Beams of electromagnetic radiation with phase singularities can transport angular momentum and exert torques on objects. In this paper we discuss the generation of such beams and present a simple analysis of the phenomenon. These beams and their effects have been studied at optical and at millimeter wavelengths. We describe a particularly efficient way of generating these beams at millimeter wavelengths employing a specially configured blazed grating.

1.
For example, D. Halliday, R. Resnick, and J. Walker, Fundamentals of Physics, Extended with Modern Physics (Wiley, New York, 1993), 4th ed., p. 997.
2.
For example, A. P. French and E. F. Taylor, An Introduction to Quantum Physics (Chapman and Hall, London, 1979), p. 628.
3.
J. T. Verdeyen, Laser Electronics (Prentice-Hall, New York, 1989), 2nd ed., pp. 62–80.
4.
H.
Kogelnik
and
T.
Li
, “Laser beams and resonators,”
Appl. Opt.
5
(
10
),
1550
1567
(
1966
).
5.
M.
Padgett
,
J.
Arlt
,
N.
Simpson
, and
L.
Allen
, “
An experiment to observe the intensity and phase structure of Laguerre–Gaussian laser modes
,”
Am. J. Phys.
64
(
1
),
77
82
(
1996
).
6.
I. V.
Basistiy
,
M. S.
Soskin
, and
M. V.
Vasnetsov
, “
Optical wavefront dislocations and their properties
,”
Opt. Commun.
119
(
5,6
),
604
612
(
1995
).
7.
G. A.
Turnbull
,
D. A.
Robertson
,
G. M.
Smith
,
L.
Allen
, and
M. J.
Padgett
, “
The generation of free-space Laguerre–Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate
,”
Opt. Commun.
127
(
4,5,6
),
183
188
(
1996
).
8.
G. F.
Brand
, “
Generation of millimetre-wave beams with phase singularities
,”
J. Mod. Opt.
44
(
6
),
1243
1248
(
1997
).
9.
G. F.
Brand
, “
The generation of phase singularities at millimetre wavelengths by the use of a blazed grating
,”
J. Mod. Opt.
45
(
1
),
215
220
(
1998
).
10.
L.
Allen
,
M. W.
Beijersbergen
,
R. J. C.
Spreeuw
, and
J. P.
Woerdman
, “
Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes
,”
Phys Rev. A
45
(
11
),
8185
8189
(
1992
).
11.
E. Hecht, Optics (Addison-Wesley, Reading, MA, 1987), 2nd ed., p. 409ff.
12.
N. R.
Heckenberg
,
R.
McDuff
,
C. P.
Smith
, and
A. G.
White
, “
Generation of optical phase singularities by computer-generated holograms
,”
Opt. Lett.
17
(
3
),
221
223
(
1992
).
13.
For example, R. D. Stuart, An Introduction to Fourier Analysis (Methuen, London, 1961), p. 25ff.
14.
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965), Eqs. 9-1-44 and 9-1-45.
15.
V. Yu.
Bazhenov
,
M. V.
Vasnetsov
, and
M. S.
Soskin
, “
Laser beams with screw dislocations in their wavefronts
,”
JETP Lett.
52
(
8
),
429
431
(
1990
).
16.
V. Yu.
Bazhenov
,
M. S.
Soskin
, and
M. V.
Vasnetsov
, “
Screw dislocations in light wavefronts
,”
J. Mod. Opt.
39
(
5
),
985
990
(
1992
).
17.
Ref. 11, p. 426ff.
18.
G. W.
Chantry
,
H. M.
Evans
,
J. W.
Fleming
, and
H.
Gebbie
, “
TPX, a new material for optical components in the far infrared spectral region
,”
Infrared Phys.
9
(
1
),
31
33
(
1969
).
19.
M. V. Klein, Optics (Wiley, New York, 1970), p. 423.
20.
H.
He
,
N. R.
Heckenberg
, and
H.
Rubinsztein-Dunlop
, “
Optical particle trapping with high-order doughnut beams produced using high efficiency computer generated holograms
,”
J. Mod. Opt.
42
(
1
),
217
223
(
1995
).
21.
M. W.
Beijersbergen
,
R. P. C.
Coerwinkel
,
M.
Kristensen
, and
J. P.
Woerdman
, “
Helical-wavefront laser beams produced with a spiral phaseplate
,”
Opt. Commun.
112
(
5,6
),
321
327
(
1994
).
22.
M.
Kristensen
,
M. W.
Beijersbergen
, and
J. P.
Woerdman
, “
Angular momentum and spin-orbit coupling for microwave photons
,”
Opt. Commun.
104
(
4,5,6
),
229
233
(
1994
).
23.
For example, J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), 2nd ed., p. 333.
24.
K. F. Riley, M. P. Hobson, and S. J. Bence, Mathematical Methods for Physics and Engineering (Cambridge U. P., Cambridge, UK, 1997), pp. 677ff.
25.
R. A.
Beth
, “
Mechanical detection and measurement of the angular momentum of light
,”
Phys. Rev.
50
(
1
),
115
(
1936
).
26.
A.
Ashkin
, “
Applications of laser radiation pressure
,”
Science
210
(
4474
),
1081
1088
(
1980
).
27.
E.
Santamato
,
B.
Daino
,
M.
Romagnoli
,
M.
Settembre
, and
Y. R.
Shen
, “
Collective rotation of molecules driven by the angular momentum of light in a nematic film
,”
Phys. Rev. Lett.
57
(
19
),
2423
2426
(
1986
).
28.
P. J.
Allen
, “
A radiation torque experiment
,”
Am. J. Phys.
34
(
12
),
1185
1192
(
1966
).
29.
H.
He
,
M. E. J.
Friese
,
N. R.
Heckenberg
, and
H.
Rubinsztein-Dunlop
, “
Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity
,”
Phys. Rev. Lett.
75
(
5
),
826
829
(
1995
).
30.
S. M.
Block
, “
Making light work with optical tweezers
,”
Nature
360
,
493
495
(
1992
).
31.
N. B.
Simpson
,
L.
Allen
, and
M. J.
Padgett
, “
Optical tweezers and optical spanners with Laguerre-Gaussian modes
,”
J. Mod. Opt.
43
(
12
),
2485
2491
(
1996
).
This content is only available via PDF.
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.