In the atmospheric boundary layer, with some exceptions very close to the ground, optical turbulence is homogeneous and isotropic obeying the Kolmogorov power spectrum model of the refractive index within the inertial sub-range. However, in free atmosphere, in particular within the stably-layered stratosphere, the Kolmogorov power spectrum might not properly describe the real turbulence behavior. In this paper we use the general non-Kolmogorov power spectrum for theoretical investigation of laser beam propagation for the double-passage problem: transmitter-target-receiver. We show that long-term beam spread and scintillation are remarkably affected by non-Kolmogorov turbulent channels. Our analysis focuses on the mono-static configuration leading to the enhanced backscattering effects. The presented results are of interest in LIDARs operating at high altitude, where non-Kolmogorov turbulence may be present.