Acousto-optics

An acousto-optic modulator

By varying the parameters of the acoustic wave, including the amplitude, phase, frequency and polarization, properties of the optical wave may be modulated. The acousto-optic interaction also makes it possible to modulate the optical beam by both temporal and spatial modulation.

A simple method of modulating the optical beam travelling through the acousto-optic device is done by switching the acoustic field on and off. When off the light beam is undiverted, the intensity of light directed at the Bragg diffraction angle is zero. When switched on and Bragg diffraction occurs, the intensity at the Bragg angle increases. So the acousto-optic device is modulating the output along the Bragg diffraction angle, switching it on and off. The device is operated as a modulator by keeping the acoustic wavelength (frequency) fixed and varying the drive power to vary the amount of light in the deflected beam.[9]

There are several limitations associated with the design and performance of acousto-optic modulators. The acousto-optic medium must be designed carefully to provide maximum light intensity in a single diffracted beam. The time taken for the acoustic wave to travel across the diameter of the light beam gives a limitation on the switching speed, and hence limits the modulation bandwidth. The finite velocity of the acoustic wave means the light cannot be fully switched on or off until the acoustic wave has traveled across the light beam. So to increase the bandwidth the light must be focused to a small diameter at the location of the acousto-optic interaction. This minimum focused size of the beam represents the limit for the bandwidth.

The principle behind the operation of acousto-optic tunable filters is based on the wavelength of the diffracted light being dependent on the acoustic frequency. By tuning the frequency of the acoustic wave, the desired wavelength of the optical wave can be diffracted acousto-optically.

There are two types of the acousto-optic filters, the collinear and non-collinear filters. The type of filter depends on geometry of acousto-optic interaction.

The polarization of the incident light can be either ordinary or extraordinary. For the definition, we assume ordinary polarization. Here the following list of symbols is used,[10]

${\displaystyle \alpha }$: the angle between the acoustic wave vector and the crystallographic axis z of the crystal;

${\displaystyle \gamma }$: the wedge angle between the input and output faces of the filter cell (the wedge angle is necessary for eliminating the angular shift of the diffracted beam caused by frequency changing);

${\displaystyle \varphi }$: the angle between the incident light wave vector and [110] axis of the crystal;

${\displaystyle \alpha _{\ell }}$: the angle between the input face of the cell and acoustic wave vector;

${\displaystyle \beta }$: the angle between deflected and non-deflected light at the central frequency;

${\displaystyle \ell }$: the transducer length.

The incidence angle ${\displaystyle \varphi }$ and the central frequency ${\displaystyle f_{i}}$ of the filter are defined by the following set of equations,[10]

${\displaystyle (7)\ n_{\varphi }={\frac {n_{0}n_{e}}{\sqrt {n_{0}^{2}\cos \varphi +n_{e}^{2}\sin ^{2}\varphi }}}}$

${\displaystyle (8)\ f_{i}(\varphi )={\frac {\nu }{\lambda }}\left[n_{\varphi }\cos(\varphi +\alpha )\pm {\sqrt {n_{0}^{2}-n_{\varphi }^{2}(\varphi )\sin ^{2}(\varphi +\alpha )}}\right]}$

Refractive indices of the ordinary (${\displaystyle n_{0}}$) and extraordinary (${\displaystyle n_{e}}$) polarized beams are determined by taking into account their dispersive dependence.

The sound velocity, ${\displaystyle v}$, depends on the angle α, such that,[10]

${\displaystyle (9)\ \nu (\alpha )=\nu _{110}{\sqrt {\cos ^{2}\alpha +\left({\frac {\nu _{001}}{\nu _{110}}}\right)^{2}\sin ^{2}\alpha }}}$

${\displaystyle v_{110}}$ and ${\displaystyle v_{001}}$ are the sound velocities along the axes [110] and [001], consecutively. The value of ${\displaystyle \alpha _{1}}$ is determined by the angles ${\displaystyle \varphi }$ and ${\displaystyle \alpha }$,[10]

${\displaystyle (10)\ \alpha _{\ell }=\varphi +\alpha }$

The angle ${\displaystyle \beta }$ between the diffracted and non-diffracted beams defines the view field of the filter; it can be calculated from the formula,[10]

${\displaystyle (11)\ \beta =\arcsin \left({\frac {\lambda f_{0}}{n_{0}\nu }}\sin \alpha +\varphi \right)}$

Input light need not be polarized for a non-collinear design. Unpolarized input light is scattered into orthogonally polarized beams separated by the scattering angle for the particular design and wavelength. If the optical design provides an appropriate beam block for the unscattered light, then two beams (images) are formed in an optical passband that is nearly equivalent in both orthogonally linearly polarized output beams (differing by the Stokes and Anti-Stokes scattering parameter). Because of dispersion, these beams move slightly with scanning rf frequency.

An acousto-optic deflector spatially controls the optical beam. In the operation of an acousto-optic deflector the power driving the acoustic transducer is kept on, at a constant level, while the acoustic frequency is varied to deflect the beam to different angular positions. The acousto-optic deflector makes use of the acoustic frequency dependent diffraction angle, where a change in the angle ${\displaystyle \Delta \theta _{d}}$ as a function of the change in frequency ${\displaystyle \Delta f}$ is given as,[11]

${\displaystyle (12)\ \Delta \theta _{d}={\frac {\lambda }{\nu }}\Delta f}$

where ${\displaystyle \lambda }$ is the optical wavelength of the beam and ${\displaystyle \nu }$ is the velocity of the acoustic wave.

AOD technology has made practical the Bose–Einstein condensation for which the 2001 Nobel Prize in Physics was awarded to Eric A. Cornell, Wolfgang Ketterle and Carl E. Wieman.[12] Another application of acoustic-optical deflection is optical trapping of small molecules.

AODs are essentially the same as acousto-optic modulators (AOMs). In an AOM, only the amplitude of the sound wave is modulated (to modulate the intensity of the diffracted laser beam), whereas in an AOD, both the amplitude and frequency are adjusted, making the engineering requirements tighter for an AOD than an AOM.