Unitarity bound on the energy loss by a charged particle travelling near a periodic radiator

The linear energy loss, or braking force, < dW/dz > of a charged particle passing at constant distance b from a semi-infinite inhomogeneous or periodic medium is related to the reflection coefficient R of an evanescent wave. Assuming that |R| < 1 as for an ordinary wave, a bound < dW/dz > <= Z(2)/( 2 pi x 137b(2)), in natural units, is obtained. Detailed bounds are also obtained for the frequency and angular spectrum of the Smith-Purcell and Cherenkov-at-distance radiations. Some examples in favor of the prolongation of |R| < 1 for evanescent waves, as well as some examples rising doubts about it, are presented.