1. Acousto-Optic Modulators
Left: Acousto-optic tunable filters. Right: Acousto-optic deflectors (Crystal Technology LLC, a Gooch and Housego Company)

2. Acousto-Optic Modulators
A schematic illustration of the principle of the acousto-optic modulator.

3. Photoelastic coefficient
Photoelastic Effect
Change
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.

4. 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

5. L << L2/l Raman-Nath Regime L = va/f Acoustic wavelength
Beam length
L << L2/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

6. L >> L2/l Bragg Regime L = va/f Acoustic wavelength Beam length
Wavelength of light
Acoustic velocity
L = va/f
Acoustic frequency
In the Bragg regime, there is a through beam and only one diffracted beam

7. Acousto-Optic Modulators
Definitions of L and H based on the transducer and the AO modulator geometry used

8. 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).

9. In terms of external angles (exterior to the crystal)
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

10. Doppler effect gives rise to a shift in frequency
Frequency Shift
Doppler effect gives rise to a shift in frequency
w = w ± W
Acoustic frequency
Diffracted light frequency
Incident light frequency
Frequency is w
Frequency is w

11. 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

12. Diffraction Efficiency hDEIi I1
Diffraction efficiency
Acoustic power
Figure of merit

13. M2: Figure of Merit Photoelastic coefficient Refractive index Density
Acoustic velocity

14. 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, "Acousto- Optic Modulators" in The Handbook of Optics, Vol. V, Ed. M. Bass et al, McGraw-Hill, 2010)
Material
LiNbO3
TeO2 Ge
GaAs
GaP
PbMoO4
Fused silica
Ge33Se55As12 glass
Useful l (mm)
0.4-5
2-20
1-11
0.6-10
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)
(0.633)
2.26 4
(10.6)
3.37
(1.15)
3.31
2.4
1.46
(0.63)
2.7
Maximum pij (0.63 mm)
(p31)
(p13)
-0.07a (p44)
-0.17b (p11)
(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 × (s3 kg-1) 7 35
181
104 45 36
1.5
248
Notes: a mm; b1.15 mm; c1.06 mm

15. 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.

16. Digital modulation of an AO modulator

17. 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.

18. 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 = 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
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

19. AO Modulator: Example
Solution
The external Bragg angle is
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
M2 for TeO

20. (Courtesy of Thorlabs)
Faraday Rotation
Free space optical isolator for use at 633 nm up to 3 W of optical power
(Courtesy of Thorlabs)