  We study time-harmonic electromagnetic and acoustic waveguides, modeled by an
infinite cylinder with a non-smooth cross section. We introduce an
infinitesimal generator for the wave evolution along the cylinder, and prove
estimates of the functional calculi of these first order non-self adjoint
differential operators with non-smooth coefficients. Applying our new
functional calculus, we obtain a one-to-one correspondence between polynomially
bounded time-harmonic waves and functions in appropriate spectral subspaces.
