A method for solving boundary problems of the electrodynamics of infinite inhomogeneous two-dimensional periodic arrays is proposed: a compensating sources method. The method represents the fields exciting and scattered by each elementary emitter of the array as expansion of a system of vector orthogonal waves. The concept of a compensating source is introduced, which is associated with an array element and creates a field in space described by a given scattered wave amplitude vector. The problem of excitation of an infinite array by a compensating source is solved, and its Green's function is obtained that relates the amplitudes of the exciting and scattered waves to the compensating source. A scheme is proposed for solving the boundary problem for an array with defects in the form of elements having a scattering operator different from the that of an element of a regular array. The solution to the problem of an array with an emitter removed is considered.
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