I've been trying to get reantiquated with electormagnetics to understand RF communications better. I have a question about TEM plane waves. The funtions which describe the plane waves in the z dirrection are: e-α cos(ωt-βz) ; in the time domain where is the rate of decay. In free space α is 0, so the plane wave function does not account for free space loss which from what I understand accounts for the fields spreading out is a sphere and the distribution of the fields across the surface of the sphere. Hence it is an inverse square law. My questions is, is it only appropriate to use the plane wave function, e-α cos(ωt-βz), for very short distances of travel, i.e. in a circuit, or through a shielding? Is it ever appropriate to use over long distances? Hope my question is making sense. Thanks.