Abstract

Two new interferometric configurations for optical vortex array generation are presented. These interferometers are different from the conventional interferometers in that they are capable of producing a large number of isolated zeros of intensity, and all of them contain optical vortices. Simulation and theory for optical vortex array generation using three-plane-wave interference is presented. The vortex dipole array produced this way is noninteracting, as there are no attraction or repulsion forces between them, leading to annihilation or creation of vortex pairs.

© 2007 Optical Society of America

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  6. V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, "Laser beams with screw dislocation in their wavefronts," JETP Lett. 52, 429-431 (1990).
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    [Crossref]
  8. Ya. Izdebskaya, V. Shvedov, and A. Volyer, "Generation of higher-order optical vortices by a dielectric wedge," Opt. Lett. 30, 2472-2474 (2004).
    [Crossref]
  9. I. Freund, N. Shvartsman, and V. Freilkher, "Optical dislocation network in highly random media," Opt. Commun. 101, 247-264 (1993).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]

2006 (2)

2004 (7)

2003 (1)

2001 (3)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photon," Nature 412, 313 (2001).
[Crossref] [PubMed]

J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21-27 (2001).
[Crossref]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photon," Nature 412, 313 (2001).
[Crossref] [PubMed]

2000 (1)

I. Freund, "Optical vortex trajectories," Opt. Commun. 181, 19-23 (2000).
[Crossref]

1999 (1)

1998 (2)

J. Batlie, E. Mouaddib, and J. Salvi, "Recent progress in coded structured light as a technique to solve the correspondence problem a survey," Pattern Recog. 31, 963-982 (1998).
[Crossref]

G. H. Kim, J. H. Jeon, Y. C. Noh, K. H. Ko, H. J. Moon, J. H. Lee, and J. S. Chang, "An array of phase singularities in a self-defocusing medium," Opt. Commun. 147, 131-137 (1998).
[Crossref]

1997 (1)

M. S. Soskin, V. N. Gorhkhov, M. V. Vanetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1997).
[Crossref]

1996 (2)

K. Dholkia, N. B. Simpson, M. J. Padgett, and L. Allen, "Second-harmonic generation and the orbital angular momentum of light," Phys. Rev. A 54, R3742-R3745 (1996).
[Crossref]

K. T. Ghaghan and G. Swartzlander Jr., "Optical vortex trapping of particles," Opt. Lett. 21, 827-829 (1996).
[Crossref]

1994 (2)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wave front laser beams produced with a spiral phase plate," Opt. Commun. 112, 321-322 (1994).
[Crossref]

P. Senthilkumaran and R. S. Sirohi, "Michelson interferometers in tandem for array generation," Opt. Commun. 105, 158-160 (1994).
[Crossref]

1993 (1)

I. Freund, N. Shvartsman, and V. Freilkher, "Optical dislocation network in highly random media," Opt. Commun. 101, 247-264 (1993).
[Crossref]

1992 (1)

1990 (2)

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, "Laser beams with screw dislocation in their wavefronts," JETP Lett. 52, 429-431 (1990).

C. Tamm and C. Weiss, "Bistability and optical switching of spatial patterns in a laser," J. Opt. Soc. Am. B 7, 1034-1038 (1990).
[Crossref]

1983 (1)

1974 (1)

J. F. Nye and M. V. Berry, "Dislocation in wave trains," Proc. R. Soc. London Ser. A 336, 165-190 (1974).
[Crossref]

Allen, L.

K. Dholkia, N. B. Simpson, M. J. Padgett, and L. Allen, "Second-harmonic generation and the orbital angular momentum of light," Phys. Rev. A 54, R3742-R3745 (1996).
[Crossref]

Batlie, J.

J. Batlie, E. Mouaddib, and J. Salvi, "Recent progress in coded structured light as a technique to solve the correspondence problem a survey," Pattern Recog. 31, 963-982 (1998).
[Crossref]

Bazhenov, V. Yu.

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, "Laser beams with screw dislocation in their wavefronts," JETP Lett. 52, 429-431 (1990).

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wave front laser beams produced with a spiral phase plate," Opt. Commun. 112, 321-322 (1994).
[Crossref]

Berry, M. V.

J. F. Nye and M. V. Berry, "Dislocation in wave trains," Proc. R. Soc. London Ser. A 336, 165-190 (1974).
[Crossref]

Chang, J. S.

G. H. Kim, J. H. Jeon, Y. C. Noh, K. H. Ko, H. J. Moon, J. H. Lee, and J. S. Chang, "An array of phase singularities in a self-defocusing medium," Opt. Commun. 147, 131-137 (1998).
[Crossref]

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wave front laser beams produced with a spiral phase plate," Opt. Commun. 112, 321-322 (1994).
[Crossref]

Courtail, J.

Courtial, J.

Dai, G.

M. D. Levenson, T. Ebihura, G. Dai, Y. Morikawa, N. Hyashi, and S. M. Tan, "Optical vortex mask via levels," J. Microlithogr. Microfabr. Microsyst. 3, 293-304 (2004).
[Crossref]

Dennis, M. R.

Dholkia, K.

K. Dholkia, N. B. Simpson, M. J. Padgett, and L. Allen, "Second-harmonic generation and the orbital angular momentum of light," Phys. Rev. A 54, R3742-R3745 (1996).
[Crossref]

Dubik, B.

J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21-27 (2001).
[Crossref]

Ebihura, T.

M. D. Levenson, T. Ebihura, G. Dai, Y. Morikawa, N. Hyashi, and S. M. Tan, "Optical vortex mask via levels," J. Microlithogr. Microfabr. Microsyst. 3, 293-304 (2004).
[Crossref]

Freilkher, V.

I. Freund, N. Shvartsman, and V. Freilkher, "Optical dislocation network in highly random media," Opt. Commun. 101, 247-264 (1993).
[Crossref]

Freund, I.

I. Freund, "Optical vortex trajectories," Opt. Commun. 181, 19-23 (2000).
[Crossref]

I. Freund, N. Shvartsman, and V. Freilkher, "Optical dislocation network in highly random media," Opt. Commun. 101, 247-264 (1993).
[Crossref]

Ghaghan, K. T.

Gibson, G.

Gorhkhov, V. N.

M. S. Soskin, V. N. Gorhkhov, M. V. Vanetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1997).
[Crossref]

Grier, D. G.

Heckenberg, N. R.

M. S. Soskin, V. N. Gorhkhov, M. V. Vanetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1997).
[Crossref]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, "Generation of optical phase singularities by computer generated hologram," Opt. Lett. 17, 221-223 (1992).
[Crossref] [PubMed]

Hyashi, N.

M. D. Levenson, T. Ebihura, G. Dai, Y. Morikawa, N. Hyashi, and S. M. Tan, "Optical vortex mask via levels," J. Microlithogr. Microfabr. Microsyst. 3, 293-304 (2004).
[Crossref]

Izdebskaya, Ya.

Jeon, J. H.

G. H. Kim, J. H. Jeon, Y. C. Noh, K. H. Ko, H. J. Moon, J. H. Lee, and J. S. Chang, "An array of phase singularities in a self-defocusing medium," Opt. Commun. 147, 131-137 (1998).
[Crossref]

Kim, G. H.

G. H. Kim, J. H. Jeon, Y. C. Noh, K. H. Ko, H. J. Moon, J. H. Lee, and J. S. Chang, "An array of phase singularities in a self-defocusing medium," Opt. Commun. 147, 131-137 (1998).
[Crossref]

Ko, K. H.

G. H. Kim, J. H. Jeon, Y. C. Noh, K. H. Ko, H. J. Moon, J. H. Lee, and J. S. Chang, "An array of phase singularities in a self-defocusing medium," Opt. Commun. 147, 131-137 (1998).
[Crossref]

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wave front laser beams produced with a spiral phase plate," Opt. Commun. 112, 321-322 (1994).
[Crossref]

Ladavac, K.

Leach, J.

J. Leach, J. Courtail, and M. J. Padgett, "Knotted threads of darkness," Nature 432, 165 (2004).
[Crossref] [PubMed]

Lee, J. H.

G. H. Kim, J. H. Jeon, Y. C. Noh, K. H. Ko, H. J. Moon, J. H. Lee, and J. S. Chang, "An array of phase singularities in a self-defocusing medium," Opt. Commun. 147, 131-137 (1998).
[Crossref]

Levenson, M. D.

M. D. Levenson, T. Ebihura, G. Dai, Y. Morikawa, N. Hyashi, and S. M. Tan, "Optical vortex mask via levels," J. Microlithogr. Microfabr. Microsyst. 3, 293-304 (2004).
[Crossref]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photon," Nature 412, 313 (2001).
[Crossref] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photon," Nature 412, 313 (2001).
[Crossref] [PubMed]

Malos, J. T.

M. S. Soskin, V. N. Gorhkhov, M. V. Vanetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1997).
[Crossref]

Masajada, J.

J. Masajada, "Small rotation-angle measurement with optical vortex interferometer," Opt. Commun. 239, 373-381 (2004).
[Crossref]

J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21-27 (2001).
[Crossref]

McDuff, R.

Moon, H. J.

G. H. Kim, J. H. Jeon, Y. C. Noh, K. H. Ko, H. J. Moon, J. H. Lee, and J. S. Chang, "An array of phase singularities in a self-defocusing medium," Opt. Commun. 147, 131-137 (1998).
[Crossref]

Morikawa, Y.

M. D. Levenson, T. Ebihura, G. Dai, Y. Morikawa, N. Hyashi, and S. M. Tan, "Optical vortex mask via levels," J. Microlithogr. Microfabr. Microsyst. 3, 293-304 (2004).
[Crossref]

Mouaddib, E.

J. Batlie, E. Mouaddib, and J. Salvi, "Recent progress in coded structured light as a technique to solve the correspondence problem a survey," Pattern Recog. 31, 963-982 (1998).
[Crossref]

Noh, Y. C.

G. H. Kim, J. H. Jeon, Y. C. Noh, K. H. Ko, H. J. Moon, J. H. Lee, and J. S. Chang, "An array of phase singularities in a self-defocusing medium," Opt. Commun. 147, 131-137 (1998).
[Crossref]

Nye, J. F.

J. F. Nye and M. V. Berry, "Dislocation in wave trains," Proc. R. Soc. London Ser. A 336, 165-190 (1974).
[Crossref]

O'Holleran, K.

Padgett, M. J.

Rotschild, C.

Salvi, J.

J. Batlie, E. Mouaddib, and J. Salvi, "Recent progress in coded structured light as a technique to solve the correspondence problem a survey," Pattern Recog. 31, 963-982 (1998).
[Crossref]

Senthilkumaran, P.

Shvartsman, N.

I. Freund, N. Shvartsman, and V. Freilkher, "Optical dislocation network in highly random media," Opt. Commun. 101, 247-264 (1993).
[Crossref]

Shvedov, V.

Simpson, N. B.

K. Dholkia, N. B. Simpson, M. J. Padgett, and L. Allen, "Second-harmonic generation and the orbital angular momentum of light," Phys. Rev. A 54, R3742-R3745 (1996).
[Crossref]

Sirohi, R. S.

P. Senthilkumaran and R. S. Sirohi, "Michelson interferometers in tandem for array generation," Opt. Commun. 105, 158-160 (1994).
[Crossref]

Smith, C. P.

Soskin, M. S.

M. S. Soskin, V. N. Gorhkhov, M. V. Vanetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1997).
[Crossref]

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, "Laser beams with screw dislocation in their wavefronts," JETP Lett. 52, 429-431 (1990).

Swartzlander, G.

Tamm, C.

Tan, S. M.

M. D. Levenson, T. Ebihura, G. Dai, Y. Morikawa, N. Hyashi, and S. M. Tan, "Optical vortex mask via levels," J. Microlithogr. Microfabr. Microsyst. 3, 293-304 (2004).
[Crossref]

Vanetsov, M. V.

M. S. Soskin, V. N. Gorhkhov, M. V. Vanetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1997).
[Crossref]

Vasnetsov, M.

Vasnetsov, M. V.

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, "Laser beams with screw dislocation in their wavefronts," JETP Lett. 52, 429-431 (1990).

Vaughan, J. M. V.

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photon," Nature 412, 313 (2001).
[Crossref] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photon," Nature 412, 313 (2001).
[Crossref] [PubMed]

Volyer, A.

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photon," Nature 412, 313 (2001).
[Crossref] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photon," Nature 412, 313 (2001).
[Crossref] [PubMed]

Weiss, C.

White, A. G.

Willetts, D. V.

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wave front laser beams produced with a spiral phase plate," Opt. Commun. 112, 321-322 (1994).
[Crossref]

Zambrini, R.

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photon," Nature 412, 313 (2001).
[Crossref] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photon," Nature 412, 313 (2001).
[Crossref] [PubMed]

Zommer, S.

Appl. Opt. (3)

J. Microlithogr. Microfabr. Microsyst. (1)

M. D. Levenson, T. Ebihura, G. Dai, Y. Morikawa, N. Hyashi, and S. M. Tan, "Optical vortex mask via levels," J. Microlithogr. Microfabr. Microsyst. 3, 293-304 (2004).
[Crossref]

J. Opt. Soc. Am. (1)

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

JETP Lett. (1)

V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, "Laser beams with screw dislocation in their wavefronts," JETP Lett. 52, 429-431 (1990).

Nature (3)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photon," Nature 412, 313 (2001).
[Crossref] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photon," Nature 412, 313 (2001).
[Crossref] [PubMed]

J. Leach, J. Courtail, and M. J. Padgett, "Knotted threads of darkness," Nature 432, 165 (2004).
[Crossref] [PubMed]

Opt. Commun. (7)

I. Freund, "Optical vortex trajectories," Opt. Commun. 181, 19-23 (2000).
[Crossref]

G. H. Kim, J. H. Jeon, Y. C. Noh, K. H. Ko, H. J. Moon, J. H. Lee, and J. S. Chang, "An array of phase singularities in a self-defocusing medium," Opt. Commun. 147, 131-137 (1998).
[Crossref]

J. Masajada, "Small rotation-angle measurement with optical vortex interferometer," Opt. Commun. 239, 373-381 (2004).
[Crossref]

P. Senthilkumaran and R. S. Sirohi, "Michelson interferometers in tandem for array generation," Opt. Commun. 105, 158-160 (1994).
[Crossref]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, "Helical-wave front laser beams produced with a spiral phase plate," Opt. Commun. 112, 321-322 (1994).
[Crossref]

I. Freund, N. Shvartsman, and V. Freilkher, "Optical dislocation network in highly random media," Opt. Commun. 101, 247-264 (1993).
[Crossref]

J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21-27 (2001).
[Crossref]

Opt. Express (4)

Opt. Lett. (3)

Pattern Recog. (1)

J. Batlie, E. Mouaddib, and J. Salvi, "Recent progress in coded structured light as a technique to solve the correspondence problem a survey," Pattern Recog. 31, 963-982 (1998).
[Crossref]

Phys. Rev. A (2)

K. Dholkia, N. B. Simpson, M. J. Padgett, and L. Allen, "Second-harmonic generation and the orbital angular momentum of light," Phys. Rev. A 54, R3742-R3745 (1996).
[Crossref]

M. S. Soskin, V. N. Gorhkhov, M. V. Vanetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1997).
[Crossref]

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

J. F. Nye and M. V. Berry, "Dislocation in wave trains," Proc. R. Soc. London Ser. A 336, 165-190 (1974).
[Crossref]

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Figures (3)

Fig. 1
Fig. 1

(a) Simulated result of three-beam interference of the resultant field. (b) Phase distribution of the resultant field. (c) Fork fringe pattern when the fourth beam is added. (d) Simulated interference pattern for the case of nonorthogonal tilt in three-beam interference.

Fig. 2
Fig. 2

(a) Experimental setup for the modified Michelson interferometer. (b) Interferogram recorded with the modified Michelson interferometer. (c) Optical vortex net with fork fringes at vortex points.

Fig. 3
Fig. 3

(a) Experimental setup for the modified Mach–Zehnder interferometer. (b) Interferogram recorded with the modified Mach–Zehnder interferometer. (c) Optical vortex net with fork fringes at the vortex points.

Equations (18)

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

U ˜ 1 ( x , y ) = a ,
U ˜ 2 ( x , y ) = a   exp ( j 2 π μ x ) ,
U ˜ 3 ( x , y ) = a exp ( j 2 π ν y ) ,
k 1 = k 1 z ^ ,
k 2 = k x x ^ + k z z ^ ,
k 3 = k y y ^ + k z z ^ ,
μ = 1 2 π k x , ν = 1 2 π k y .
U ˜ r ( x , y ) = U ˜ 1 ( x , y ) + U ˜ 2 ( x , y ) + U ˜ 3 ( x , y ) .
I = a 2 { 3 + 2 [ cos ( 2 π μ x ) + cos ( 2 π ν y ) + cos 2 π ( μ x ν y ) ] } .
I ( x , y ) = a 2 { 3 + 2 [ cos α + cos β + cos ( α β ) ] } ,
cos α + cos β + cos ( α β ) = 3 2 .
1 + cos α + cos β = 0 ,
sin α + sin β = 0 .
α = β , cos α = 1 2 .
cos ( α β ) = cos ( 2 α ) = 1 2 .
α = ( m + 1 3 ) 2 π , m = 2 , 1 , 0 , 1 , 2 ,   …   ,  
α = ( n + 2 3 ) 2 π , n = 2 , 1 , 0 , 1 , 2 ,   …
U ˜ 4 ( x , y ) = a exp ( j 2 π μ 0 x ) .

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