Propagation and Time Reversal of Wave Beams in Atmospheric Turbulence

We analyze wave propagation in turbulent media using the Gaussian white-noise approximation. We consider two rigorous Gaussian white-noise models: one for the wave field and the other for the Wigner distribution associated with the wave field. Using the white-noise model for the Wigner distribution we show that the interaction of a wave field with the turbulent medium can be characterized in terms of the turbulence-induced entrance aperture. This aperture is proportional to the turbulence-induced coherence length and inversely proportional to the turbulence-induced spread of the wave energy in the transverse wavevectors. The effect of the turbulent medium is important when the turbulence-induced entrance aperture is smaller than the actual entrance aperture. We also study time reversal of the wave field in a turbulent medium and introduce the notion of a turbulence-induced time-reversal aperture which we show is proportional to the turbulence-induced spread in the transmitted wave energy. When the effect of the turbulent medium is important, the turbulence-induced time-reversal aperture corresponds to a time-reversal resolution much better than the resolution in the absence of the turbulent medium. The propagation and spreading of a wave field can be related to time reversal and refocusing of the wave field by a general duality relation, and we present this duality in terms of the uncertainty principle.