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Degrees of freedom of an electromagnetic wave

We present a rigorous formalism for evaluating the degrees of freedom (d.o.f.) in communication with electromagnetic waves. We show that, although in principle there is an infinity of d.o.f., the effective number is finite. This is in agreement with the restricted classical theories. We further show that the best transmitting functions are the solutions of a specific eigenvalue equation. The analysis is valid for electromagnetic waves under arbitrary boundary conditions communicating between domains in 3D space. The practical implications of this theory will be discussed.