Analytical model for the grazing reflection of a narrow beam

We propose an analytical model for the grazing reflection of a narrow beam. For the special incidence condition, the output field is the superposition of the incidence and reflected fields, so the incidence cutoff frequency is defined in the angular spectrum. With the definition, we deduce the effective plane-wave-reflection coefficient, together with angular spectrum of the output field. The model is verified by numerical simulation. Calculation in ordinary linear, nonabsorbing media with this model reveals some remarkable characteristics of the output fields, such as negative lateral shift and a beam-width compression effect.