Photoacoustic Doppler Effect - Theory

Theory

To be simple, consider a clear medium firstly. The medium contains small optical absorbers moving with velocity vector . The absorbers are irradiated by a laser with intensity modulated at frequency . Thus, the intensity of the laser could be described by:

When is zero, an acoustic wave with the same frequency as the light intensity wave is induced. Otherwise, there is a frequency shift in the induced acoustic wave. The magnitude of the frequency shift depends on the relative velocity, the angle between the velocity and the photon density wave propagation direction, and the angle between the velocity and the ultrasonic wave propagation direction. The frequency shift is given by:

Where is the speed of light in the medium and is the speed of sound. The first term on the right side of the expression represents the frequency shift in the photon density wave observed by the absorber acting as a moving receiver. The second term represents the frequency shift in the photoacoustic wave due to the motion of the absorbers observed by the ultrasonic transducer.

In practice, since and, only the second term is detectable. Therefore, the above equation reduces to:

In this approximation, the frequency shift is not affected by the direction of the optical radiation. It is only affected by the magnitude of velocity and the angle between the velocity and the acoustic wave propagation direction.

This equation also holds for a scattering medium. In this case, the photon density wave becomes diffusive due to light scattering. Although the diffusive photon density wave has a slower phase velocity than the speed of light, its wavelength is still much longer than the acoustic wave.