Acousto-optics - Acousto-optic Effect

Acousto-optic Effect

The acousto-optic effect is a specific case of photoelasticity, where there is a change of a material's permittivity, due to a mechanical strain . Photoelasticity is the variation of the optical indicatrix coefficients caused by the strain given by,

where is the photoelastic tensor with components, = 1,2,…,6.

Specifically in the acousto-optic effect, the strains 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,

where is the undisturbed refractive index, is the angular frequency, is the wavenumber, and is the amplitude of variation in the refractive index generated by the acoustic wave, and is given as,

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 from the original direction, and is given by,

where is the wavelength of the optical wave, is the wave length of the acoustic wave and 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, .

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, . 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,

where is the wavelength of the incident light wave (in a vacuum), is the acoustic frequency, is the velocity of the acoustic wave, is the refractive index for the incident optical wave, and 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 >> 1 and Q << 1 respectively, where Q is given by,

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.