We describe a simple experiment on the diffraction of monochromatic light by interfering liquid surface waves. The surface wave profile, which acts as a reflection phase grating for incident light, is generated by electrically driven vertical oscillations of two or more slightly immersed exciters. The theoretical intensity of the diffracted light agrees well with observations. In particular, we show the relation between the intensity and the amplitude (height) of the surface wave. Although invisible to the naked eye, the interference of liquid surface waves can be optically detected from the characteristic features of the diffraction pattern. In addition, we can measure the amplitude, wavelength, and phase velocity of the surface wave that propagates along the line joining the exciters.

1.
E. Hecht, Optics, 4th ed. (Pearson Education, Singapore, 2003), pp. 460–464.
2.
D. P.
Morgan
, “
A history of surface acoustic wave devices
,”
Int. J. High Speed Electron. Syst.
10
,
553
602
(
2000
), and references therein.
3.
A.
Khan
,
R.
Rimeika
,
D.
Ciplys
,
R.
Gaska
, and
M. S.
Shur
, “
Optical guided modes and surface acoustic waves in GaN grown on (0001) sapphire substrates
,”
Phys. Status Solidi B
216
,
477
480
(
1999
).
4.
C. S.
Tsai
, “
Integrated acoustooptic circuits and applications
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
39
,
529
554
(
1992
).
5.
C.
Deger
,
E.
Born
,
H.
Angerer
,
O.
Ambacher
,
M.
Stutzmann
,
J.
Hornsteine
,
E.
Riha
, and
G.
Fischeraurer
, “
Sound velocity of AlxGa1−xN thin films obtained by surface acoustic wave measurements
,”
Appl. Phys. Lett.
72
,
2400
2402
(
1998
).
6.
R.
Rimeika
,
D.
Ciplys
,
R.
Gaska
,
J. W.
Yang
,
M. A.
Khan
,
M. S.
Shur
, and
E.
Towe
, “
Diffraction of optical waves by surface acoustic waves in GaN
,”
Appl. Phys. Lett.
77
,
480
482
(
2000
).
7.
P. A.
Hess
, “
Surface acoustic waves in materials science
,”
Phys. Today
55
(
3
),
42
47
(
2002
).
8.
G. I.
Stegeman
, “
Optical probing of surface waves and surface wave devices
,”
IEEE Trans. Sonics Ultrason.
SU-23
,
33
63
(
1976
), and references therein.
9.
J. P.
Monchalin
, “
Optical detection of ultrasound
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
33
,
485
498
(
1986
).
10.
F. R.
Watson
, “
Surface tension at the interface of two liquids determined experimentally by the method of ripple waves
,”
Phys. Rev.
12
,
257
278
(
1901
);
F. R.
Watson
and
W. A.
Shewhart
, “
A study of ripple wave motion
,”
Phys. Rev.
7
,
226
231
(
1916
).
11.
J. C.
Earnshaw
and
R. C.
McGivren
, “
Photon correlation spectroscopy of thermal fluctuations of liquid surface
,”
J. Phys. D
20
,
82
92
(
1987
);
J. C.
Earnshaw
and
E.
McCoo
, “
Mode mixing of liquid surface waves
,”
Phys. Rev. Lett.
72
,
84
87
(
1994
).
12.
Light Scattering by Liquid Surfaces and Complementary Techniques, edited by D. Langevin (Dekker, New York, 1992).
13.
K. Y.
Lee
,
T.
Chou
,
D. S.
Chung
, and
E.
Mazur
, “
Direct measurement of the spatial damping of capillary waves at liquid–vapor interfaces
,”
J. Phys. Chem.
97
,
12876
12878
(
1993
).
14.
V.
Kolevzon
and
G.
Gerbeth
, “
Light scattering spectroscopy of a liquid gallium surface
,”
J. Phys. D
29
,
2071
2081
(
1996
);
V.
Kolevzon
,
G.
Gerbeth
, and
G.
Pozdniakov
, “
Light-scattering study of the mercury liquid–vapor interface
,”
Phys. Rev. E
55
,
3134
3142
(
1997
).
15.
W. M.
Klipstein
,
J. S.
Radnich
, and
S. K.
Lamoreaux
, “
Thermally excited liquid surface waves and their study through the quasielastic scattering of light
,”
Am. J. Phys.
64
,
758
765
(
1996
).
16.
R.
Miao
,
Z.
Yang
,
J.
Zhu
, and
C.
Shen
, “
Visualization of low frequency liquid surface acoustic waves by means of optical diffraction
,”
Appl. Phys. Lett.
80
,
3033
3035
(
2002
).
17.
Spatial damping of the surface acoustic waves is measured by the decay constant δ=3α/4Ω, where η is the viscosity of the liquid (see Ref. 13). For acoustic waves on the surface of water at 220 Hz, δ≅44 mm, which is much larger than the spot size of the laser beam (1.8 mm).
18.
The wave function for two-dimensional surface waves is, in general, more complicated. However, for our purposes here, the sinusoidal form is adequate and produces reasonable results.
19.
J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), p. 62.
20.
B. D.
Duncan
, “
Visualization of surface acoustic waves by means of synchronous amplitude-modulated illumination
,”
Appl. Opt.
39
,
2888
2895
(
2000
).
21.
V. G. Levich, Physicochemical Hydrodynamics (Prentice Hall, Englewood Cliffs, NJ, 1962), p. 596.
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