We propose a method based on a Mach–Zehnder interferometer to analyze the superposition of polarized laser beams at a given angle. The focus of our study is the spatially varying polarization state of the resulting field, also known as a polarization grating, generated by this setup. Our proposal combines a description of the resulting field in terms of its Stokes parameters with an experimental demonstration of the existence of such a polarization grating due to the effects of polarization on beam interference experiments.

1.
T.
Young
, “
Experiments and calculations relative to physical optics
,”
Philos. Trans. R. Soc. London
94
,
1
16
(
1804
).
2.
D. F. J.
Arago
and
A. J.
Fresnel
, “
On the action of rays of polarized light upon each other
,”
Ann. Chem. Phys.
2
,
288
304
(
1819
).
3.
J. L.
Hunt
and
G.
Karl
, “
Interference with polarized light beams
,”
Am. J. Phys.
38
,
1249
1259
(
1970
).
4.
D.
Pescetti
, “
Interference of elliptically polarized light
,”
Am. J. Phys.
40
,
735
740
(
1972
).
5.
S.
Mallick
, “
Interference with polarized light
,”
Am. J. Phys.
41
,
583
584
(
1973
).
6.
C.
Pontiggia
, “
Interference with polarized light
,”
Am. J. Phys.
39
,
679
(
1971
).
7.
J. L.
Ferguson
, “
A simple, bright demonstration of the interference of polarized light
,”
Am. J. Phys.
52
,
1141
1142
(
1984
).
8.
E. F.
Carr
and
J. P.
McClymer
, “
A laboratory experiment on interference of polarized light using a liquid crystal
,”
Am. J. Phys.
59
,
366
367
(
1991
).
9.
M.
Henry
, “
Fresnel–Arago laws for the interference in polarized light: A demonstration experiment
,”
Am. J. Phys.
49
,
690
691
(
1981
).
10.
B.
Kanseri
,
N. S.
Bisht
,
H. C.
Kandpal
, and
S.
Rath
, “
Observation of the Fresnel and Arago laws using the Mach–Zehnder interferometer
,”
Am. J. Phys.
76
,
39
42
(
2008
).
11.
E.
Collett
, “
Mathematical formulation of the interference laws of Fresnel and Arago
,”
Am. J. Phys.
39
,
1483
1495
(
1971
).
12.
P.
Andrés
,
A.
Pons
, and
J.
Ojeda-Castañeda
, “
Young’s experiment with polarized light: Properties and applications
,”
Am. J. Phys.
53
,
1085
1088
(
1985
).
13.
T. F.
Jordan
, “
Choosing and rechoosing to have or have not interference
,”
Am. J. Phys.
69
,
155
157
(
2001
).
14.
W. R.
Mellen
, “
Interference patterns from circularly polarized light using a Michelson interferometer
,”
Am. J. Phys.
58
,
580
581
(
1990
).
15.
L. Z.
Cai
and
X. L.
Yang
, “
Interference of circularly polarized light: contrast and application in fabrication of three dimensional periodic microstructures
,”
Opt. Laser Technol.
34
,
671
674
(
2002
).
16.
E.
Garbusi
,
E. M.
Frins
, and
J. A.
Ferrari
, “
Phase-shifting shearing interferometry with a variable polarization grating recorded on Bacteriorhodopsin
,”
Opt. Commun.
241
,
309
314
(
2004
).
17.
S. K.
Mohanty
,
K.
Divakar Rao
, and
P. K.
Gupta
, “
Optical trap with spatially varying polarization
,”
Appl. Phys. B: Lasers Opt.
80
,
631
634
(
2005
).
18.
R. C.
Jones
, “
A new calculus for the treatment of optical systems
,”
J. Opt. Soc. Am.
31
,
488
493
(
1941
).
19.
E.
Collett
, “
The description of polarization in classical physics
,”
Am. J. Phys.
36
,
713
725
(
1968
).
20.
F.
Gori
, “
Measuring Stokes parameters by means of a polarization grating
,”
Opt. Lett.
24
,
584
586
(
1999
).
21.
B.
Schaefer
,
E.
Collett
,
R.
Smyth
,
D.
Barrett
, and
B.
Fraher
, “
Measuring the Stokes polarization parameters
,”
Am. J. Phys.
75
,
163
169
(
2007
).
22.
J. W.
Simmons
and
M. J.
Guttmann
,
States, Waves and Photons
(
Addison-Wesley
,
Reading, MA
,
1970
).
23.
M.
Born
and
E.
Wolf
,
Principles of Optics
, 7th ed. (
Cambridge U. P.
,
Cambridge
,
1999
).
24.
J.
Tervo
,
T.
Setälä
, and
A. T.
Friberg
, “
Degree of coherence for electromagnetic fields
,”
Opt. Express.
10
,
1137
1143
(
2003
).
25.
H.
Roychowdhury
and
E.
Wolf
, “
Young’s interference experiment with light of any state of coherence and of polarization
,”
Opt. Commun.
252
,
268
274
(
2005
).
26.
E.
Wolf
,
Introduction to the Theory of Coherence and Polarization of Light
, 12th ed. (
Cambridge U. P.
,
Cambridge
,
2007
).
27.
B. M.
Rodríguez-Lara
and
I.
Ricardez-Vargas
, “
Stokes parameters for the superposition of two slightly non-collinear light beams with orthogonal polarizations
,” ⟨demonstrations.wolfram.com/StokesParametersForTheSuperpositionOfTwoSlightlyNoncollinear/⟩.
28.
B. M.
Rodríguez-Lara
and
I.
Ricardez-Vargas
, “
Stokes parameters for the superposition of two slightly noncollinear polarized beams
,” ⟨demonstrations.wolfram.com/StokesParametersForSuperpositionOfTwoSlightlyNoncollinearPol/⟩.
29.
D. N.
Moothoo
,
J.
Arlt
,
R. S.
Conroy
,
F.
Akerboom
,
A.
Voit
, and
K.
Dholakia
, “
Beth’s experiment using optical tweezers
,”
Am. J. Phys.
69
,
271
276
(
2001
).
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