Abstract

We propose and experimentally demonstrate the singular surface plasmon beam that presents a dark channel generated by a point dislocation and a long diffraction-free propagation distance up to 70λsp. The singular surface beam is the result of the interference of two surface plasmon polariton (SPP) plane waves, which are launched by two coupling gratings with lateral displacement. An aperture-type near-field scanning optical microscope is used to map the intensity distribution of the singular SPP waves. The propagating point dislocation embedded in the beam is shown by full-wave calculations and is later verified by near-field interference in the experiment.

© 2013 Optical Society of America

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  1. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).
  2. L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, Appl. Phys. Lett. 91, 081101 (2007).
    [CrossRef]
  3. H. W. Gao, J. Henzie, and T. W. Odom, Nano Lett. 6, 2104 (2006).
    [CrossRef]
  4. J. F. Nye and M. V. Berry, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 336, 165 (1974).
    [CrossRef]
  5. D. V. Petrov, Opt. Commun. 188, 307 (2001).
    [CrossRef]
  6. H. Kim, J. Park, S. W. Cho, S. Y. Lee, M. Kang, and B. Lee, Nano Lett. 10, 529 (2010).
    [CrossRef]
  7. P. S. Tan, G. H. Yuan, Q. Wang, N. Zhang, D. H. Zhang, and X.-C. Yuan, Opt. Lett. 36, 3287 (2011).
    [CrossRef]
  8. V. E. Lembessis, M. Babiker, and D. L. Andrews, Phys. Rev. A 79, 011806 (2009).
    [CrossRef]
  9. V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
    [CrossRef]
  10. T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, Nat. Methods 8, 417 (2011).
    [CrossRef]
  11. C. J. R. Sheppard and T. Wilson, IEE J. Microwaves Opt. Acoust. 2, 105 (1978).
    [CrossRef]
  12. J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef]
  13. J. Arlt and K. Dholakia, Opt. Commun. 177, 297 (2000).
    [CrossRef]
  14. A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 107, 116802 (2011).
    [CrossRef]
  15. L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, Phys. Rev. Lett. 107, 126804 (2011).
    [CrossRef]
  16. J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Founel, and F. Capasso, Phys. Rev. Lett. 109, 093904 (2012).
    [CrossRef]
  17. B. Lee, S. Kim, H. Kim, and Y. Lim, Prog. Quantum Electron. 34, 47 (2010).
    [CrossRef]
  18. B. Wang, L. Aigouy, E. Bourhis, J. Gierak, J. P. Hugonin, and P. Lalanne, Appl. Phys. Lett. 94, 011114 (2009).
    [CrossRef]
  19. E. Ozbay, Science 311, 189 (2006).
    [CrossRef]
  20. M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, Phys. Rev. Lett. 100, 186804 (2008).
    [CrossRef]
  21. K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, Nano Lett. 10, 3506 (2010).
    [CrossRef]

2012

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Founel, and F. Capasso, Phys. Rev. Lett. 109, 093904 (2012).
[CrossRef]

2011

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, Nat. Methods 8, 417 (2011).
[CrossRef]

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 107, 116802 (2011).
[CrossRef]

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, Phys. Rev. Lett. 107, 126804 (2011).
[CrossRef]

P. S. Tan, G. H. Yuan, Q. Wang, N. Zhang, D. H. Zhang, and X.-C. Yuan, Opt. Lett. 36, 3287 (2011).
[CrossRef]

2010

H. Kim, J. Park, S. W. Cho, S. Y. Lee, M. Kang, and B. Lee, Nano Lett. 10, 529 (2010).
[CrossRef]

B. Lee, S. Kim, H. Kim, and Y. Lim, Prog. Quantum Electron. 34, 47 (2010).
[CrossRef]

K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, Nano Lett. 10, 3506 (2010).
[CrossRef]

2009

B. Wang, L. Aigouy, E. Bourhis, J. Gierak, J. P. Hugonin, and P. Lalanne, Appl. Phys. Lett. 94, 011114 (2009).
[CrossRef]

V. E. Lembessis, M. Babiker, and D. L. Andrews, Phys. Rev. A 79, 011806 (2009).
[CrossRef]

2008

M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, Phys. Rev. Lett. 100, 186804 (2008).
[CrossRef]

2007

L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, Appl. Phys. Lett. 91, 081101 (2007).
[CrossRef]

2006

H. W. Gao, J. Henzie, and T. W. Odom, Nano Lett. 6, 2104 (2006).
[CrossRef]

E. Ozbay, Science 311, 189 (2006).
[CrossRef]

2002

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

2001

D. V. Petrov, Opt. Commun. 188, 307 (2001).
[CrossRef]

2000

J. Arlt and K. Dholakia, Opt. Commun. 177, 297 (2000).
[CrossRef]

1987

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

1978

C. J. R. Sheppard and T. Wilson, IEE J. Microwaves Opt. Acoust. 2, 105 (1978).
[CrossRef]

1974

J. F. Nye and M. V. Berry, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 336, 165 (1974).
[CrossRef]

Aigouy, L.

B. Wang, L. Aigouy, E. Bourhis, J. Gierak, J. P. Hugonin, and P. Lalanne, Appl. Phys. Lett. 94, 011114 (2009).
[CrossRef]

Andrews, D. L.

V. E. Lembessis, M. Babiker, and D. L. Andrews, Phys. Rev. A 79, 011806 (2009).
[CrossRef]

Arlt, J.

J. Arlt and K. Dholakia, Opt. Commun. 177, 297 (2000).
[CrossRef]

Babiker, M.

V. E. Lembessis, M. Babiker, and D. L. Andrews, Phys. Rev. A 79, 011806 (2009).
[CrossRef]

Berry, M. V.

J. F. Nye and M. V. Berry, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 336, 165 (1974).
[CrossRef]

Betzig, E.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, Nat. Methods 8, 417 (2011).
[CrossRef]

Bourhis, E.

B. Wang, L. Aigouy, E. Bourhis, J. Gierak, J. P. Hugonin, and P. Lalanne, Appl. Phys. Lett. 94, 011114 (2009).
[CrossRef]

Capasso, F.

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Founel, and F. Capasso, Phys. Rev. Lett. 109, 093904 (2012).
[CrossRef]

Cho, S. W.

H. Kim, J. Park, S. W. Cho, S. Y. Lee, M. Kang, and B. Lee, Nano Lett. 10, 529 (2010).
[CrossRef]

Cluzel, B.

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Founel, and F. Capasso, Phys. Rev. Lett. 109, 093904 (2012).
[CrossRef]

Crozier, K. B.

K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, Nano Lett. 10, 3506 (2010).
[CrossRef]

Davidson, M. W.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, Nat. Methods 8, 417 (2011).
[CrossRef]

de Founel, F.

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Founel, and F. Capasso, Phys. Rev. Lett. 109, 093904 (2012).
[CrossRef]

Dellinger, J.

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Founel, and F. Capasso, Phys. Rev. Lett. 109, 093904 (2012).
[CrossRef]

Dholakia, K.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

J. Arlt and K. Dholakia, Opt. Commun. 177, 297 (2000).
[CrossRef]

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Fainman, Y.

L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, Appl. Phys. Lett. 91, 081101 (2007).
[CrossRef]

Feng, L.

L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, Appl. Phys. Lett. 91, 081101 (2007).
[CrossRef]

Galbraith, C. G.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, Nat. Methods 8, 417 (2011).
[CrossRef]

Galbraith, J. A.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, Nat. Methods 8, 417 (2011).
[CrossRef]

Gao, H. W.

H. W. Gao, J. Henzie, and T. W. Odom, Nano Lett. 6, 2104 (2006).
[CrossRef]

Gao, L.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, Nat. Methods 8, 417 (2011).
[CrossRef]

Garces-Chavez, V.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

Genevet, P.

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Founel, and F. Capasso, Phys. Rev. Lett. 109, 093904 (2012).
[CrossRef]

Gierak, J.

B. Wang, L. Aigouy, E. Bourhis, J. Gierak, J. P. Hugonin, and P. Lalanne, Appl. Phys. Lett. 94, 011114 (2009).
[CrossRef]

Girard, C.

M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, Phys. Rev. Lett. 100, 186804 (2008).
[CrossRef]

Henzie, J.

H. W. Gao, J. Henzie, and T. W. Odom, Nano Lett. 6, 2104 (2006).
[CrossRef]

Hugonin, J. P.

B. Wang, L. Aigouy, E. Bourhis, J. Gierak, J. P. Hugonin, and P. Lalanne, Appl. Phys. Lett. 94, 011114 (2009).
[CrossRef]

Janunts, N.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 107, 116802 (2011).
[CrossRef]

Kang, M.

H. Kim, J. Park, S. W. Cho, S. Y. Lee, M. Kang, and B. Lee, Nano Lett. 10, 529 (2010).
[CrossRef]

Kim, H.

H. Kim, J. Park, S. W. Cho, S. Y. Lee, M. Kang, and B. Lee, Nano Lett. 10, 529 (2010).
[CrossRef]

B. Lee, S. Kim, H. Kim, and Y. Lim, Prog. Quantum Electron. 34, 47 (2010).
[CrossRef]

Kim, S.

B. Lee, S. Kim, H. Kim, and Y. Lim, Prog. Quantum Electron. 34, 47 (2010).
[CrossRef]

Kivshar, Y. S.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 107, 116802 (2011).
[CrossRef]

Klein, A. E.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 107, 116802 (2011).
[CrossRef]

Lalanne, P.

B. Wang, L. Aigouy, E. Bourhis, J. Gierak, J. P. Hugonin, and P. Lalanne, Appl. Phys. Lett. 94, 011114 (2009).
[CrossRef]

Lee, B.

B. Lee, S. Kim, H. Kim, and Y. Lim, Prog. Quantum Electron. 34, 47 (2010).
[CrossRef]

H. Kim, J. Park, S. W. Cho, S. Y. Lee, M. Kang, and B. Lee, Nano Lett. 10, 529 (2010).
[CrossRef]

Lee, S. Y.

H. Kim, J. Park, S. W. Cho, S. Y. Lee, M. Kang, and B. Lee, Nano Lett. 10, 529 (2010).
[CrossRef]

Lembessis, V. E.

V. E. Lembessis, M. Babiker, and D. L. Andrews, Phys. Rev. A 79, 011806 (2009).
[CrossRef]

Li, L.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, Phys. Rev. Lett. 107, 126804 (2011).
[CrossRef]

Li, T.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, Phys. Rev. Lett. 107, 126804 (2011).
[CrossRef]

Lim, Y.

B. Lee, S. Kim, H. Kim, and Y. Lim, Prog. Quantum Electron. 34, 47 (2010).
[CrossRef]

Lin, J.

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Founel, and F. Capasso, Phys. Rev. Lett. 109, 093904 (2012).
[CrossRef]

Lomakin, V.

L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, Appl. Phys. Lett. 91, 081101 (2007).
[CrossRef]

McGloin, D.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

Melville, H.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

Milkie, D. E.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, Nat. Methods 8, 417 (2011).
[CrossRef]

Minovich, A.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 107, 116802 (2011).
[CrossRef]

Neshev, D. N.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 107, 116802 (2011).
[CrossRef]

Nye, J. F.

J. F. Nye and M. V. Berry, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 336, 165 (1974).
[CrossRef]

Odom, T. W.

H. W. Gao, J. Henzie, and T. W. Odom, Nano Lett. 6, 2104 (2006).
[CrossRef]

Ozbay, E.

E. Ozbay, Science 311, 189 (2006).
[CrossRef]

Park, J.

H. Kim, J. Park, S. W. Cho, S. Y. Lee, M. Kang, and B. Lee, Nano Lett. 10, 529 (2010).
[CrossRef]

Pertsch, T.

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 107, 116802 (2011).
[CrossRef]

Petrov, D.

M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, Phys. Rev. Lett. 100, 186804 (2008).
[CrossRef]

Petrov, D. V.

D. V. Petrov, Opt. Commun. 188, 307 (2001).
[CrossRef]

Planchon, T. A.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, Nat. Methods 8, 417 (2011).
[CrossRef]

Quidant, R.

M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, Phys. Rev. Lett. 100, 186804 (2008).
[CrossRef]

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).

Righini, M.

M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, Phys. Rev. Lett. 100, 186804 (2008).
[CrossRef]

Schonbrun, E.

K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, Nano Lett. 10, 3506 (2010).
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard and T. Wilson, IEE J. Microwaves Opt. Acoust. 2, 105 (1978).
[CrossRef]

Sibbett, W.

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

Slutsky, B.

L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, Appl. Phys. Lett. 91, 081101 (2007).
[CrossRef]

Steinvurzel, P.

K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, Nano Lett. 10, 3506 (2010).
[CrossRef]

Tan, P. S.

Tetz, K. A.

L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, Appl. Phys. Lett. 91, 081101 (2007).
[CrossRef]

Volpe, G.

M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, Phys. Rev. Lett. 100, 186804 (2008).
[CrossRef]

Wang, B.

B. Wang, L. Aigouy, E. Bourhis, J. Gierak, J. P. Hugonin, and P. Lalanne, Appl. Phys. Lett. 94, 011114 (2009).
[CrossRef]

Wang, K.

K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, Nano Lett. 10, 3506 (2010).
[CrossRef]

Wang, Q.

Wang, S. M.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, Phys. Rev. Lett. 107, 126804 (2011).
[CrossRef]

Wilson, T.

C. J. R. Sheppard and T. Wilson, IEE J. Microwaves Opt. Acoust. 2, 105 (1978).
[CrossRef]

Yuan, G. H.

Yuan, X.-C.

Zhang, C.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, Phys. Rev. Lett. 107, 126804 (2011).
[CrossRef]

Zhang, D. H.

Zhang, N.

Zhu, S. N.

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, Phys. Rev. Lett. 107, 126804 (2011).
[CrossRef]

Appl. Phys. Lett.

B. Wang, L. Aigouy, E. Bourhis, J. Gierak, J. P. Hugonin, and P. Lalanne, Appl. Phys. Lett. 94, 011114 (2009).
[CrossRef]

L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, Appl. Phys. Lett. 91, 081101 (2007).
[CrossRef]

IEE J. Microwaves Opt. Acoust.

C. J. R. Sheppard and T. Wilson, IEE J. Microwaves Opt. Acoust. 2, 105 (1978).
[CrossRef]

Nano Lett.

H. W. Gao, J. Henzie, and T. W. Odom, Nano Lett. 6, 2104 (2006).
[CrossRef]

K. Wang, E. Schonbrun, P. Steinvurzel, and K. B. Crozier, Nano Lett. 10, 3506 (2010).
[CrossRef]

H. Kim, J. Park, S. W. Cho, S. Y. Lee, M. Kang, and B. Lee, Nano Lett. 10, 529 (2010).
[CrossRef]

Nat. Methods

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, Nat. Methods 8, 417 (2011).
[CrossRef]

Nature

V. Garces-Chavez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef]

Opt. Commun.

J. Arlt and K. Dholakia, Opt. Commun. 177, 297 (2000).
[CrossRef]

D. V. Petrov, Opt. Commun. 188, 307 (2001).
[CrossRef]

Opt. Lett.

Phys. Rev. A

V. E. Lembessis, M. Babiker, and D. L. Andrews, Phys. Rev. A 79, 011806 (2009).
[CrossRef]

Phys. Rev. Lett.

J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).
[CrossRef]

A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, Phys. Rev. Lett. 107, 116802 (2011).
[CrossRef]

L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, Phys. Rev. Lett. 107, 126804 (2011).
[CrossRef]

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Founel, and F. Capasso, Phys. Rev. Lett. 109, 093904 (2012).
[CrossRef]

M. Righini, G. Volpe, C. Girard, D. Petrov, and R. Quidant, Phys. Rev. Lett. 100, 186804 (2008).
[CrossRef]

Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.

J. F. Nye and M. V. Berry, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 336, 165 (1974).
[CrossRef]

Prog. Quantum Electron.

B. Lee, S. Kim, H. Kim, and Y. Lim, Prog. Quantum Electron. 34, 47 (2010).
[CrossRef]

Science

E. Ozbay, Science 311, 189 (2006).
[CrossRef]

Other

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).

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Figures (3)

Fig. 1.
Fig. 1.

Schematic of singular SPP beam generation. (a) Two SPP plane waves are launched by two gratings with grooves of length D. The red dotted line behind the upper source (blue solid line) indicates the mirrored position of the lower plane-wave source (red solid line). We introduce a π phase shift over the two SPP sources by moving the upper SPP source along the propagating direction by λsp/2. The singular SPP beam is formed in the overlapping region of the two SPP plane waves. (b) Scanning electron microscopy (SEM) micrograph of the sample. D is 10 μm, and the tilted angle θ is 10°. The groove width is about 240 nm. (c) Experimental setup. The 633 nm x-polarized Gaussian beam at normal incidence is slightly focused by an objective lens (10×, NA=0.3) onto the silver film. Aperture-type NSOM is used to map the near-field distributions of the SPP waves.

Fig. 2.
Fig. 2.

Singular SPP beam generated by two overlapped coupling gratings as shown in Fig. 1(b). (a), (b) Near-field intensity distributions obtained from (a) FDTD simulation and (b) NSOM measurement. (c), (d) Corresponding transverse intensity distributions at various propagation distances labeled by A and B in (a) and (b).

Fig. 3.
Fig. 3.

Point dislocation in a singular SPP beam. (a) SEM micrograph of a single-groove device. (b) Near-field intensity distribution obtained by NSOM. The fringes are formed by the interference between the singular SPP beam generated by a single-groove device and the background light. (c) Small region of the interference fringes outlined by the blue box in (b). At a specific propagation distance (labeled as A), the singular beam interferes with the transmitted light destructively in the upper part and constructively in the lower part. The period of fringes is defined as the distance between lines A and B, which matches the theoretical value λsp/cosθ. (d) Transient amplitude distribution obtained from FDTD calculation in the same region as in (c). The blue and red colors represent positive and negative values of the real part of the complex amplitude at a given moment, respectively. A π phase jump can be found across the singular line in the propagation axis.

Metrics