Higher Order Characteristics of Waves on a Sinusoidally Modulated Reactance Surface

The propagation of two-dimensional waves guided along a reactance surface with a weak sinusoidal modulation is investigated by a perturbation procedure up to fourth-order in the modulation index n for the wave vector of the guided wave parallel to the grating vector. The periodicity of the modulation is chosen such that only one fast leaky wave exists. The correction to the propagation coefficient of the guided wave due to the reactance modulation is obtained up to fourth-order in n. The correctness of the leakage coefficient up to fourth-order in n is verified by developing a power conservation relation valid up to that order in n. The higher-order expression for the leakage coefficient indicates the presence of saturation for large values of n. This higher-order treatment has yielded the correct exponential growth of the fast leaky wave perpendicular to the reactance surface and has revealed that some of the slow Floquet modes which do not carry power away from the reactance surface also contribute to the decay of the guided wave in the propagation direction.