  We study the simultaneous paraxial and white-noise limit of the Helmholtz
equation in randomly layered media where the refractive index fluctuations are
in the direction of propagation. We consider the regime in which the wavelength
is of the same order as the correlation length of the random fluctuations of
the refractive index. We show that this simultaneous limit can be taken in this
regime by introducing into the equation an arbitrarily small regularization
parameter. The corresponding paraxial white-noise approximation that we derive
is different from that of the previously studied high-frequency regime. Since
the correlation length of the refractive index fluctuations due to atmospheric
turbulence varies substantially, our results are relevant for numerous
different propagation scenarios including microwave and radiowave propagation
through various regions of the atmosphere.
