Department of Physics, Middlebury College 1992-93
Modern Physics Laboratory


III. The Acousto-Optic Modulator and Optical Heterodyning


Discussion

The beat note is a familiar and useful acoustic phenomenon to musicians. The acoustic guitarist can set the tension of the A string by placing a struck, 440 Hz, concert A tuning fork against the soundboard of the guitar and listening to the beat note that results from the frequency difference between the plucked A string and the tuning fork. When the frequency of the A string is 1 Hz above or below the 440 Hz tuning fork frequency, a rise and fall of the sound amplitude at a 1 Hz beat frequency is clearly audible. A proper tuning of the A string is indicated when the beat frequency falls to zero.

Beat notes are also familiar at radio frequencies, especially in the AM broadcast band (540-1600 kHz) during the late evening hours when broadcast stations from around the country, and from South America, can be heard because of improved propagation of low frequency electromagnetic waves by the nighttime ionosphere. As a typical situation, consider the case when one AM broadcasting station has a carrier frequency of 600 kHz and another station has a carrier frequency of 601 kHz. In this case, a 1 kHz beat note will be heard in an AM receiver in the form of steady whistle, even when no speech or music is being broadcast by either AM station. Many of these beat notes or whistles can be heard while tuning across the AM broadcast band late at night and they can be very annoying when trying to listen to a weak station.

The two examples given above illustrate the same general physical phenomenon: the production of a beat note at a frequency given by the difference in frequency of two interfering signals. As much as these examples may seem similar, the two cases are very different when the medium for wave propagation in the two cases is considered. The musician's beat note occurs for acoustic waves in air, while the radio signals travel at the speed of light in the absence of a material medium. In the context of your newly acquired skills in experimental optics, it probably occurs to you to ask if beat frequency phenomena can be observed with light waves. The answer is yes, and in this experiment you will generate an audio beat note from the interference of two laser light beams of slightly different frequency. This result is amazing when you consider that the frequency of the HeNe laser light (= 6328 Å) is about 4.7 x 1014 Hz or, put more impressively, 470,000,000,000,000 Hz, and yet you will be able to produce two light beams that differ in frequency by as little as 1 Hz. Stable beat frequencies as small as 20 Hz can be produced with visible light and can be exploited for extremely sensitive measurements of crystal growth rates. For beat frequencies in the range 20-20,000 Hz you will be able to hear the light beams beating together using a loudspeaker. As a final bonus in this experiment, you will put your voice on a light beam to demonstrate a coherent, single sideband, optical communications scheme.

The transverse mode profiles you photographed during the HeNe laser experiment and the fringe patterns that you observed while using the Michelson interferometer are both examples of stationary spatial interference patterns, and in more technical terms, they are said to be examples of interference in the spatial domain. The light beating phenomena you will observe in this experiment are complementary in the sense that the interference is dynamic and observation takes place in the time domain.

(1) The Acousto-Optic Modulator.

The principal optical component in this experiment is the acousto-optic modulator (AOM). Because of the central importance of the acousto-optic modulator to this experiment and to numerous technical applications such as laser printers and optical spectrum analyzers, the acousto-optic modulator will be described in some detail. Although some details of the physical principles underlying the operation of the acousto-optic modulator will be given here, the major emphasis will be on the useful role the acousto-optic modulator can play in the optics laboratory.

The acousto-optic effect occurs when a light beam passes through a transparent material, such as glass, in which travelling acoustic waves are also present, as depicted in Fig. 1.2 Acoustic waves are generated in the glass by a piezoelectric transducer that is driven by a RF signal source. The spatially periodic density variations in the glass corresponding to compressions and rarefactions of the travelling acoustic wave are accompanied by corresponding changes in the index of refraction for propagation of light in the medium. These travelling waves of index of refraction variation diffract the incident light much as the atomic planes of a crystal diffract x-rays in Bragg scattering.2 For acoustic waves of sufficiently high power, most of the light incident on the acousto-optic modulator can be diffracted and therefore deflected from its incident direction.

For acoustic waves of frequency f travelling at the speed of sound in a medium, vs, the wavelength of the acoustic waves, , and therefore the spacing between the planes of index of refraction variation, is given by the usual wave relation vs = f. A light beam passing through the acoustically driven medium will be diffracted to angles given by

sin = ( m / 2 )      (1)

where m = 0, 1, 2, ... is called the diffraction order.2 In this experiment only the m 0 and m = +1 diffraction orders will be important. Note the similarity of Eq. (1) to the analogous formula for Bragg diffraction of x-rays by atomic planes separated by a distance d:3

sin = ( m / 2d )         

From Fig. 1, the angle between a diffracted beam and the undiffracted beam is given by

sin( / 2 ) = ( m / 2 )
= ( mf / 2vs )      (2)

At this point it is helpful to consider numerical estimates for these quantities for the IntraAction ADM-40, flint glass, acousto-optic modulator/deflectors used in this experiment. The "40" in the model number signifies that these acousto-optic modulators have been optimized for operation at an acoustic frequency f = 40 MHz, but the manufacturer guarantees good performance over the range 30-50 MHz. Although vs for the flint glass material used in the ADM-40 is not given by the manufacturer, an estimate can be made using the speed of sound in clear lead glass, vs = 3800 m/s, from Ref. 4. The acoustic wavelength will therefore be = vs/f = 9.5 m. For deflection of a HeNe laser beam, the deflection angle for the first order (m = 1) diffracted beam is less than a degree, so that the usual small angle approximation can be made in Eq.(2) to give

= (f/vs)
= ((6328 x 10-10 m)(40 x 106 s-1)/3800 m/s)
= 6.7 x 10-3 rad = 0.380 (3)

a very small, but useful deflection.

Three common operating modes of the acousto-optic modulator will be described in detail.

(a) Deflection. Under optimal conditions, the ADM-40 can diffract nearly 85-90% of the incident light into the first order diffracted beam.5 By simply turning the acoustic energy source on and off, the acousto-optic modulator can act as a rapid light deflector. The switching of the incident light beam to the first order diffracted beam can occur in a very short period of time (< 5 s) depending only on how rapidly the acoustic wave field can be turned on and off in the volume of the flint glass traversed by the laser beam. From Eq. (3) it can be seen that an acousto-optic modulator can deflect a laser beam to different angles by simply varying the acousto-optic modulator frequency f. The diffracted beam emerging from the ADM-40 can be swept through an angular range of 3.3 mrad when the acoustic driver frequency is swept from 30 to 50 MHz. This property can be used to move a laser beam rapidly in space - without moving parts - in such applications as the laser printer and direct laser display devices.

From Eq. (3) it can be seen that the deflection angle depends on the wavelength of the incident light beam. The acousto-optic modulator can therefore be used to deflect beams of polychromatic light into component colors or wavelengths, in a manner reminiscent of the dispersive prism.

(b) Modulation. The amount of laser light diffracted to the first order beam depends on the amplitude of the acoustic waves that diffract the incident laser beam, and therefore, by modulating the power level of the acoustic wave source, the intensity of the diffracted light beam can be modulated. By this means an electrical signal containing voice, music, or television can modulate the intensity of a light beam as part of an optical communications system.

(c) Frequency shifting. This is one of the most useful properties of the acousto-optic modulator. The ability of the acousto-optic modulator to shift the frequency of a laser light beam by a precise and stable amount is crucial to production of a beat note from two light beams in this experiment. The similarity of Eq. (1) for the acousto-optic effect to Eq. (2) for Bragg diffraction of x-rays belies an important difference between the two diffraction situations. Bragg diffraction of x-rays occurs for atomic planes that are at rest in the laboratory, while acousto-optic diffraction occurs from acoustic wave planes that travel at the relatively high speed vs with respect to the laboratory. The fact that the diffracting acoustic planes move with respect to the laboratory leads to a Doppler shift of the frequency of the diffracted beams. Although a derivation of the Doppler effect expected for this case will not be given here, the answer for the Doppler shifted frequency of the diffracted beam is very simple to state: the frequency of the first order diffracted beam is shifted by an amount exactly equal to the acousto-optic modulator frequency f. If 0 is the frequency of the light incident on the acousto-optic modulator, the frequency of the first order beam will be upshifted to 0+f in the case that the acoustic planes have a component of motion toward the incident light beam, as in the configuration of Fig. 2(a), and downshifted to 0-f when the acoustic planes have a component of motion away from the incident light beam, as in Fig. 2(b).

The frequency shift produced by an acousto-optic modulator can be used to transform a fixed frequency laser like the HeNe laser, into a tunable laser, although only over the small range of frequencies (20 MHz for the ADM-40) over which the acousto-optic modulator can be operated.

(2) Optical heterodyning.

A diagram of the apparatus used for optical heterodyning measurements is given in Fig. 3. The beam from a HeNe laser is split into two beams by a beamsplitter BS1 and the two beams pass to two acousto-optic modulators AOM1 and AOM2. The AOMs upshift the two light beams by different acoustic frequencies f1 and f2 producing light beams of frequency 0+f1 and 0+f2, respectively. The acoustic power at frequencies f1 and f2 is generated by two highly stable amateur radio transmitters operating at their maximum transmitting frequency near 29.9 MHz, just slightly below the frequency range 30-50 MHz recommended by IntraAction. The two frequency shifted laser beams are then recombined at beamsplitter BS2 and the combined beams pass on to a lens L that expands the beams for viewing on the laboratory wall and to a photodiode detector PD that detects electronically the beating of the two light beams.

At the active surface of the photodiode PD, the two light beams consist of sinusoidally varying electric fields E1(t) and E2(t) that can be written as

E1(t) = E1sin[2 (o+f1)t]         

and

E2(t) = E2sin[2 (o+f2)t]         

where any constant phase difference between the two beams has been ignored. By superposition, the resultant electric field at the photodiode is given by

E(t) = E1(t) + E2(t)
= E1sin[2 (o+f1)t] + E2sin[2 (o+f2)t].
The instantaneous intensity I(t) of the resultant light beam is proportional to the square of E(t), so that

I(t) <=> E12 sin2[2 (o+f1)t] + E22 sin2[2 (o+f2)t]
+ 2E1E2 sin[2 (o+f1)t] sin[2 (o+f2)t].

Using the trigonometric identity 2sinAsinB = cos(A-B)-cos(A+B), this result may be rewritten as

I(t) <=> E12 sin2[2 (o+f1)t] + E22 sin2[2 (o+f2)t]
+ E1E2 {cos[2 (f1-f2)t] - cos[2 (2o+f1-f2)t]}. (4)

A photodiode detector does not measure the instantaneous value of I(t) because the electrical response of the photodiode is too slow; the photodiode used in this experiment can only give an instantaneous response to frequency components below about 100 MHz. For frequency components above 100 MHz the photodiode can only give a time averaged response. The oscillatory terms in Eq. (4) at frequencies o+f1, o+f2, and 2o+f1+f2 involve frequencies near 1014 Hz, well above the 100 MHz response limit of the photodiode. These terms must therefore be replaced by their time averages to compute the photodiode response. The time averages of sin2[2 (o+f1)t] and sin2[2 (o+f2)t] are each 1/2 and the time average contribution of the last term in Eq. (4) is zero. The photodiode will give a faithful, sinusoidally varying response to the term cos[2 (f1-f2)t] because the range of beat frequencies f1-f2 investigated in this experiment lie in the range 0-100 kHz, well within the frequency response of the photodiode. The voltage V(t) produced by the photodiode detector is therefore given by

V(t) <=> 1/2 E12 + 1/2 E22 + E1E2 cos[2 (f1-f2)t].      (5)

The terms 1/2 E12 and 1/2 E22 in Eq. (5) represent DC voltages produced at the photodiode by beams 1 and 2, respectively. The term E1E2 cos[2 (f1-f2)t] is a sinusoidally varying photodiode voltage at the beat frequency f1-f2 of the two light beams. By adjusting the frequencies of acousto-optic modulators AOM1 and AOM2, the beat frequency f1-f2 can be put in the range of audio frequencies and made audible throughout the laboratory with a loudspeaker.

The interaction of two waves of different frequency in a nonlinear detector (here the photodetector) to produce a beat frequency is technically known as heterodyning, a term that you might have encountered in connection with superheterodyne radio receivers, such as FM stereo or short wave receivers. The phenomenon realized in the present experiment is often called offset homodyning, because two light beams of different frequency are derived by a frequency offset process from a single, parent laser beam of frequency o. In this experiment it should be understood that the frequency difference between the two light beams can be held stable to within a few Hz for over a period of minutes, even though the parent laser frequency o is jumping rapidly and randomly over a range of several hundred MHz during the same time interval. The two laser beams that produce a stable audio beat note do not have an absolute frequency stability of a few Hz.

Procedure

Remember to take the usual precautions against accidental exposure of the eyes to intense laser light beams. Use white index cards to locate beam spots throughout the apparatus and at no time should you bring your eyes to the horizontal plane of the laser beams.

The alignment of the optical heterodyning arrangement is not significantly more difficult than for the Michelson interferometer. The optical arrangement used in this experiment must be perfectly planar and this can be accomplished by adjusting the laser beam to be at the same vertical height above the optical table top at all points along the optical path. The following steps are intended to guide you through the alignment procedure.

(1) First you will make preliminary measurements with a single acousto-optic modulator to gain experience aligning it with the three axis rotatable stage. Secure the HeNe laser and AOM1 to optical table top as shown in Fig. 3. Get all other optical components out of the way for simplicity. As in the Michelson interferometer experiment, it is important that the beam from the HeNe laser be at the same vertical height above the optical table top at all points in this experiment. You can set the HeNe for a level output beam by moving a white index card along the table and noting whether the HeNe beam remains at a constant vertical height on the index card.

Adjust the vertical and horizontal position of the rotatable stage supporting AOM1 so that the HeNe laser beam passes through the centers of the entrance and exit apertures of AOM1. Connect an IntraAction DE-40M Deflector Driver to AOM1 and turn on the RF acoustic power. While observing the diffraction spots on the laboratory wall, adjust the three knobs of the rotatable stage until the first order diffracted beam is observed to be much more intense than the undeflected beam. The diffracted beam can be identified by turning on and off the RF power to AOM1. Make sure that you can distinguish the frequency upshift and downshift geometries for AOM1 using Figs. 2(a) and 2(b).

For acoustic frequencies of 30, 40, and 50 MHz, measure the spacing between the first order diffracted beamspot and the undeflected beamspot on a screen on the wall located along the direction HeNe-AOM1-M1 in Fig. 3. Measure the distance from the center of AOM1 to the wall. Use this data to determine the deflection angle at 30, 40, and 50 MHz. With the small angle approximation for a in Eq. (3), use your data to calculate the speed of sound in the flint glass of the ADM-40 acousto-optic modulator. Is your value reasonable when compared to the value for vs used for illustration purposes in section (1) of the Discussion?

(2) Remove AOM1 and install beamsplitters BS1, BS2 and mirrors M1,M2 to form the rectangle BS1-M1-BS2-M2 of Fig. 3. The rectangle must form a perfect horizontal plane above the optical table top. If your alignment is good you should obtain interference fringes in the beams that emerge from beamsplitter BS2. Keep alert to the intrusion of unwanted, but unavoidable, reflections from the faces of the beamsplitters BS1 and BS2.

(3) After you have observed interference fringes in the beams emerging from BS2, insert AOM1 and AOM2 with the acousto-optic RF power off. The distance (around the rectangle) from each AOM to beamsplitter BS2 should be the same to within 2 mm. This positioning is necessary to ensure that the diffracted beams from AOM1 and AOM2 emerge from BS2 at the same angles, and can be made collinear over large distances. Adjust the vertical and horizontal positions of the AOMs so that the interference patterns in the beams emerging from beamsplitter BS2 are maintained as in step (2). Then turn on acoustic power to AOM1 using TX1, an ICOM 745 transceiver set to transmit at 29.900 MHz using upper sideband (USB) modulation and supplied with a 1 kHz sine wave at its microphone jack. Adjust the rotatable stage for AOM1 to obtain maximum laser intensity in the first order diffracted beam. Adjust the angle of AOM1 for a diffracted beam that is frequency upshifted, as in Fig. 2(a). When the first order diffracted beam emerging from AOM1 is optimized, turn off the RF power to AOM1.

Turn on the RF acoustic power to AOM2 using TX2 and align AOM2 for optimum intensity in the first order diffracted beam. Be sure that AOM2 is set to produce a frequency upshifted, first order diffracted beam.

The ICOM 745 transmitter is capable of delivering far more RF power than can be dissipated by the piezoelectric transducer in the AOMs. The RF acoustic power to the AOMs should therefore be monitored frequently on the oscilloscope to insure that damage to the AOMs does not occur. Consult the instructor for proper setting of the RF acoustic power level to the AOMs.

(4) Turn on the RF acoustic power from the radio transceivers to both AOMs and observe the beams emerging from BS2. An optical heterodyning signal at PD will only be obtained if the two first order diffracted beams from AOM1 and AOM2 are recombined at beamsplitter BS2 to produce perfectly collinear beams along the lines BS2-PD and BS2-L in Fig. 3. Along both BS2-PD and BS2-L, the beamspots of the undeflected beams and the beamspots of the first order diffracted beams must overlap from BS2 to the laboratory walls. The collinearity of the two beams can be checked by moving a white index card continuously from BS2 to the wall. This condition can be achieved by adjusting the tilt of each AOM, and the orientations of mirror M1 and beamsplitter BS2. It should not be necessary to adjust the orientation of mirror M2 or beamsplitter BS1.

(5) If the collinearity of the undiffracted beams along BS2-L and BS2-PD is satisfactory they will produce high quality Michelson interference fringes. When you think the collinearity of the first order diffracted beams is satisfactory, adjust the frequency of one of the AOMs, either f1 or f2, to make the two frequencies equal. When the frequencies f1 and f2 are within a few Hz of each other, a slowly drifting Michelson interference fringe pattern will appear on the wall at the overlap spot made by the combined first order diffracted beams. These fringes will drift in either direction depending on whether f1 is greater or less than f2.

The photograph of Fig. 4 shows photodiode detector PD placed in the first order diffracted beams that combine along the direction BS2-PD in Fig. 3. Interference fringes produced by these two frequency shifted beams are clearly visible on the face of the detector. To have the fringes appear sharply on the face of the detector in Fig. 4, it was necessary to maintain f1 equal to f2 to better than 0.1 Hz during the few second photographic exposure, so that a slow horizontal drift of the fringes did not blur the photograph. The shadow of detector PD can be seen on the screen in the background of the photograph. The brighter fringe pattern to the right of the first order diffracted pattern is due to the interference of the undiffracted beams; this fringe pattern does not drift because it is produced by two light beams that are of the same frequency, o.

When the beat frequency f1-f2 is a few Hz, the fringe pattern is seen to drift left or right across the detector face depending on the relative magnitudes of f1 and f2. The time varying light intensity of the drifting fringe pattern produces a sinusoidally varying voltage at the output of the photodiode that can be amplified for a loudspeaker by a PAR 113 Preamplifier.

Adjust the two frequencies f1 and f2, and observe the photodiode detector signal on the oscilloscope, especially within a few Hz of f1 = f2. For how large a frequency difference f1-f2 can you still observe the drifting of the fringes on the face of the photodiode with your eyes?

Use the oscilloscope camera to record beat frequency signals from the photodiode detector PD for beat frequencies of 100, 1000, and 10,000 Hz. Record simultaneously the frequency spectrum of the photodiode signal using the Tektronix 7L5 Spectrum Analyzer. A sample of the photodiode signal and its frequency spectrum at a beat frequency of 2 kHz is given in Fig. 5. Be sure to record in your lab notebook the relevant oscilloscope voltage and time base settings corresponding to your photographs. Photographs should be affixed securely to a page in your laboratory notebook.

(6) Single sideband optical communications. This part of the experiment is just for fun and it is meant to reward you for the hard work and perseverance necessary to get to this point. Disconnect the Tektronix CFG250 Function Generator from the microphone jack of TX1. Connect a standard push-to-talk microphone to the microphone jack. Push the microphone button down and talk. You should hear your voice, perhaps sounding a bit like Donald Duck, in the loudspeaker. Adjust the frequency of either transceiver in order to make the speech clear. Small adjustments of the mirrors and beamsplitters will likely improve the overall quality of the speech in the loudspeaker. Congratulations, you've just demonstrated a coherent, homodyning, single sideband, optical communications system.

You don't need to make any measurements or make any detailed comments in your lab notebook about how such a system might work. But just in case you're curious, a brief explanation will be given here.

When voice information is to be broadcast by a radio transmitter the least technically demanding method is amplitude modulation (AM). An AM transmitter is based around a fixed frequency oscillator that provides a steady sinusoidal output at what is called the carrier frequency, as shown in Fig. 6(a). When the carrier oscillator signal is mixed with a voice signal, the output signal contains a complicated frequency spectrum, such as that shown in Fig. 6(b). In Fig. 6(b) the carrier frequency has been taken to be 29.900 MHz and the range of voice modulation frequencies has been restricted to the audio range 20-20,000 Hz. From Fig. 6(b) it is apparent the amplitude modulation process has produced additional frequency components called sidebands near the AM carrier frequency.

Because the carrier contains no information and only one sideband is necessary for the recovery of the modulating information at a receiving station, it is often desirable to remove the carrier and one sideband with a filter before the final amplifier section of the transmitter. The final amplifier then only dissipates power when modulation is taking place, that is, when someone is talking into the microphone of the transmitter. The final amplifier of the transmitter is therefore able to operate at significantly lower average power levels than would be the case for an AM transmitter. When only a single sideband (SSB) is transmitted, one has the cases of upper sideband (USB) as in Fig. 6(c), or lower sideband (LSB) as in Fig. 6(d).

Although single sideband modulation leads to less power dissipation at the transmitter, it creates problems at the receiving end where SSB signals are rendered unintelligible by an AM receiver. To make SSB signals intelligible at an AM receiver, the receiver must generate a signal at the original transmitter carrier frequency using what is called a local oscillator. The local oscillator signal generated by the receiver is mixed with the received SSB signal to produce a beat signal that contains the original voice information at audio frequencies. Because the receiver's local oscillator frequency must be set to produce proper beating with the incoming SSB signal, the tuning of SSB radio stations on a SSB receiver is a bit tricky and requires some practice.

In the optical homodyning arrangement of Fig. 3, AOM1 simply translates the information contained in an USB signal generated at 29.9 MHz by TX1 to optical frequencies near o + 29.9 MHz. Successful demodulation of the optical USB signal generated by AOM1 requires carrier insertion which is provided by the unmodulated, local oscillator beam from AOM2 at o + 29.9 MHz . Carrier insertion is essential for proper demodulation of the optical USB signal, as you can verify easily by listening to your voice on the loudspeaker while blocking the beam from AOM2.

References
1. E. Mazur, D.S. Chung, and K.Y. Lee, in Laser Spectroscopy IX, edited by M.S. Feld, J.E. Thomas, and A. Mooradian (Academic Press, New York, 1989), pp. 216-219.
2. J. Wilson and J.F.B. Hawkes, Optoelectronics, 2nd ed. (Prentice-Hall, Englewood Cliffs, NJ, 1989), pp. 99-104.
3. R.A. Serway, C.J. Moses, and C.A. Moyer, Modern Physics (Saunders College Publishing, Philadelphia, 1989), pp. 58-61.
4. A. Yariv and P. Yeh, Optical Waves in Crystals (John Wiley & Sons, New York, 1984), p. 374.
5. Model ADM-40 Acousto-Optic Light Deflector Modulator and Model DE-40M VCO Deflector Driver with Modulation, manuals, (IntraAction Corp., Bellwood, Illinois).
6. J.E. Appleby, Offset Homodyning: Applications in Lightwave Communications and Optical Spectroscopy, B.A. thesis, Middlebury College, 1991.

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