Modal treatment in two dimensions theoretical foundations of VLF-radio wave propagation using the normalized airy functions

The goal is to take advantage of the Earth -ionosphere wave guide's fundamentally two-dimensional wave propagation, utilizing the normalized Airy functions (NAFs) in a complex domain. It is demonstrated that the typical working formula of VLF radio -mode theory may be obtained simply from orthogonality reflections, devoid of the requirement of sophisticated argumentation in the open unit disk. The combination of the expressions is given by considering the symmetry -convex illustration of the NAFs.