The acousto-optic effect is a specific case of
photoelasticity, where there is a change of a material's
permittivity, \varepsilon, due to a
mechanical strain a. Photoelasticity is the variation of the optical indicatrix coefficients B_i caused by the strain a_j given by, : (1) \ \Delta B_i = p_{ij} a_j, \, where p_{ij} is the photoelastic
tensor with components, i,j = 1,2,...,6. Specifically in the acousto-optic effect, the strains a_j are a result of the acoustic wave which has been excited within a
transparent medium. This then gives rise to the variation of the refractive index. For a plane acoustic wave propagating along the z axis, the change in the refractive index can be expressed as : (2) \ n(z,t)=n_0+\Delta n \cos (\Omega t - Kz), \, where n_0 is the undisturbed refractive index, \Omega is the
angular frequency, K is the
wavenumber of the acoustic wave, and \Delta n is the amplitude of variation in the refractive index generated by the acoustic wave, and is given as, : (3) \ \Delta n = - \frac{1}{2} \sum_j n_0^3p_{zj} a_j, The generated refractive index, (2), gives a
diffraction grating moving with the
velocity given by the speed of the sound wave in the medium. Light which then passes through the transparent material, is diffracted due to this generated refraction index, forming a prominent
diffraction pattern. This diffraction pattern corresponds with a conventional diffraction grating at angles \theta_n from the original direction, and is given by, : (4) \ \Lambda \sin (\theta_m) = m\lambda,\, where \lambda is the
wavelength of the optical wave, \Lambda is the wavelength of the acoustic wave and m is the integer order maximum. Light diffracted by an acoustic wave of a single
frequency produces two distinct diffraction types. These are
Raman–Nath diffraction and
Bragg diffraction. Raman–Nath diffraction is observed with relatively low acoustic frequencies, typically less than 10 MHz, and with a small acousto-optic interaction length, ℓ, which is typically less than 1 cm. This type of diffraction occurs at an arbitrary angle of incidence, \theta_0. In contrast, Bragg diffraction occurs at higher acoustic frequencies, usually exceeding 100 MHz. The observed diffraction pattern generally consists of two diffraction maxima; these are the zeroth and the first orders. However, even these two maxima only appear at definite incidence angles close to the Bragg angle, \theta_B. The first order maximum or the Bragg maximum is formed due to a selective reflection of the light from the wave fronts of ultrasonic wave. The Bragg angle is given by the expression, : (5) \ \sin \theta_B = - \frac{\lambda f}{2 n_i \nu}\left[ 1+\frac{\nu^2}{\lambda^2 f^2 } \left( n_i^2 - n_d^2 \right) \right], where \lambda is the wavelength of the incident light wave (in a vacuum), f is the acoustic frequency, v is the velocity of the acoustic wave, n_i is the refractive index for the incident optical wave, and n_d is the refractive index for the diffracted optical waves. In general, there is no point at which
Bragg diffraction takes over from Raman–Nath diffraction. It is simply a fact that as the acoustic frequency increases, the number of observed maxima is gradually reduced due to the angular selectivity of the acousto-optic interaction. Traditionally, the type of diffraction, Bragg or Raman–Nath, is determined by the conditions Q \gg 1 and Q \ll 1 respectively, where Q is given by, : (6) \ Q = \frac{2\pi\lambda \ell f^2}{n \nu^2}, which is known as the Klein–Cook parameter. Since, in general, only the first order diffraction maximum is used in acousto-optic devices,
Bragg diffraction is preferable due to the lower optical losses. However, the acousto-optic requirements for
Bragg diffraction limit the frequency range of acousto-optic interaction. As a consequence, the speed of operation of acousto-optic devices is also limited. ==Acousto-optic devices==