Nieminen, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 10, 115005 (2008).
[CrossRef]

2007 (1)

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, Phys. Rev. Lett. 99, 073901 (2007).
[CrossRef]

2006 (1)

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

2001 (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

1997 (1)

1959 (1)

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Ahlawat, S.

Aiello, A.

P. Banzer, M. Neugebauer, A. Aiello, C. Marquardt, N. Lindlein, T. Bauer, and G. Leuchs, JEOS RP 8, 13032 (2013).

J. Korger, A. Aiello, C. Gabriel, P. Banzer, T. Kolb, C. Marquardt, and G. Leuchs, Appl. Phys. B 102, 427 (2011).
[CrossRef]

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, Phys. Rev. A 82, 063825 (2010).
[CrossRef]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
[CrossRef]

Allen, L.

Alonso, M. A.

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, Phys. Rev. A 82, 063825 (2010).
[CrossRef]

Banzer, P.

P. Banzer, M. Neugebauer, A. Aiello, C. Marquardt, N. Lindlein, T. Bauer, and G. Leuchs, JEOS RP 8, 13032 (2013).

J. Korger, A. Aiello, C. Gabriel, P. Banzer, T. Kolb, C. Marquardt, and G. Leuchs, Appl. Phys. B 102, 427 (2011).
[CrossRef]

P. Banzer, U. Peschel, S. Quabis, and G. Leuchs, Opt. Express 18, 10905 (2010).
[CrossRef]

Bauer, T.

P. Banzer, M. Neugebauer, A. Aiello, C. Marquardt, N. Lindlein, T. Bauer, and G. Leuchs, JEOS RP 8, 13032 (2013).

Bekshaev, A.

A. Bekshaev, K. Bliokh, and M. Soskin, J. Opt. 13, 053001 (2011).
[CrossRef]

Bliokh, K.

A. Bekshaev, K. Bliokh, and M. Soskin, J. Opt. 13, 053001 (2011).
[CrossRef]

Bliokh, K. Y.

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, Phys. Rev. A 82, 063825 (2010).
[CrossRef]

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

Bliokh, Y. P.

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

Chiu, D. T.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, Phys. Rev. Lett. 99, 073901 (2007).
[CrossRef]

Dasgupta, R.

Dholakia, K.

Edgar, J. S.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, Phys. Rev. Lett. 99, 073901 (2007).
[CrossRef]

Fan, D. Y.

H. L. Luo, S. C. Wen, W. X. Shu, Z. X. Tang, Y. H. Zou, and D. Y. Fan, Phys. Rev. A 80, 043810 (2009).
[CrossRef]

Fedoseyev, V. G.

V. G. Fedoseyev, J. Opt. 13, 064025 (2011).
[CrossRef]

Feng, X. B.

Gabriel, C.

J. Korger, A. Aiello, C. Gabriel, P. Banzer, T. Kolb, C. Marquardt, and G. Leuchs, Appl. Phys. B 102, 427 (2011).
[CrossRef]

Gong, Q. H.

Grier, D. G.

H. Shpaisman, D. B. Ruffner, and D. G. Grier, Appl. Phys. Lett. 102, 071103 (2013).
[CrossRef]

Gupta, P. K.

He, H. Y.

Heckenberg, N. R.

T. A. Nieminen, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 10, 115005 (2008).
[CrossRef]

Hermosa, N.

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

Jeffries, G. D. M.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, Phys. Rev. Lett. 99, 073901 (2007).
[CrossRef]

Kolb, T.

J. Korger, A. Aiello, C. Gabriel, P. Banzer, T. Kolb, C. Marquardt, and G. Leuchs, Appl. Phys. B 102, 427 (2011).
[CrossRef]

Kong, L.

L. Kong, S. Qian, Z.-C. Ren, X. Wang, and H. Wang, Phys. Rev. A 85, 035804 (2012).
[CrossRef]

Korger, J.

J. Korger, A. Aiello, C. Gabriel, P. Banzer, T. Kolb, C. Marquardt, and G. Leuchs, Appl. Phys. B 102, 427 (2011).
[CrossRef]

Leuchs, G.

P. Banzer, M. Neugebauer, A. Aiello, C. Marquardt, N. Lindlein, T. Bauer, and G. Leuchs, JEOS RP 8, 13032 (2013).

J. Korger, A. Aiello, C. Gabriel, P. Banzer, T. Kolb, C. Marquardt, and G. Leuchs, Appl. Phys. B 102, 427 (2011).
[CrossRef]

P. Banzer, U. Peschel, S. Quabis, and G. Leuchs, Opt. Express 18, 10905 (2010).
[CrossRef]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
[CrossRef]

Li, C.-F.

C.-F. Li, Phys. Rev. A 80, 063814 (2009).
[CrossRef]

Li, Y.

Lindlein, N.

P. Banzer, M. Neugebauer, A. Aiello, C. Marquardt, N. Lindlein, T. Bauer, and G. Leuchs, JEOS RP 8, 13032 (2013).

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
[CrossRef]

Liu, Z. P.

Luo, H.

X. Zhou, Z. Xiao, H. Luo, and S. Wen, Phys. Rev. A 85, 043809 (2012).
[CrossRef]

Z. Xiao, H. Luo, and S. Wen, Phys. Rev. A 85, 053822 (2012).
[CrossRef]

Luo, H. L.

H. L. Luo, S. C. Wen, W. X. Shu, Z. X. Tang, Y. H. Zou, and D. Y. Fan, Phys. Rev. A 80, 043810 (2009).
[CrossRef]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Mansuripur, M.

M. Mansuripur, Phys. Rev. A 84, 033838 (2011).
[CrossRef]

Marquardt, C.

P. Banzer, M. Neugebauer, A. Aiello, C. Marquardt, N. Lindlein, T. Bauer, and G. Leuchs, JEOS RP 8, 13032 (2013).

J. Korger, A. Aiello, C. Gabriel, P. Banzer, T. Kolb, C. Marquardt, and G. Leuchs, Appl. Phys. B 102, 427 (2011).
[CrossRef]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
[CrossRef]

McGloin, D.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, Phys. Rev. Lett. 99, 073901 (2007).
[CrossRef]

Merano, M.

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

Neugebauer, M.

P. Banzer, M. Neugebauer, A. Aiello, C. Marquardt, N. Lindlein, T. Bauer, and G. Leuchs, JEOS RP 8, 13032 (2013).

Nieminen, T. A.

T. A. Nieminen, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 10, 115005 (2008).
[CrossRef]

Ostrovskaya, E. A.

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, Phys. Rev. A 82, 063825 (2010).
[CrossRef]

Padgett, M. J.

Peschel, U.

Qian, S.

L. Kong, S. Qian, Z.-C. Ren, X. Wang, and H. Wang, Phys. Rev. A 85, 035804 (2012).
[CrossRef]

Qin, Y.

Quabis, S.

Ren, Z.-C.

L. Kong, S. Qian, Z.-C. Ren, X. Wang, and H. Wang, Phys. Rev. A 85, 035804 (2012).
[CrossRef]

Richards, B.

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Rubinsztein-Dunlop, H.

T. A. Nieminen, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 10, 115005 (2008).
[CrossRef]

Ruffner, D. B.

H. Shpaisman, D. B. Ruffner, and D. G. Grier, Appl. Phys. Lett. 102, 071103 (2013).
[CrossRef]

She, W.

Shpaisman, H.

H. Shpaisman, D. B. Ruffner, and D. G. Grier, Appl. Phys. Lett. 102, 071103 (2013).
[CrossRef]

Shu, W. X.

H. L. Luo, S. C. Wen, W. X. Shu, Z. X. Tang, Y. H. Zou, and D. Y. Fan, Phys. Rev. A 80, 043810 (2009).
[CrossRef]

Simpson, N. B.

Soskin, M.

A. Bekshaev, K. Bliokh, and M. Soskin, J. Opt. 13, 053001 (2011).
[CrossRef]

Stilgoe, A. B.

T. A. Nieminen, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 10, 115005 (2008).
[CrossRef]

Tang, Z. X.

H. L. Luo, S. C. Wen, W. X. Shu, Z. X. Tang, Y. H. Zou, and D. Y. Fan, Phys. Rev. A 80, 043810 (2009).
[CrossRef]

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Verma, R. S.

Wang, H.

L. Kong, S. Qian, Z.-C. Ren, X. Wang, and H. Wang, Phys. Rev. A 85, 035804 (2012).
[CrossRef]

Wang, X.

L. Kong, S. Qian, Z.-C. Ren, X. Wang, and H. Wang, Phys. Rev. A 85, 035804 (2012).
[CrossRef]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Wen, S.

X. Zhou, Z. Xiao, H. Luo, and S. Wen, Phys. Rev. A 85, 043809 (2012).
[CrossRef]

Z. Xiao, H. Luo, and S. Wen, Phys. Rev. A 85, 053822 (2012).
[CrossRef]

Wen, S. C.

H. L. Luo, S. C. Wen, W. X. Shu, Z. X. Tang, Y. H. Zou, and D. Y. Fan, Phys. Rev. A 80, 043810 (2009).
[CrossRef]

Woerdman, J. P.

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

Wolf, E.

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Xiao, Y. F.

Xiao, Z.

Z. Xiao, H. Luo, and S. Wen, Phys. Rev. A 85, 053822 (2012).
[CrossRef]

X. Zhou, Z. Xiao, H. Luo, and S. Wen, Phys. Rev. A 85, 043809 (2012).
[CrossRef]

Yao, A. M.

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Zhao, Y.

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, Phys. Rev. Lett. 99, 073901 (2007).
[CrossRef]

Zhou, X.

X. Zhou, Z. Xiao, H. Luo, and S. Wen, Phys. Rev. A 85, 043809 (2012).
[CrossRef]

Zhu, W.

Zou, Y. H.

H. L. Luo, S. C. Wen, W. X. Shu, Z. X. Tang, Y. H. Zou, and D. Y. Fan, Phys. Rev. A 80, 043810 (2009).
[CrossRef]

Adv. Opt. Photon. (1)

Appl. Phys. B (1)

J. Korger, A. Aiello, C. Gabriel, P. Banzer, T. Kolb, C. Marquardt, and G. Leuchs, Appl. Phys. B 102, 427 (2011).
[CrossRef]

Appl. Phys. Lett. (1)

H. Shpaisman, D. B. Ruffner, and D. G. Grier, Appl. Phys. Lett. 102, 071103 (2013).
[CrossRef]

J. Opt. (2)

A. Bekshaev, K. Bliokh, and M. Soskin, J. Opt. 13, 053001 (2011).
[CrossRef]

V. G. Fedoseyev, J. Opt. 13, 064025 (2011).
[CrossRef]

J. Opt. A (1)

T. A. Nieminen, A. B. Stilgoe, N. R. Heckenberg, and H. Rubinsztein-Dunlop, J. Opt. A 10, 115005 (2008).
[CrossRef]

JEOS RP (1)

P. Banzer, M. Neugebauer, A. Aiello, C. Marquardt, N. Lindlein, T. Bauer, and G. Leuchs, JEOS RP 8, 13032 (2013).

Nature (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).
[CrossRef]

Opt. Express (5)

Opt. Lett. (2)

Phys. Rev. A (8)

M. Mansuripur, Phys. Rev. A 84, 033838 (2011).
[CrossRef]

C.-F. Li, Phys. Rev. A 80, 063814 (2009).
[CrossRef]

L. Kong, S. Qian, Z.-C. Ren, X. Wang, and H. Wang, Phys. Rev. A 85, 035804 (2012).
[CrossRef]

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

H. L. Luo, S. C. Wen, W. X. Shu, Z. X. Tang, Y. H. Zou, and D. Y. Fan, Phys. Rev. A 80, 043810 (2009).
[CrossRef]

Z. Xiao, H. Luo, and S. Wen, Phys. Rev. A 85, 053822 (2012).
[CrossRef]

X. Zhou, Z. Xiao, H. Luo, and S. Wen, Phys. Rev. A 85, 043809 (2012).
[CrossRef]

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, Phys. Rev. A 82, 063825 (2010).
[CrossRef]

Phys. Rev. Lett. (3)

Y. Zhao, J. S. Edgar, G. D. M. Jeffries, D. McGloin, and D. T. Chiu, Phys. Rev. Lett. 99, 073901 (2007).
[CrossRef]

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

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, Phys. Rev. Lett. 103, 100401 (2009).
[CrossRef]

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

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1.
Fig. 1.

Illustration of the generation of transverse AM and transverse barycenter shift of a light field focused by a high-NA lens. The light field of an input ray carries a longitudinal AM jin=(σ+l)z^. After it is focused, the ray shifts in the plane perpendicular to the z axis to satisfy the conservation law of longitudinal AM. The transverse shift will induce a transverse extrinsic OAM, which, together with the transverse part of SAM, make up the total transverse AM.

Fig. 2.
Fig. 2.

(a) The dependences of the average longitudinal component of SAM, normalized total longitudinal OAM, and average extrinsic and intrinsic longitudinal OAM on the opening angle of the sector aperture, b. The black dashed line is the zero line. (b) The dependences of the barycenter shift and (c) average transverse SAM on b. In calculation, σ=1, l=2, and ϕ0 is set to be π/2.

Fig. 3.
Fig. 3.

Density patterns of light intensity (a1, b1 and c1) and the x component of SAM (a2, b2 and c2) in the focal plane for fixed σ=1 and different l=2 (a1,a2), 0 (b1,b2), 2 (c1,c2), where the white dashed line represents the y axis, and the dimension of the focal plane is 2λ×2λ. (d) The dependences of transverse shifts of the barycenter of the focal field on the input OAM, l, for σ=±1.

Equations (16)

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

E(x,y,z)=iAπdΩE˜(θ,ϕ)exp[ikzcosθ+iksinθ(xcosϕ+ysinϕ)],
T0(ϕ)=1ϕ0<ϕ<ϕ0+b0other
rs=[σ(cosθ1)l]wksinθe^ϕ,
rsσ=l(cosθ+1)2w4ksinθe^ϕ,
rsσ=(2σ+l)(cosθ1)2w4ksinθe^ϕ,
rsz=sinθ2(σ+l)w2ksinθe^ϕ,
W=wdΩ,
Rs=|rsdΩ|/W,
Sz=szdΩ/W.
Lz=lzdΩ/W,
ELz=rsdΩ×wksinθ(cosϕx^+sinϕy^)dΩ/W2,
ILz=LzELz.
s=wσsinθ(cosϕx^+sinϕy^),
l=rs×pz=l+σ(cosθ1)sinθwcosθ(cosϕx^+sinϕy^),
j=l+s=[lcosθ+σ(cosθ1)]sinθw(cosϕx^+sinϕy^).
T1(ϕ)=exp(ilϕ)e^σϕ0<ϕ<ϕ0+π(1)l+1exp(ilϕ)e^σother.

Metrics