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In order to compute the band structure of 3D photonic crystals, the plane wave expansion method was utilized. This method involves using a set of plane waves as a basis for the calculation of the electronic density of states. The expansion coefficients are chosen in such a way that they approximate the wave function of the system to be studied. This allows for the calculation of the electronic properties of the photonic crystal, such as its band gap structure and the nature of its electronic states. The calculations can be performed using a variety of software packages and computational tools, depending on the complexity of the system and the desired level of accuracy. Overall, the plane wave expansion method provides a powerful tool for the study of photonic crystals and their electronic properties.