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Today I read an introduction on an optical device called an acousto-optic modulator, which is used in many optical experiments. It is the first time I have heard of this element. The material showed one example of having a laser beam shinning on the intensity-modulated acousto-optic modulator which is driven by a RF signal of some frequency (e.g. 80 MHz). So the output light will be separated into 0th, +/-1st order, +/- second order and etc.

I wonder if the 1st order (or any higher order) light carries both the laser frequency and the 80MHz (the driving signal) or just the laser frequency? The example seems that it is only used for changing the direction of the laser light based on the driving frequency, but will it change the laser frequency also?

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The acoustic wave in the material causes a variation in refractive index and the amount of light scattered at a particular angle (its similar to Bragg scattering) depends on the intensity of the modulation. The scattered light does carry both frequencies in the form of blue or red shifting. It shifts by mf where f is the driving frequency and m is the order.

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The answer to your question is generally yes, but it depends on how the AOM is driven. Typically AOMs have a piezoelectric transducer on one side of the crystal. In this case the frequency of the diffracted beams is shifted; if the laser frequency is $\omega_0$ and the modulation frequency is $\omega_m$, then the light in the first order beams will have frequency $\omega_0\pm\omega_m$, and the light in the second order beams will have frequency $\omega_0\pm2\omega_m$.

As is mentioned in this Wikipedia article, this is due classically to the fact that the light is diffracted off of compression waves which are moving across the crystal. This causes the diffracted beams to pick up a Doppler shift. In the condensed matter world they would say that the photons absorb or emit a phonon (lattice vibration), and that conservation of energy and momentum implies that the shifted beams must be shifted in frequency.

In some AOMs there are piezoelectric transducer elements on both sides, and driving both of them at the same time produces a standing wave. In this case the diffracted beams do not experience a frequency shift.

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The first order is shifted by +80 Mhz. The -1st order is shifted by -80 Mhz The second order is shifted by +160 Mhz.

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