<title>Wavelength and altitude dependence of laser beam propagation in dense fog</title>

The availability of free-space laser communications systems critically depends upon estimating the accuracy of atmospheric attenuation in different weather conditions. Fog and extreme rain are the primary types of weather that can affect shorter wavelength laser communication links. Traditionally, designers and users of free-space laser communication equipment assumed that light suffers from less atmospheric attenuation at longer infrared wavelengths such as 1.55 and 3.5 microns compare to 0.85 microns. Thought, as some experimental studies show, it is not safe to assume that the performance of detection systems in IR is always better in fogs than at visual wavelengths. In dense stages in long persisting fogs the attenuation at longer wavelengths often becomes large, or even larger, than that in the visible. To investigate performance of laser systems in the dense fog, we ran extensive MODTRAN calculations of atmospheric transmission for the different types of dense fog at visible-IR range of wavelengths. Our results show that an atmospheric attenuation in such fogs slightly increases with wavelengths in the range 0.5 - 4 micrometers and then decreases with the longer wavelengths. This is in contrast with widely used parameterization that states decreasing of the fog attenuation beyond visible. To investigate this further, we used concentrations and size distributions data collected in dense persisting fogs at different altitudes, and performed Mie scattering calculations. We determined fog extinction in a range of altitudes (10 - 100m) and at four wavelengths used in free-space communication: 0.85, 1.55, 3.5, and 10.6 microns. We found that atmospheric attenuation in dense fog sharply increases with altitude, slightly increases at 3.5 microns compared to 0.85 microns and then decreases at 10.6 microns.