# Where I can find a simple acousto-optic math model based on Maxwell's equations?

In my degree work, I have to create a program which can modeling acousto-optic effect. The best explanation about that I found in this book: "Fundamentals of Photonics" Bahaa E. A. Saleh, Malvin Carl Teich, Chapter 20. Firstly I want to understand the simple math model which can describe the optical process in the acoustic medium. My question can someone helm me with some books or useful resource which describe the math model of acousto-optic?

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You should learn how an Acoustic-Optical Modulator works via the acoustic-optical effect.

$$n(z,t) = n_0 + \Delta n \cos(\Omega t - Kz)$$

As shown here, K is the wavenumber of the acoustic wave, $\Omega$ is the angular frequency, and $\Delta$ n is how the refractive index changes due to the acoustic wave:

$$\Delta n = - \frac{1}{2}\sum_j n_0^3 p_{zj} a_j$$

$a_j$ describes strain in the material due to the wave, while $p_{zj}$ describes how the permittivity changes due to that strain. (The permittivity part changing is where you can relate such acoustic effects to Maxwell's Equations.)

I would play around with different stress tensors $p_{zj}$ and see what types of changes in the index of refraction you can induce depending on different stress tensors. You can play around with how different types of strain affect the system.

Also, it's important in an experimental setting to understand how brag scattering creates a spatially discrete number of frequency shifted light field.

Some impressive things you could try to model:

• How does an AOM's efficiency change as a function of incident angle?
• Does change the frequency at which you drive your AOM change the angle of the frequency-shifted outputs?
• How does changing the amplitude of the wave generated by the AOM change the efficiency of the frequency conversion?