Acousto-Optic Modulators
Left: Acousto-optic tunable filters. Right: Acousto-optic deflectors
(Crystal Technology LLC, a Gooch and Housego Company)
Acousto-Optic Modulators
A schematic illustration of the principle of the acousto-optic modulator.
Photoelastic Effect
Change
1
 2   pe S
n 
Strain
Refractive
index
Photoelastic
coefficient
The strain changes the density of the crystal and distorts the bonds (and
hence the electron orbits), which lead to a change in the refractive index n.
Acousto-Optic Modulation Regime
Illustration of (a) Raman-Nath and (b) Bragg regimes of operation for an acousto-optic
modulator. In the Raman regime, the diffraction occurs as if it were occurring from a line
grating. In the Bragg regime, there is a through beam and only one diffracted beam
Raman-Nath Regime
Acoustic
wavelength
Beam length
L <<
2
L /l
Wavelength of light
Acoustic velocity
L = va/f
Acoustic frequency
Raman-Nath regime, the diffraction occurs as if it were occurring from a line grating,
that is L is very short
Bragg Regime
Acoustic
wavelength
Beam length
L >>
2
L /l
Wavelength of light
Acoustic velocity
L = va/f
Acoustic frequency
In the Bragg regime, there is a through beam and only one diffracted beam
Acousto-Optic Modulators
Definitions of L and H based on the transducer and the AO modulator geometry used
Bragg Regime
Consider two coherent optical waves A and B being reflected from two adjacent acoustic
wave fronts to become A1 and B1. These reflected waves can only constitute the diffracted
beam if they are in phase. The angle q is exaggerated (typically, this is a few degrees).
Bragg Regime
A diffracted beam is generated, only when the incidence angle q (internal to the
crystal) satisfies
2Lsinq = l/n ;
q  qB
The angle q that satisfies this equation is called the
Bragg angle qB
q is small so that sinq  q
In terms of external angles (exterior to the crystal)
2Lsinq = l/n ;
q  qB
Frequency Shift
Doppler effect gives rise to a shift in frequency
w = w ± W
Diffracted light frequency
Acoustic frequency
Incident light frequency
Frequency is w
Frequency is w
We can also use photon and phonon interaction
Incoming
photon
Scattered
photon
Consider energy and
momentum conservation
Phonon
in the
crystal
w = w ± W
2Lsinq = l/n
Diffraction Efficiency DE
Ii
I1
Diffraction efficiency
DE
Acoustic power
1/ 2

I1
 
2   L
  sin  
M 2 Pa  
Ii
 
 l  2 H
Figure of merit
M2: Figure of Merit
Refractive index
6
Photoelastic coefficient
2
n p
M2 
3
v a
Density
Acoustic velocity
M2: Figure of Merit
Properties and figures of merit M2 for various acousto-optic materials. n is the refractive index, v is the acoustic
velocity, and pij is the maximum photoelastic coefficient . (Extracted from I-Cheng Chang, Ch 6, "AcoustoOptic Modulators" in The Handbook of Optics, Vol. V, Ed. M. Bass et al, McGraw-Hill, 2010)
Material
LiNbO3
TeO2
Ge
GaAs
GaP
PbMoO4
Fused
Ge33Se55As12
silica
glass
Useful l (mm)
0.6- 4.5
0.4-5
2-20
1-11
0.6-10
0.4-1.2
0.2-4.5
1.0-14
 (g cm-3)
4.64
6.0
5.33
5.34
4.13
6.95
2.2
4.4
n
2.2
2.26
4
3.37
3.31
2.4
1.46
2.7
(at mm)
(0.633)
(0.633)
(10.6)
(1.15)
(1.15)
(0.633)
(0.63)
Maximum pij
0.18
0.34
-0.07a
-0.17b
-0.151
0.3
0.27
0.21c
(0.63 mm)
(p31)
(p13)
(p44)
(p11)
(p11)
(p33)
(p12)
(p11, p12)
va (km s-1)
6.6
4.2
5.5
5.3
6.3
3.7
6
2.5
M2 × 10-15 (s3 kg-1)
7
35
181
104
45
36
1.5
248
Notes: a2.0-2.2 mm; b1.15 mm; c1.06 mm
Analog Modulation
Analog modulation of an AO modulator. Ii is the input intensity, I0 is the zero-order diffraction, i.e. the
transmitted light, and I1 is the first order diffracted (reflected) light.
Digital Modulation
Digital modulation of an AO modulator
SAW Based Waveguide AO Modulator
A simplified and schematic illustration of a surface acoustic wave (SAW) based
waveguide AO modulator. The polarity of the electrodes shown is at one instant,
since the applied voltage is from an ac (RF) source.
AO Modulator: Example
Example: Suppose that we generate 150 MHz acoustic waves on a TeO2 crystal. The RF
transducer has a length (L) of 10 mm and a height (H) of 5 mm. Consider modulating a
red-laser beam from a He-Ne laser, l = 632.8 nm. Calculate the acoustic wavelength and
hence the Bragg deflection angle. What is the Doppler shift in the wavelength? What is the
relative intensity in the first order reflected beam if the RF acoustic power is 1.0 W
Solution
f = Frequency of the acoustic waves
L = Acoustic wavelength
v a (4.2  103 m s-1 )
-5
L


2
.
8

10
m
6 -1
f
(150  10 s )
L2/l =(2.8×10-5 m)2/(0.6328×10-6 m) = 1.2 mm.
L = 10 mm >> 1.2 mm, we can assume Bragg regime
AO Modulator: Example
Solution
The external Bragg angle is
l
(632.8  10-9 m )
sin q 

 0.0113
-5
2L
2(2.8  10 m)
so that q = 0.65° or a deflection angle 2q of 1.3°. Note that we could have
easily used sinq  q.
The Doppler shift in frequency = 150 MHz.
The diffraction efficiency into the first order is
DE
1/ 2

I1

L

 
2
  sin  
M 2 Pa  
Ii
 
 l  2 H
DE
1/ 2
-3

 10  10
 

2
-15

 sin 
(35  10 )(1)    0.64 or 67%
-9 
-3
 (632.8  10 )  2(5  10 )
 
M2 for TeO
Faraday Rotation
Free space optical isolator for use at 633 nm up to 3 W of optical power
(Courtesy of Thorlabs)