Theory of beam light pulse propagation through thick clouds: effects of beamwidth and scatterers behind the light source on pulse broadening.

Pulse propagation of beam waves from a source immersed in a slab of scatterers is investigated by means of analytically solving the diffusion equation. The on- and off-axis pulse intensities are calculated for collimated beam waves transmitted in the two typical directions of the slab. To a good approximation, the effect of finite beamwidth on the pulse intensity appears only through the diffusion factor in the radial direction of the beam, resulting in a faster decrease of the intensity in the tail part compared with that of the corresponding plane wave pulse. Also, the pulse shape does not appreciably change when the beamwidth is changed within the range of practical use. An analytical expression is obtained for the pulse width broadening and is applied to several typical cases leading to some simple expressions. The influence of the scatterers existing behind the source is discussed in some detail particularly in connection with pulse shape and width broadening, showing that, in many situations, the pulse width is determined mostly by the total optical thickness of the slab independently of the relative position of the wave source within the slab.