Parabolic Approximation, Radiative Transfer and Time Reversal

We first present a new formulation of parabolic approximation of the Maxwell equations for heterogeneous dielectric materials. We then discuss rigorous results about selfaveraging scaling limits of parabolic waves in terms of the Wigner distribution function. Among the 6 possible scaling limits two are exactly solvable. We use the Green function to analyze the time reversal operation in turbulent media with power-law spectral density. We show that the time-reversed refocused spot size depends superlinearly on the wavelength and thus has the potential of breaking the diffraction limit when the wavelength is small. We also derive an uncertainty principle for random media which has the forward wave spread and the turbulence-induced resolution as conjugate quantities.