Model of Raman–Nath acousto-optic diffraction
Cuncheng Weng (翁存程)
1
and Xiaoman Zhang (章小曼)
2,
*
1
College of Physics and Energy, Fujian Normal University, Fuzhou 350007, China
2
College of Photonic and Electronic Engineering, Fujian Normal University, Fuzhou 350007, China
*Corresponding author: xmzhang@fjnu.edu.cn
Received April 16, 2015; accepted August 19, 2015; posted online September 11, 2015
In this Letter, we discuss Raman–Nath acousto-optic diffraction, and a new model of Raman–Nath acousto-optic
diffraction is presented. The model is based on the individual and simultaneous occurrences of phase-grating
diffraction and the Doppler effect and optical phase modulation and photon–phonon scattering. We find that
the optical phase modulation can cause temporal and spatial fluctuations of the diffracted light power escaping
from the acoustic field.
OCIS codes: 170.5120, 290.1350, 290.4210, 290.7050.
doi: 10.3788/COL201513.101701.
Back in 1922, the scattering of light by an sound wave,
known as Brillouin or acousto-optic scattering, was first
predicted by Brillouin
[1]
. He also predicted that the scat-
tered light had shifted in frequency. Brillouin scattering
was first observed by Gross in liquids
[2]
. An acoustic signal
produces regions of compression and rarefactio n as it
propagates through a medium. The induced strains
change the refractive index of the medium. This provides
a moving phase grating that may diffract an incident light
beam into a single diffraction order, the Bragg diffraction,
or multiple diffraction orders, the Raman–Nath diffrac-
tion (RNd)
[1,3–7]
.
In 1967, Klein and Cook introduced the Q-parameter to
distinguish between the two diffraction regimes
[3]
. It is well
known that the acoustic actions in the RNd simultane-
ously cause the diffraction and phase shift and frequency
shift of the incident light
[1,2,8]
. Conventionally, the RNd is
analyzed independently by using a moving thin-phase gra-
ting diffraction model
[1,3,5]
. According to the model, the in-
cident light is frequency shifted by the Doppler effect and
is diffracted simultaneously by the grating. After the
introduction of laser in the 1960s, the ideas of quantum
mechanics were also employed to el ucidate the RNd
[1,5]
.
Since then, the RNd has also been regarded independently
as the collision process of a photon and one or more pho-
nons, which are known as photon–phonon scatterings.
This collision process takes two forms: absorption and
emission processes. During the absorption process, one
or more phonons are annihilated by the incoming photon,
and a higher-energy photon leaves the scattering site. In
the emission process, one or more phonons are created
by the incoming photon, and a lower-energy photon leaves
the scattering site.
In the two models, the optical phase shift is ignored. Ad-
ditionally, the acousto-optic interactions can in fact simul-
taneously cause the moving thin-phase grating diffraction
and photon–phonon scattering, especially in an acousto-
optic crystal
[1,5,8]
. Obviously, the conventional models
are insufficient to describe the RNd. But, because of
optical scatterings, the photon–phonon scattering model
can still analyze the RNd in an optically scattering
medium. Additionally, in case of ignoring the optical
phase modulation, the grating diffraction model can still
well explain the RNd in this kind of optically transparent
media such as water, in which the photon–phonon scatter-
ing is very weak
[9]
.
In this Letter, we present a new RNd model stemming
from the simultaneous occurrences of phase-grating dif-
fraction and the Doppler effect and optical phase modu-
lation and photon–phonon scattering.
The RNd we will deal with is two dimensional. A typical
configuration is seen in Fig.
1. An idealized sound beam
is contained between planes z ¼ 0 and z ¼ l inside an
optically transparent medium of refractive index n
0
.
For a plane longitudinal sound wa ve with angular fre-
quency ω and velocity v in the medium, the refractive
index nðt; yÞ at position y and time t obeys
[1–3,5]
nðt; yÞ¼n
0
1 þ m sin ω
t þ
y
v
; (1)
where m is the modulation constant of refractive index
and depends on the acoustic power. From Eq. (
1), the
refractive index is modulated spatially and temporally
by the sound wave.
In order to show the differences between the conven-
tional and presented RNd models, we begin by introduc-
ing the moving thin-phase grating diffraction model.
Based on the grating diffraction model, the diffracted light
Eðl; tÞ is given by
[1–3,5]
Eðl; tÞ¼E
0
expðjkn
0
lÞ
X
þ∞
q¼−∞
J
q
ðkn
0
lmÞ
× exp½jðω
0
þ qωÞtδ
n
0
cos θ
λ
−
q
λ
u
; (2)
where E
0
is the electric field of the incident light; k, ω
0
,
and λ are the wave vector, angular frequency, and wave-
length of the incident light in the vacuum, respectively;
COL 13(10), 101701(2015) CHINESE OPTICS LETTERS October 10, 2015
1671-7694/2015/101701(5) 101701-1 © 2015 Chinese Optics Letters