# Acousto-Optic Modulators Left: Acousto-optic tunable filters. Right: Acousto-optic deflectors...

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Acousto-Optic Modulators

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

StrainRefractive indexChangePhotoelastic coefficientThe 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 RegimeIllustration 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 RegimeRaman-Nath regime, the diffraction occurs as if it were occurring from a line grating, that is L is very shortL > L2/lWavelength of lightBeam lengthAcoustic wavelengthL = va/f Acoustic frequencyAcoustic velocity

Acousto-Optic ModulatorsDefinitions of L and H based on the transducer and the AO modulator geometry usedBragg RegimeConsider 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 Regime2Lsinq = l/n ; q = qBA diffracted beam is generated, only when the incidence angle q (internal to the crystal) satisfiesThe angle q that satisfies this equation is called the Bragg angle qBq is small so that sinq q 2Lsinq = l/n ; q = qBIn terms of external angles (exterior to the crystal)

Frequency Shiftw = w WDoppler effect gives rise to a shift in frequencyAcoustic frequencyIncident light frequencyDiffracted light frequencyFrequency is wFrequency is wWe can also use photon and phonon interactionIncoming photonScatteredphotonPhononin thecrystal

2Lsinq = l/nConsider energy and momentum conservationw = w W

IiI1Diffraction Efficiency hDE

Acoustic powerFigure of meritDiffraction efficiencyM2: Figure of Merit

Acoustic velocityDensityRefractive indexPhotoelastic coefficientM2: Figure of MeritMaterialLiNbO3TeO2GeGaAsGaPPbMoO4FusedsilicaGe33Se55As12glassUseful l (mm)0.6- 4.50.4-52-201-110.6-100.4-1.20.2-4.51.0-14r (g cm-3)4.646.05.335.344.136.952.24.4n(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)2.7Maximum 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)6.64.25.55.36.33.762.5M2 10-15 (s3 kg-1)73518110445361.5248Notes: a2.0-2.2 mm; b1.15 mm; c1.06 mmProperties 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 ModulationAnalog 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 ModulationDigital modulation of an AO modulator

SAW Based Waveguide AO ModulatorA 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: ExampleExample: 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 WSolutionf = Frequency of the acoustic wavesL = Acoustic wavelength

L2/l =(2.810-5 m)2/(0.632810-6 m) = 1.2 mm. L = 10 mm >> 1.2 mm, we can assume Bragg regimeAO Modulator: ExampleSolutionThe 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 TeOFaraday RotationFree space optical isolator for use at 633 nm up to 3 W of optical power

(Courtesy of Thorlabs)

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