In this project we tested the method of optical phase shifting suggested by Enbang Li, et al. in a paper published last January. Here is a link to the original presentation of this same material.
Reference: Li, E.,
ways of introducing a phase shift are mechanical, like translating mirrors or a
diffraction grating. These methods must be calibrated- in the paper they go so
far as to say "tedious and time consuming". Another method is using
an electro-optic modulator, but this changes the polarization of the beam.
Using Acousto-optic modulators, this group from
An acousto-optic modulator (AOM) is basically a crystal with a transducer glued to one end. The transducer is a tiny piezoelectric quartz crystal which changes physical dimensions when there is a current passing through it. When the transducer squeezes in and out it produces a sound wave that travels through the crystal. Because sound waves are density waves, you can think of this traveling acoustic wave as a traveling pattern of density (thus index of refraction) fluctuations, like a moving diffraction grating. A beam of light incident on these fluctuations will reflect from these boundaries. If the light comes in at the Bragg angle, the diffracted light will be coherent, and there should only be + and - first order diffraction. Because the wave is traveling, the light frequency is also changed, due to the Doppler effect.
Our Electronic Setup:
The voltage controlled oscillator generates an RF frequency determined by the input voltage from the control voltage source. So the voltage source sends a specific voltage to the oscillator, which we can vary. Depending on this voltage being sent to the oscillator, it puts out a certain frequency RF signal. We use a power splitter to split the signal to go into two different Acousto-optic modulators.
There are a few different ways to change cause a phase delay between the two AOMs. Ways which we tried:
Change the cable length between the two using a trombone or computerized delay line
Physically translate one AOM, effectively lengthing the path the acoustic wave must travel through the crystal
By changing the input voltage:
· The Phase difference in the RF signal between the two AOMs= speed of RF/Frequency over path length
· The cables are of different lengths. This is what is going to cause the initial phase shift between the two RF signals. These lengths are now set, and never need to be changed. When we change the voltage in the control voltage source, the frequency of the signal will be different, and so this path difference is going to correspond to different phase differences. Now we position the two modulators in such a way that in one, we will have a sound wave traveling in one direction, and in the other, our sound wave is going to be traveling in the other direction. If a beam of light is shone through both in order, the frequency shift from the last modulator is going to counteract the frequency shift from the first, and the outgoing beam will be the same frequency as the incoming beam.
So now our light has the exact frequency it started with, but its phase has changed. The way we test this is to create an interferometer, so we can see interference fringes.
We know that the intensity of the diffracted beam is going to get smaller, because each selected beam is only one of the many diffracted beams. This can be a problem for applications of this method of phase shifting. We compensated for this by using a light attenuator in the other beam to intensities. This is important because it could affect our interference fringes enough that they could not be noticed. When we built this interferometer we actually had a lot of trouble just getting it to work. One thing was that the AOM's were vertically polarizing the light a little, so we vertically polarized all the light before we did anything to it. Another thing was that at the beginning the path difference between the two beams was longer than the coherence length of the laser. This was our last main problem. We tried a million things and couldn't get it to work, and then as soon as we brought the mirrors in closer, we got our fringes.
Originally we just magnified the fringes onto the wall with a microscope objective, but to measure them more carefully we put in a linear photodiode array to see the fringes on the oscilloscope. The micrometer stage is another way we could introduce a phase change. When we move the second AOM this is like changing the acoustic wave path length.
The oscilloscope gave us a picture of Intensity vs. position. One important thing we used this for was to determine the velocity of the acoustic wave in the crystal of the AOM. By translating one AOM on the micrometer stage, Andy measured the distance it took to go between fringe minimums. We used this to calculate the Wavelength of the acoustic wave. Multiplying by the frequency will give the velocity of the wave.
80 MHz: half wavelength~=6ns