Waves guided by a boundary with time¿space periodic modulation

We here consider electromagnetic waves guided by a plane surface impedance which is modulated periodically in time and space in the travelling-wave sense. The problem treated is a linearised statement of the nonlinear parametric interaction of waves on an open waveguide structure. In this linear treatment we take the rigorous approach formerly used on purely spatial periodic structures. We examine parametric-wave interactions of both the stable and the potentially unstable type. The regions of operation for bound surface waves, as opposed to radiating leaky waves, are determined rigorously for this structure. A region of operation called the `sonic¿ region is found, which represents a form of an electromagnetic shock wave. This sonic region precludes, for the model chosen, the possibility of travelling-wave amplification along the length of the structure. The above results are obtained only from the complete treatment, including the effects of all time-space harmonics. Finally, the power-mixing principle for all harmonic waves is determined to be the Manley¿Rowe power/frequency relation applied at the boundary surface.