Abstract

The interaction of optical vortices (or phase singularities, or screw dislocations) with ordinary matter is treated with a simple approach. Using the total internal reflection phenomenon and the superposition of four plane waves incident on a material with a refractive index lower than the original propagating medium, we are able to show the birth and annihilation of optical vortices in an evanescent field with curved topological features. Until now, this phenomenon has been explored only in free space propagation. By a suitable tuning process involving the incident angles and the amplitudes of the incident plane waves, it is possible to create unusual topological features of optical vortices in the vicinity of the material. We believe that this work can open new aspects of curved optical vortex manipulation in near-field optics.

© 2011 Optical Society of America

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2010 (1)

2009 (2)

Y. Zhao, D. Shapiro, D. Mcgloin, D. T. Chiu, and S. Marchesini, Opt. Express 17, 23316 (2009).
[CrossRef]

M. Mazilu, J. Baumgartl, T. Cimr, and K. Dholakia, Proc. SPIE 7430, 74300C (2009).
[CrossRef]

2007 (1)

J. Courtial and K. O’Holleran, Eur. J. Phys. Spec. Top. 145, 35 (2007).
[CrossRef]

2006 (3)

2004 (2)

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, Nature 432, 165 (2004).
[CrossRef] [PubMed]

J. Leach, E. Yao, and M. J. Padgett, New J. Phys. 6, 71 (2004).
[CrossRef]

2002 (2)

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[CrossRef]

2001 (1)

M. V. Berry and M. R. Dennis, Proc. R. Soc. A 457, 2251 (2001).
[CrossRef]

2000 (1)

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

1998 (1)

1997 (1)

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 4064 (1997).
[CrossRef]

1996 (1)

1995 (1)

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 119, 604 (1995).
[CrossRef]

1992 (2)

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

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
[CrossRef] [PubMed]

1974 (1)

J. F. Nye and M. V. Berry, Proc. R. Soc. A 336, 165 (1974).
[CrossRef]

1936 (1)

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

Allen, L.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

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

Arlt, J.

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

Basistiy, I. V.

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 119, 604 (1995).
[CrossRef]

Baumgartl, J.

M. Mazilu, J. Baumgartl, T. Cimr, and K. Dholakia, Proc. SPIE 7430, 74300C (2009).
[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]

Berry, M. V.

M. V. Berry and M. R. Dennis, Proc. R. Soc. A 457, 2251 (2001).
[CrossRef]

J. F. Nye and M. V. Berry, Proc. R. Soc. A 336, 165 (1974).
[CrossRef]

Beth, R. A.

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

Chiu, D. T.

Cimr, T.

M. Mazilu, J. Baumgartl, T. Cimr, and K. Dholakia, Proc. SPIE 7430, 74300C (2009).
[CrossRef]

Courtial, J.

J. Courtial and K. O’Holleran, Eur. J. Phys. Spec. Top. 145, 35 (2007).
[CrossRef]

J. Courtial, R. Zambrini, M. R. Dennis, and M. Vasnetsov, Opt. Express 14, 938 (2006).
[CrossRef] [PubMed]

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, Nature 432, 165 (2004).
[CrossRef] [PubMed]

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[CrossRef]

Dai, H. T.

Dennis, M. R.

Dholakia, K.

M. Mazilu, J. Baumgartl, T. Cimr, and K. Dholakia, Proc. SPIE 7430, 74300C (2009).
[CrossRef]

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

Gahagan, K. T.

Gorshkov, V. N.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 4064 (1997).
[CrossRef]

Grier, D. G.

D. G. Grier and Y. Roichman, Appl. Opt. 45, 880 (2006).
[CrossRef] [PubMed]

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[CrossRef]

Heckenberg, N. R.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 4064 (1997).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, Opt. Lett. 17, 221 (1992).
[CrossRef] [PubMed]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, 1999).

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[CrossRef]

Leach, J.

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, Nature 432, 165 (2004).
[CrossRef] [PubMed]

J. Leach, E. Yao, and M. J. Padgett, New J. Phys. 6, 71 (2004).
[CrossRef]

Liu, Y. J.

Luo, D.

MacVicar, I.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

Malos, J. T.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 4064 (1997).
[CrossRef]

Marchesini, S.

Mazilu, M.

M. Mazilu, J. Baumgartl, T. Cimr, and K. Dholakia, Proc. SPIE 7430, 74300C (2009).
[CrossRef]

McDuff, R.

Mcgloin, D.

Nye, J. F.

J. F. Nye and M. V. Berry, Proc. R. Soc. A 336, 165 (1974).
[CrossRef]

O’Holleran, K.

J. Courtial and K. O’Holleran, Eur. J. Phys. Spec. Top. 145, 35 (2007).
[CrossRef]

K. O’Holleran, M. J. Padgett, and M. R. Dennis, Opt. Express 14, 3039 (2006).
[CrossRef] [PubMed]

O’Neil, A. T.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

Padgett, M. J.

K. O’Holleran, M. J. Padgett, and M. R. Dennis, Opt. Express 14, 3039 (2006).
[CrossRef] [PubMed]

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, Nature 432, 165 (2004).
[CrossRef] [PubMed]

J. Leach, E. Yao, and M. J. Padgett, New J. Phys. 6, 71 (2004).
[CrossRef]

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

Roichman, Y.

Shapiro, D.

Smith, C. P.

Soskin, M. S.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 4064 (1997).
[CrossRef]

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 119, 604 (1995).
[CrossRef]

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]

Sun, X. W.

Swartzlander, G. A.

Vasnetsov, M.

Vasnetsov, M. V.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 4064 (1997).
[CrossRef]

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 119, 604 (1995).
[CrossRef]

White, A. G.

Woerdman, J. P.

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

Yao, E.

J. Leach, E. Yao, and M. J. Padgett, New J. Phys. 6, 71 (2004).
[CrossRef]

Zambrini, R.

Zhao, Y.

Appl. Opt. (1)

Eur. J. Phys. Spec. Top. (1)

J. Courtial and K. O’Holleran, Eur. J. Phys. Spec. Top. 145, 35 (2007).
[CrossRef]

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

Nature (1)

J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, Nature 432, 165 (2004).
[CrossRef] [PubMed]

New J. Phys. (1)

J. Leach, E. Yao, and M. J. Padgett, New J. Phys. 6, 71 (2004).
[CrossRef]

Opt. Commun. (3)

I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, Opt. Commun. 119, 604 (1995).
[CrossRef]

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

J. E. Curtis, B. A. Koss, and D. G. Grier, Opt. Commun. 207, 169 (2002).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. (1)

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

Phys. Rev. A (2)

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

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, Phys. Rev. A 56, 4064 (1997).
[CrossRef]

Phys. Rev. Lett. (1)

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

Proc. R. Soc. A (2)

J. F. Nye and M. V. Berry, Proc. R. Soc. A 336, 165 (1974).
[CrossRef]

M. V. Berry and M. R. Dennis, Proc. R. Soc. A 457, 2251 (2001).
[CrossRef]

Proc. SPIE (1)

M. Mazilu, J. Baumgartl, T. Cimr, and K. Dholakia, Proc. SPIE 7430, 74300C (2009).
[CrossRef]

Other (1)

J. D. Jackson, Classical Electrodynamics (Wiley, 1999).

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Figures (3)

Fig. 1
Fig. 1

Annihilation of optical vortices in the evanescent field. Parameters used in the simulation: θ 1 = 1.2 θ c , θ 2 = 1.5 θ c , θ 3 = 1.6 θ c , θ 4 = 1.7 θ c , ϕ 1 = 0 , ϕ 2 = π / 2 , ϕ 3 = π , ϕ 4 = 3 π / 2 , n 1 = 1.5 , and n 2 = 1.0 . (a) Phase profile of the evanescent field. The blue and red curve indicates singularities with opposed topological charges. (b) Vortex path of the singularities indicated in (a) as a function of z.

Fig. 2
Fig. 2

(a) Amplitudes of a 1 + a 4 and a 2 + a 3 as a function of z for the annihilation of optical vortices case. (b) Amplitudes of a 1 + a 4 and a 2 + a 3 as a function of z for the birth of optical vortices case.

Fig. 3
Fig. 3

Creation of optical vortices in the evanescent field. Parameters used in the simulation: θ 1 = 1.2 θ c , θ 2 = 1.2 θ c , θ 3 = 1.2 θ c , θ 4 = 1.7 θ c , ϕ 1 = 0 , ϕ 2 = π / 2 , ϕ 3 = π , ϕ 4 = 3 π / 2 , n 1 = 1.5 , n 2 = 1.0 , ; amplitude of the fourth plane wave is 5.5. (a) Phase profile of the evanescent field. Blue and red curve indicates singularities with opposed topological charges. (b) Vortex path of the singularities indicated in (a) as a function of z.

Equations (1)

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E ev ( x , y , z > 0 ) = j = 1 4 2 n 1 E j 0 cos θ j n 1 cos θ j + ( n 2 2 n 1 2 sin 2 θ j ) 1 / 2 × exp [ i k ( x cos ϕ j sin θ j ) ] × exp [ i k ( y sin θ j sin ϕ j + z cos θ j ) ] ,

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