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
Spn e
2
1
Strain
Refractive index
Change
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
Raman-Nath regime, the diffraction occurs as if it were occurring from a line grating, that is L is very short
L << L2/lWavelength of light
Beam lengthAcoustic wavelength
L = va/f Acoustic frequency
Acoustic velocity
Bragg Regime
In the Bragg regime, there is a through beam and only one diffracted beam
L >> L2/lWavelength of light
Beam lengthAcoustic wavelength
L = va/f Acoustic frequency
Acoustic velocity
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
2Lsinq = l/n ; = qqB
A diffracted beam is generated, only when the incidence angle q (internal to the crystal) satisfies
The angle q that satisfies this equation is called the Bragg angle qB
q is small so that sinq q
2Lsinq = l/n ; = qqB
In terms of external angles (exterior to the crystal)
Frequency Shift
w = w ± W
Doppler effect gives rise to a shift in frequency
Acoustic frequency
Incident light frequency
Diffracted light frequency
Frequency is wFrequency is w
We can also use photon and phonon interaction
Incoming photon
Scatteredphoton
Phononin thecrystal
2Lsinq = l/n
Consider energy and momentum conservation
w = w ± W
2/1
221
DE 2sin a
i
PMH
L
I
I
Ii I1
Diffraction Efficiency hDE
Acoustic power
Figure of merit
Diffraction efficiency
M2: Figure of Merit
3va
pnM
26
2
Acoustic velocityDensity
Refractive indexPhotoelastic coefficient
M2: Figure of Merit
Material LiNbO3 TeO2Ge GaAs GaP PbMoO4
Fused
silica
Ge33Se55As12
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
r (g cm-3) 4.64 6.0 5.33 5.34 4.13 6.95 2.2 4.4
n
(at mm)
2.2
(0.633)
2.26
(0.633)
4
(10.6)
3.37
(1.15)
3.31
(1.15)
2.4
(0.633)
1.46
(0.63)
2.7
Maximum pij
(0.63 mm)
0.18
(p31)
0.34
(p13)
-0.07a
(p44)
-0.17b
(p11)
-0.151
(p11)
0.3
(p33)
0.27
(p12)
0.21c
(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 248Notes: a2.0-2.2 mm; b1.15 mm; c1.06 mm
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, "Acousto-
Optic Modulators" in The Handbook of Optics, Vol. V, Ed. M. Bass et al, McGraw-Hill, 2010)
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
m 108.2)s 10150(
)s m 102.4( 516
13
fav
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: ExampleSolution
The external Bragg angle is
0113.0)m 108.2(2
) m 108.632(
2sin
5
9
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
%67or64.0)1)(1035()105(2
1010
)108.632(sin
2/1
153
3
92
DE
2/1
221
DE 2sin a
i
PMH
L
I
I
M2 for TeO
Faraday Rotation
Free space optical isolator for use at 633 nm up to 3 W of optical power
(Courtesy of Thorlabs)
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