# Phase-shifting by Acousto-Optic modulators

I am working on a project where I need to be able to introduce a phase-shift to a light pulse, without any mechanical parts involved. One of the options is to use an acousto-optic modulator:

Associated with each AO (acousto-optic modulator) is a continuously propagating longitudinal acoustic wave in the refractive index of the medium, which acts on the incident pulse as a diffraction grating. Because the pulse velocity $c=2.99\times10^8\rm\, m\, s^{−1}$ is much greater than the acoustic speed $2200\rm\, m\, s^{−1}$, each pulse experiences an essentially stationary density grating. As a consequence of the Bragg condition, the phase of the acoustic wave is imparted to the pulse at the instant that it is reflected. For each consecutive pulse, the phase of the AO index grating advances by an amount $\Omega T_j$.

Specifically, I am talking about a AOM with a single piezo-electric transducer, i.e. the acoustic waves are moving, not stable.

I understand that the Bragg condition is required to conserve the momentum of the system, and for constructive interference. But why is the phase of the acoustic wave at the moment of reflection imparted to the light pulse?

• I think it's more accurate to say that a phase shift of the acoustic wave causes a phase shift of the diffracted light. One way to see this is to think about an incident light beam that is smaller than the spacing of the acoustic wave, it will see an effective index of refraction and will get a phase shift from that index and the path length through the crystal – KF Gauss Jul 3 '18 at 12:36
• If you change the phase of the acoustic wave of will change the index of refraction and give you a new phase – KF Gauss Jul 3 '18 at 12:37
• Is there a way to do the calculation in the framework of phonons - photons interaction? – Akerai Jul 3 '18 at 13:04
• Please describe the kind and amount of phase shift you need. For example, do you need a fixed phase shift of, e.g., 0.25 pi? Or do you need to modulate the phase over a particular range at a given speed? The phase of an AO modulator's drive signal will modulate the phase of the output beam; but it also modulates the frequency of the output beam. – S. McGrew Jul 3 '18 at 13:57
• I am using two AOMs with different driving frequencies to (pseudo)continuously modulate the interference contribution of two pulsed light beams, i.e. I am setting a known phase relation between the two beams such that over time I sweep the phase difference from 0 to 2pi. Similarly as in the following paper (part III is relevant): J Chem Phys. 2006 Nov 21;125(19):194303. – Akerai Jul 3 '18 at 14:37