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The paper deals with diffraction on high reflecting surfaces with periodically modulated dielectric properties. Period of the structure is supposed to be close to the wavelength multiplied by an integer and, consequently, for close-to-normal incidence of a p-polarized wave there exists the resonance (Wood anomaly) caused by simultaneous excitation of two surface plasmon polaritons (SPP). We present the analytical solution of the problem using the surface impedance as the small parameter that enables us to consider variety of metals and semiconductors in red and infrared regions. The simple explicit solution obtained makes it possible to present the results in a closed analytical form and examine them in detail for arbitrary grating form. We present the dependence of the polariton, specular and other reflected waves phases and amplitudes on the angle of incidence, wavelength, and on the grating period and form. We derive the universal self-similar representation of the solution in the close resonance vicinity. This enables us to carry out a thorough investigation of the strong resonance peculiarities fine structure. There are formulated conditions on the grating parameters that correspond to the specific redistribution of the radiation flux between outgoing waves and the SPPS. In particular, we demonstrate that in spite of the geometric symmetry, excitation of one of the polaritons can be suppressed totally. The total suppression of any subset of the outgoing diffracted waves is also possible, and a variety of other energy redistributions between them is possible as well. The results are of interest both from theoretical point of view and in view of a wide field of possible applications for the novel optic and opto-electronic problems concerning light transformation and control.
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