We present the results of a theoretical study of underwater pulse propagation. The vector radiative transfer equation (VRTE) underlies our calculations of the main characteristics of the scattered light field in the pulse. Under the assumption of highly forward scattering in seawater, three separate equations for the basic modes are derived from the exact VRTE. These three equations are further solved both within the small-angle approximation and numerically. The equation for the intensity is analyzed for a power-law parametrization of the wings of the sea water phase function. The distribution of early arrival photons in the pulse, including the peak intensity, is calculated. Simple relations are also presented for the variance of the angular distribution of radiation, the effective duration of the signal and other parameters of the pulse. For linearly and circularly polarized pulses, the temporal profile of the degree of polarization is calculated for actual data on the scattering matrix elements. The degree of polarization is shown to be described by the self-similar dependence on some combination of the transport scattering coefficient, the temporal delay and the source-receiver distance. Our results are in agreement with experimental and Monte-Carlo simulation data. The conclusions of the paper offer a theoretical groundwork for application to underwater imaging, communication and remote sensing.
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