Abstract
The effects of altering the angle of incidence & acoustic intensity were investigated using a lead molybdate crystal with a Piezo-electric transducer attached. A HeNe laser was used as a light source for the investigation. The angle of diffraction at which the first order beam was found to be 0.027 Rad ± 0.009 Rad & the acoustic intensity in the crystal at 140MHz was 14.3×104 W m-2 ± 2.9×104 W m-2.
Introduction
The interaction between of light & sound has been observed & investigated since ancient Greece. However, Leon Brillion a French-American physicist, was first to predict diffraction of light by sound in 1922(1). Bragg’s angle is given by the Bragg’s law(2-4) & explains the scattering of electromagnetic waves both coherently & incoherently through a crystalline structure. In this investigation the sound waves propagating through the lead molydbate(8) crystal change the refractive index. A photon at one instance may experience, for instance a refractive index of 2.3, where as a photon a moment later will experience a different refractive index from atoms in the crystal being displaced by the pressure of the sound wave(9). This means the photons will be travelling at different speeds through the medium, so when it emerges the beams of light then interact & interfere with each other. This creates the maxima & minima from the constructive & deconstructive interference. Bragg’s Law(4-7) describes the condition at which the constructive interference takes place. The source of the sound waves which propagate through the crystal is a Piezo-electric transducer. 140Mhz was applied to the transducer by the RF Driver which can alternate the magnitude of the sound wave produced. The transducer was mounted on a rotational stage allowing the effects of transmitted light intensity when the angle of incidence of the light onto the modulator crystal was altered. A HeNe laser was used in the experiment as the light source. A viewing screen was used, so the diffraction characteristics could be seen & a metre rule was used to measure the distsance from the acousto-optic modulator to the viewing screen & photo detector.
Method

Fig.1 shows the setup of the experiment. The position, on the optical axis, of both the lens & aperture & acousto-optic modulator with the rotation stage was unchanged throughout the investigation. A) Familiarisation with RF Driver & Acousto-optic Modulator
The Laser was switched on, as well as the RF driver, photo detector & digital mulitmeter. The Bragg modulator & rotational stage controls were familiarized with. The viewing screen was placed 50cm from the front of the acousto-optic modulator. The control of the RF Driver & rotational stage were then altered & the effects noted.
B) Measurement of the Bragg angle
The viewing screen from part A) was placed, so that the centre of the screen was at the centre of the zero order beam. The rotational stage was then rotated until the 1st order beams were both at their brightest. Each millimeter on the micrometer was found to be 1.69° change in angle. The number of squares was then measured from the right edge of the Zero order beam to the right edge of the right 1st order beam & the right edge of the left 1st order beam. This gave the Bragg angle by using simple trigonometry. Then the answer was compared to the analytically found value. The following equation shows Sell’s law applied to the incident beam & show how the light will be diffracted by the medium; Where Λ is the acoustic wavelength, Θ is the angle from the conversion from the micrometer reading & λ/n the optical path length through the material, n being the Refractive index & λ being the wavelength of the laser light. The acoustic wavelength can be found by using the electronic frequency & the speed of sound in the material, Lead Molybdate being 3750 m/s.
Approximating for small angles, Equ.1 can be written as;
Rafraction will occur at the crystal faces, allowing this gives the Bragg angle; .Where λ was taken as 632.9nm laser light.
Part C) Investigating the intensity of diffracted light with changing acousto-optic modulator angle The Photo detector was placed 50cm from the base of the modulator. It was aligned so the zero order maximum was entering the ‘Slow detector’ input & the iris on the front of the photo detector was adjusted so that the full beam width could enter the detector & no more. The slow detector output was then hooked up to the digital multimeter. The viewing screen was then placed to block infront of the acousto-optic modulator to block the laser light & the multimeter reading was taken to give the ambient light or 0% reading. The laser light was then allowed to hit the photo detector, with no power applied from the RF drive to the modulator & the reading was taken from the multimeter. This gave the full 100% intensity reading. The value of RF drive power that gave the minimum zero order reading was then found & the RF power was then set at that value for the rest of the experiment. The modulator angle was set at 5.5mm & the output power was recorded. Steps of 0.05mm were then taken & the output power at each value was recorded. This was then repeated with the right first order beam, with the same start point & increments. The values on the micrometer were then converted to angles in degrees & the output power values were converted to percentages of the zero order maximum value. The Acoustic Intensity was then found using the equation;
Where, Iac is the acoustic intensity, λ is the laser light wavelength (632.8nm), L is the beam width (approximately 15mm) & Pdif & Pinc are the light power diffracted & incident light power respectively. D) The Apparatus remained in the same setup as before. The Transistor-Transistor-Logic Gate (TTL) was then turned on. A square wave with an initial frequency was set. This causes the power into the RF driver to alternate between the manually set option on the knob & completely off & has a rise fall time of 50ns. The modulator was set to maximize the 1st order beam & the angle was set to 5mm on the micrometer (8.45°). The photo detector (still 50cm from the base of the modulator) was connected to the oscilloscope. The input from the TTL was also connected to the oscilloscope & the signal from both the input TTL & photo detector were shown. The photo detector was 1st placed in alignment with e zero order wave & the result was recorded. The photo detector was then placed on the right hand side 1s order beam & the resulting signals were recorded. The frequency was then increased to find at what value the signal was still modulated. Results
Part A)It was found that increasing the RF drive power caused 1st order beams to appear & a futher increase caused 2nd order beams to appear. Rotating the platform, from no rotation, 0mm on the micrometer, caused the 2nd order beam to dim & disappear on the left hand side of the zero order maxima. The 1st order on the left hand side became brighter, then dimmed as the micrometer reading was increased. The zero order beam started dim, but as the micrometer reading was increased & the acousto-optic modulator on the rotational stage became orthogonal to the viewing screen the beam became brighter. As the acousto-optic modulator moved past being orthogonal, the zero order dimmed & the 1st order beam on the right hand side became brighter & the 2nd order beam on the right hand side appeared. Part B) The angle between the right hand 1st order & the zero order beam was found to be 0.0260 Rad ± 0.009 Rad. The left hand 1st order beam was found to have 0.0280 Rad ± 0.009 Rad angle between itself & the zero order beam. The theoretical Bragg angle was found to be 0.0118 Rad, taking the the spped sound in Lead Molybdate to be 3750 & the electrical frequency to be 140MHz. Part C) Fig.2 shows the results for the part of the experiment Using the graph & Equ.5, the Acoustic intensity was found to be 14.3 x 104 W m-2 ± 2.9 x 104 W m-2. Part D) the following figure shows the results from the zero order beam & 1st order beam against the TTL input signal; Fig.3 shows the signal from the photo detector on channel 1, with the TTL square wave on channel 2. This figure shows the waves are in phase (the larger wave being from the TTL, the slightly hazier signal being from the photo detector) Fig.4 shows the signal from the photo detector on channel 1 again & the TTL signal is on channel 2, showing this time the signals are out of phase. The delay between the zero order beam beam & the TTL signal fluctuating between the zero & 1 state was found to be 140nS ± 10nS. As the pulse generator frequency was increased the beam was found to change to not resemble the TTL input signal. The maximum value where the beam was still modulated was found to be 110MHz ± 10MHz.
Discussion
The experiments in this investigation were relatively easy to set up after some familiarsation took place. The control on the RF driver was a knob that had no indication of what magnitude the dial was set at, so it was difficult to identify if the setting had changed during readings being taken. In part A) it was fairly difficult to establish the edge of the zero order & 1st order beams on the viewing screen. The laser itself was found not to give a stable reading, which made parts C) & D) difficult. The reading from the laser on the multimeter fluctuated by roughly 10mV for each reading taken in part C). A larger amount of error was introduced by the instability of the laser, however if the investigation was to be repeated more measurements could be taken & averages for values would give a clearer relationship. When the RF driver power was set to give the minimum zero order value, the 2nd order maxima were not visible. They gave readings witch fluctuated to the 0% reading or reading for the ambient light. This meant only the 1st order maxima could be investigated. Experimental judgments throughout this investigation cause error. Conclusion Through analysis, the angle at which the light diverged from the zero order maxima should be 0.012 Rad. It was found on this experiment that the first order maxima diverged from the acoustically modulated crystal at an angle of 0.027 Rad ± 0.009 Rad. Through further investigation the 1st order maxima was found to be π Rad out of phase with the zero order beam. The acoustic intensity in experienced in the crystal was found to be 14 x 104 W m-2 ± 2.9 x 104 W m-2.
References

Leon Brillouin,Ann. Phys.(Paris) 17, 88 (1922).
John M. Cowley (1975)Diffraction physics(North-Holland, Amsterdam)ISBN 0-444-10791-6
H. Eklund, A. Roos, S. T. Eng. Rotation of laser beam polarization in acousto-optic devices.Optical and Quantum Electronics. 1975;7(2):73–79.doi:10.1007/BF00631587
R.Y.Chiao, C.H.Townes and B.P.Stoicheff, “Stimulated Brillouin scattering and coherent generation of intense hypersonic waves,”Phys. Rev. Lett.,12, 592 (1964)
Carl. R. Nave.Bragg’s Law. HyperPhysics, Georgia State University. Retrieved 2008-07-19
Bragg, W.L. (1913). “The Diffraction of Short Electromagnetic Waves by a Crystal”.Proceedings of the Cambridge Philosophical Society17: 43–57.
F.L. Liu, P.St.J. Russell, L.Dong, Acousto-optic modulator using a fibre Bragg Grating, Optoelectronics Res. Cen., University of Southampton
G. A. Coquin, D. A. Pinnow, A. W. Warner, Physical Properties of Lead Molybdate Relevant to Acousto-Optic Device Applications, J. App. Phy. A 6, Vol 42 (May 1971)
A.Rosencwaig, A. Gersho, “Theory of the Photoacoustic Effect with Solids”, Journal of Applied Physics, 47(1), 64-69 (1976)
A. Yarvin, P. Yen, “Wave Propagation in Periodic Media” in Optical electronics in modern communication, (Oxford 2007), pp. 539-82