The elementary statistical properties of electromagnetic fields in complex cavities

It is shown that the components of the electromagnetic field amplitudes in a perfectly conducting cavity with a complex shape are distributed according to a normal (Gaussian) distribution. The proof is obtained by expanding the field quantities in a complete set of orthogonal eigenvectors whose amplitudes are shown to have a normal distribution. This result is independent of the eigenvalue (mode number) and the shape of the cavity, requiring only that the shape of the cavity be complex. The proof that the components of the field amplitudes have a normal distribution follows immediately. Extensions of the theory to cavities with losses and sources is straightforward