Modulation of multiply scattered coherent light by ultrasonic pulses: an analytical model

We present an analytical solution for the acousto-optical modulation of multiply scattered light in a medium irradiated with a train of ultrasound pulses. Previous theory is extended to cases where the ultrasound-induced optical phase increments between the different scattering events are strongly correlated, and it is shown that the approximate similarity relation still holds. The relation between the ultrasound induced motions of the background fluid and the optical scatterers is generalized, and it is shown that correlation exists between the optical phase increments that are due to the scatterer movement and the optical phase increments that are due to the modulation of the optical index of refraction. Finally, it is shown that compared with the spectrum of ultrasound pulses, the power spectral density of acousto-optically modulated light is strongly attenuated at the higher ultrasound frequencies.