Acousto-Optic Effect

The Acousto-Optic Effect arises when an acoustic wave propagates through a transparent medium, generating a periodic refractive-index modulation via the elasto-optic interaction. This transient grating diffracts incident light, shifting its frequency by the ultrasound frequency and deflecting it according to the Bragg condition:

$$\sin(\theta_B) = \frac{\lambda\,f_{US}}{2\,v_{US}},$$

where λ is the optical wavelength (500–1000 nm), f_US the ultrasound frequency (1–10 MHz), and v_US the speed of sound (~1540 m/s). Typical Bragg angles are 1–30 mrad.

The magnitude of the index modulation is:

$$\Delta n = -\frac{n_0^3\,p\,P}{2\,\rho\,c^2},$$

with n₀≈1.36, p≈0.10 (elasto-optic coefficient), P (acoustic pressure) of 0.1–1 MPa, ρ≈1000 kg/m³, and c≈1540 m/s. This yields Δn ≈10⁻⁶–10⁻⁵ and diffraction efficiencies from 10⁻⁵ to 10⁻² over interaction lengths of millimeters to centimeters.