Intensity interference in Bragg scattering by acoustic waves with thermal statistics
M. V. Chekhova, S. P. Kulik, A. N. Penin, and P. A. Prudkovskii
Department of Quantum Radiophysics, Moscow State University, 119899 Moscow, Russia
Received 5 February 1996; revised manuscript received 8 August 1996
Angular distributions of the intensity and the fourth-order correlation function are studied for light scattered
by acoustic waves with thermal statistics. In the case when the beam diameter exceeds the coherence length of
the acoustic wave, the fourth-order correlation function is found to contain an interference structure, whereas
the intensity angular distribution has a one-peak shape. S1050-29479650911-X
PACS numbers: 42.50.Ar, 42.25.Hz
Does the intensity correlation function the fourth-order
correlation function, in Glauber’s notation provide any in-
formation that is not contained in the intensity distribution?
For coherent light and for light with thermal statistics, the
answer is at first sight trivial: higher-order intensity moments
can be expressed via the average intensity. On the other
hand, the well-known experiment by Brown and Twiss 1
demonstrated that the measurement of the intensity correla-
tion function has some advantages over the measurement of
the field correlation function. In particular, it was success-
fully used for determining the angular diameters of stars 2.
There is no contradiction in these two statements. The
fourth-order correlation function differs essentially from the
second-order one, whenever the light under study contains a
superposition of independent fields. As a simple example,
one can consider the interference from two monochromatic
sources with thermal statistics: if the sources are indepen-
dent, they form no second-order interference pattern, but the
fourth-order correlation function contains interference
fringes, which can be used for measuring the angular dis-
tance between the sources 3.
In the present paper we show how the measurement of the
intensity correlation function of light scattered by acoustic
waves can provide information that is not contained in the
intensity distribution. The experimental setup is shown in
Fig. 1. A single-model He-Ne laser beam, whose aperture l
can be varied by means of the diaphragm D 0 within the
range 0.8–3 mm, is directed into a block of fused silica FS.
In the silica the beam is scattered by an acoustic wave propa-
gating normally to the beam. The acoustic wave has quasith-
ermal statistics, for it is excited in the following way. A
photomultiplier tube PMT0 operating in a photon counting
regime is illuminated by the radiation of a stabilized light-
emitting diode LD, and its amplified pulses form a continu-
ous spectral distribution in the frequency range from 10 to
100 MHz. This ‘‘white noise’’ is sent to a narrow-band ac-
tive filter AF, which amplifies the signal within the band of
f =2.5 MHz with central frequency f =/2=50 MHz.
According to the principles of statistical radiophysics, such a
procedure gives a random signal with Gaussian thermal
statistics. The spectrum of the electric signal is analyzed by
means of a spectrum analyzer SA. This signal is fed to a
piezoelectric element PE, which is used to generate the
acoustic wave in the silica. Thus, we obtain a quasithermal
acoustic wave with coherence length 1.5 mm. Light scattered
by this quasithermal wave must also possess thermal statis-
tics. This fact, perhaps obvious enough, is to be discussed in
detail in Ref. 4; for its theoretical proof, see Ref. 5.
Light scattered at the Bragg angle is analyzed by means
of the Brown-Twiss interferometer. It is split by a beam
splitter BS and the two beams are fed to a pair of photon
counting photomultipliers PMT1 and PMT2. The output
pulses of the PMT’s are sent to a digital correlator CORR
that provides the coincidence counting rate R
c
and the count-
ing rates of both detectors R
1
and R
2
. An IBM personal
computer calculates the normalized second intensity mo-
ment, the bunching parameter g
(2)
= I
2
/ I
2
, which is re-
lated to R
c
as g
(2)
=R
c
/ R
1
R
2
, time parameter being de-
termined by the resolution of the correlator. The distance
between the sample and each of the detectors L =5 m; that
is, the scattering is observed in the far field zone. A 0.4-mm
diaphragm D1 at the input of PMT1 selects radiation
scattered at the Bragg angle. At the input of the other PMT
the angle of scattering is scanned by means of an adjustable
0.4-mm diaphragm D 2 connected by fiber F with the PMT.
The diaphragm can be displaced within the vicinity of 15
mm, this corresponding to the scattering angle variation
by 0.2°.
The experimental results are represented by R
c
/ R
1
R
2
and
R
2
plotted against the coordinate of D 2. The first value is
equal to g
(2)
multiplied by the effective coincidence resolu-
tion , which was equal to 7.5 ns. We obtained a set of such
dependences for the following diameters of the pump beam:
FIG. 1. The experimental setup. LD, light-emitting diode;
PMT0, PMT1, PMT2, photomultiplier tubes; AF, active filter;
SA, spectrum analyzer; PE, piezoelectric element; FS, fused
silica; D0, diaphragm with variable diameter; BS, beam splitter;
D1 and D2, pinholes; F , fiber; CORR, correlation circuit; PC,
computer.
PHYSICAL REVIEW A DECEMBER 1996 VOLUME 54, NUMBER 6
54 1050-2947/96/546/46454/$10.00 R4645 © 1996 The American Physical Society