The present work is devoted to the clarification of the conditions necessary for step-by-step justification of the possibility of reduction of the homogeneous system of linear algebraic equations for the spectral problems of 2-D photonic crystals by the plane waves method. The issues related to the algorithms and the numerical solutions of these spectral problems are analyzed. The possibility of analytical regularization is investigated, and the ways to improve the convergence of the obtained results are identified.
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