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Calculation of density of states in a 2D photonic crystal with separable profile of permittivity

When the periodic permittivity of two-dimensional (2D) photonic crystal (PC) can be separated in x- and y- coordinates, one can consider the structure as two separate 1D photonic crystals, one of them being periodic in x coordinate and the other in y coordinate. If it is possible to find a proper separable permittivity function, we can approximate a 2D PC with two distinct 1D structures. One of the advantages is rapid calculation the density of state of a 2D PC. In this article an analytical calculation of the density of states for such a 2D PC has been done with the aim of taking this advantage. For calculating the density of states we use the effective resonance approach to analyze the 1D PC.