This paper discusses the diffraction of an electromagnetic wave at a grating consisting of parallel dielectric bars with the cross section of a regular polygon. The problem is solved by the method of integral equations. The logarithmic singularity of the kernel of the integral equation is separated out in explicit form, and this makes it possible to use quadrature formulas of the highest accuracy and to reduce the integral equation to a system of linear algebraic equations. The result of these analytic transformations is good convergence of the algorithm. This paper presents the angular and spectral dependences of the transmittance obtained by means of the described algorithm for various shapes of the cross section of the dielectric bars.
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