Long and short-term beam spread by turbulence and optimization of the beam geometry

Oceanic turbulence causes distortions of the bounded beam waves propagating underwater. The most obvious effects are the beam spread and beam wandering. Propagation theory identifies two distinct measures of the beam spread: Long-Term (LT) beam spread when the beam size is measured in the fixed coordinate system, and the Short-Term (ST) beam spread when the beam size is measured relative to the instantaneous position of the beam center. The LT beam size is not a very practicable measure of the beam spread because it requires a very stable setup both for the transmitter and receiver that cannot be provided on the mobile platforms. LT beam size is also sensitive to the pointing errors and large-scale gradients of the refractive index that are not associated with turbulence. The ST beam spread is free of these drawbacks, but have not been studied as thorough as the LT case. We present a theoretical model for the ST beam irradiance that is based on the parabolic equation for the beam wave propagation in random media, and Markov approximation for calculation of the statistics of the optical field. We propose approximation that allows introduction of the isoplanatic ST PSF, but retains the specifics of the beam wave. Unlike the LT PSF the ST PSF depends on the overall beam geometry. This offers an opportunity to optimize the beam geometry in terms of maximizing the axial ST irradiance. Calculations supporting this conjecture will be presented.