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In this paper, the Mutiple Multipoles method is employed to solve nonlinear eigenvalue problem and calculate band structure for a 2D photonic crystal. Band structure is calculated for both TE and TM polarizations. Simulation space is implemented for the first Brillouin zone by using physical properties such as rods radius, permittivity and susceptibility. To model fields inside and outside of object, Multipole centers were located around it and Bessel series inside the object is shown complex fields. We used Bloch theory to implement fictitious periodic boundary conditions for the first Brillouin zone. To validate the code, we simulated the band structure of a cubic lattice and compare the results with Plane Wave Expansion Method which illustrates the accuracy of the code. It is shown that this method can be applied to investigate photonic crystals with irregular shapes and different materials for different lattices such as cubic, trigonal and honeycomb. Furthermore it could be used for dielectric or dispersive material and experimental data. Numerical calculation shows that MMP method is accurate, fast and it can be used on Personal Computers.

Keywords: Photonic band gap, Photonic crystal, MMP method, computational method

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