Evolution of temporal and frequency characteristics of spherical photon density waves in scattering media

The paper reports on the numerical study of temporal characteristics, frequency and phase responses of the photon density waves generated by a point-sized source in scattering media with different scattering anisotropy and absorption index. The study is performed with time-resolved Monte-Carlo simulations for a wide range of medium optical properties covering values typical for aerosols and sea water. We demonstrate that although the normalized pulse delay increases monotonically with distance in the course of propagation in the medium, for particular sets of optical properties its normalized width shows a non-monotonous trend with a maximum corresponding to distances where ballistic and multiply scattered photons give comparable contribution to the irradiance field. In the frequency responses of photon density waves for certain combinations of optical prop-erties at particular distances a deep minimum is formed, also associated with the interference of partial waves. The dimensionless frequency corresponding to this minimum monotonically increases with the increase in anisotropy factor. Dependencies of local and averaged phase and group velocities on distance derived from phase responses revealed a formation of a minima in local group velocities dependencies with further increase to the average velocity values at higher distances, which is also associated with relative contribution of low-and multiply scattered photons. The revealed dependencies can be useful for verifying the analytical models of nonstationary radiation transfer and directly for assessing the achievable parameters of optical systems for various purposes operating in natural scattering media, such as the atmosphere and sea water.