  The concept of optimal communication channels shapes our understanding of
wave-based communication. Its analysis, however, always pertains to specific
communication-domain geometries, without a general theory of scaling laws or
fundamental limits. In this article, we derive shape-independent bounds on the
coupling strengths and information capacities of optimal communication channels
for any two domains that can be separated by a spherical surface. Previous
computational experiments have always observed rapid, exponential decay of
coupling strengths, but our bounds predict a much slower, sub-exponential
optimal decay, and specific source/receiver distributions that can achieve such
performance. Our bounds show that domain sizes and configurations, and not
domain shapes, are the keys to maximizing the number of non-trivial
communication channels and total information capacities. Applicable to general
wireless and optical communication systems, our bounds reveal fundamental
limits to what is possible through engineering the communication domains of
electromagnetic waves.
