An optical vortex is a screw dislocation in a light field that carries quantized orbital angular momentum and, due to cancellations of the twisting along the propagation axis, experiences zero intensity at its center. When viewed in a perpendicular plane along the propagation axis, the vortex appears as a dark region in the center surrounded by a bright concentric ring of light. We give detailed instructions for generating optical vortices and optical vortex structures by computer-generated holograms and describe various methods for manipulating the resulting structures.

1.
J. F.
Nye
and
M. V.
Berry
, “
Dislocations in wave trains
,”
Proc. R. Soc. London, Ser. A
336
,
165
190
(
1974
).
2.
K. T.
Gahagan
and
G. A.
Swartzlander
, Jr.
, “
Optical vortex trapping of particles
,”
Opt. Lett.
21
,
827
829
(
1996
).
3.
N. B.
Simpson
,
K.
Dholakia
,
L.
Allen
, and
M. J.
Padgett
, “
Mechanical equivalence of spin and orbital angular momentum of light: An optical spanner
,”
Opt. Lett.
22
,
52
54
(
1997
).
4.
A. H.
Carlsson
,
J. N.
Malmberg
,
D.
Anderson
,
M.
Lisak
,
E. A.
Ostrovskaya
,
T. J.
Alexander
, and
Y. S.
Kivshar
, “
Linear and nonlinear waveguides induced by optical vortex solitons
,”
Opt. Lett.
25
,
660
662
(
2000
).
5.
J. R.
Salgueiro
,
A. H.
Carlsson
,
E.
Ostrovskaya
, and
Y.
Kivshar
, “
Second-harmonic generation in vortex-induced waveguides
,”
Opt. Lett.
29
,
593
595
(
2004
).
6.
G.
Foo
,
D. M.
Palacios
, and
G. A.
Swartzlander
, Jr.
, “
Optical vortex coronagraph
,”
Opt. Lett.
30
,
3308
3310
(
2005
).
7.
A.
Mair
,
A.
Vaziri
,
G.
Welhs
, and
A.
Zeilinger
, “
Entanglement of the orbital angular momentum states of photons
,”
Nature (London)
412
,
313
316
(
2001
).
8.
M. R.
Matthews
,
B. P.
Anderson
,
P. C.
Haljan
,
D. S.
Hall
,
C. E.
Wieman
, and
E. A.
Cornell
, “
Vortices in a Bose-Einstein condensate
,”
Phys. Rev. Lett.
83
,
2498
2501
(
1999
).
9.
G. W.
Rayfield
and
F.
Reif
, “
Quantized vortex rings in superfluid helium
,”
Phys. Rev. A
136
,
A1194
A1208
(
1964
).
10.
C.
López-Mariscal
and
J. C.
Gutiérrez-Vega
, “
The generation of nondiffracting beams using inexpensive computer-generated holograms
,”
Am. J. Phys.
75
,
36
42
(
2007
).
11.
The Amateur Scientist, “
Homemade hologram
,”
Sci. Am. (Int. Ed.)
216
,
122
129
(
1967
).
12.
T.
Seymour
, “
Computer simulated holography and computer generated holograms
,”
Am. J. Phys.
64
,
472
478
(
1995
).
13.
A. G.
Porter
and
S.
George
, “
An elementary introduction to practical holography
,”
Am. J. Phys.
43
,
954
959
(
1975
).
14.
J. S.
Marsh
and
R. C.
Smith
, “
Computer holograms with a desk-top calculator
,”
Am. J. Phys.
44
,
774
777
(
1976
).
15.
I. D.
Maleev
and
G. A.
Swartzlander
, Jr.
, “
Composite optical vortices
,”
J. Opt. Soc. Am. B
20
,
1169
1176
(
2003
).
16.
M. P.
MacDonald
,
K.
Volke-Sepulveda
,
L.
Paterson
,
J.
Arlt
,
W.
Sibbett
, and
K.
Dholakia
, “
Resolving interference patterns for the rotation of optically trapped particles
,”
Opt. Commun.
201
,
21
28
(
2002
).
17.
D. G.
Grier
and
Y.
Roichman
, “
Holographic optical trapping
,”
Appl. Opt.
45
,
880
887
(
2006
).
18.
M.
Brambilla
,
F.
Battipede
,
L. A.
Lugiato
,
V.
Penna
,
F.
Prati
,
C.
Tamm
, and
C. O.
Weiss
, “
Transverse patterns. 1. Phase singularity crystals
,”
Phys. Rev. A
43
,
5090
5113
(
1991
).
19.
M. W.
Beijersbergen
,
L.
Allen
,
H. E. I. O.
van der Veen
, and
J. P.
Woeman
, “
Astigmatic laser mode converters and transfer of orbital angular momentum
,”
Opt. Commun.
96
,
123
132
(
1996
).
20.
N. R.
Heckenberg
,
R.
McDuff
,
C. P.
Smith
, and
A. G.
White
, “
Generation of optical-phase singularities by computer-generated holograms
,”
Opt. Lett.
17
,
221
223
(
1992
).
21.
P.
Coullet
,
L.
Gill
, and
F.
Rocca
, “
Optical vortices
,”
Opt. Commun.
73
,
403
408
(
1989
).
22.
G. E.
Volovik
, “
On the Kelvin-Helmholtz instability in superfluids
,”
JETP Lett.
75
,
418
422
(
2002
).
23.
S. E.
Korshunov
, “
Analog of Kelvin-Helmholtz instability on a free surface of a superfluid liquid
,”
JETP Lett.
75
,
423
425
(
2002
).
24.
R. P.
Feynman
, “
Atomic theory of the two-fluid model of liquid helium
,”
Phys. Rev.
94
,
262
277
(
1954
).
25.
R.
Blaauwgeers
,
V. B.
Eltsov
,
G.
Eska
,
A. P.
Finne
,
R. P.
Haley
,
M.
Krusius
,
J. J.
Ruohio
,
L.
Skrbek
, and
G. E.
Volovik
, “
Shear flow and Kelvin-Helmholtz instability in superfluids
,”
Phys. Rev. Lett.
89
,
155301
1
(
2002
);
[PubMed]
A. P.
Finne
,
T.
Araki
,
R.
Blaauwgeers
,
V. B.
Eltsov
,
N. B.
Kopnin
,
M.
Krusius
,
L.
Skrbek
,
M.
Tsubota
, and
G. E.
Volovik
, “
An intrinsic velocity-independent criterion for superfluid turbulence
,”
Nature (London)
424
,
1022
1025
(
2003
).
26.
M.
Vaupel
,
K.
Staliunas
, and
C. O.
Weiss
, “
Hydrodynamic phenomena in laser physics: Modes with flow and vortices behind an obstacle in an optical channel
,”
Phys. Rev. A
54
,
880
892
(
1996
).
27.
M. P.
Alonso
and
H.
Michinel
, “
Superfluidlike motion of vortices in light condensates
,”
Phys. Rev. Lett.
94
,
093901
1
(
2005
).
28.
C.
Nore
,
M. E.
Brachet
, and
S.
Fauve
, “
Numerical study of hydrodynamics using the nonlinear schrodinger-equation
,”
Physica D
65
,
154
162
(
1993
);
R. Y.
Chiao
,
T. H.
Hansson
,
J. M.
Leinaas
, and
S.
Viefers
, “
Two-dimensional ‘photon fluid:’ Effective photon-photon interaction and physical realizations
,”
J. Phys. B
37
,
S81
S89
(
2004
).
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.