acousto-optic modulators left: acousto-optic tunable filters. right: acousto-optic deflectors...

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)