Ultraviolet scattering propagation modeling: analysis of path loss versus range

Modeling of the complex atmospheric propagation of deep-ultraviolet (UV) radiation is important for applications such as non-line-of-sight (NLOS) UV communications. Building upon prior work in which it was observed that short-range, singly scattered NLOS path loss varies linearly with range, we formalize this relationship, generalizing it to consider any order of scattering and more-general system characteristics. In particular, we derive the approximate relationship PL[proportionality]r(2-n) between path loss PL and range r for nth-order scattered radiation, and investigate the region of validity of this approximation. Insight arising from the analysis can be invaluable in the development and study of UV systems, as demonstrated by numerical results that illustrate implications of the analysis.