An algebraic eigenvalue problem for analyzing the propagation characteristics of electromagnetic waves inside the PBG Structure consisting of complex medium is established by using Bloch theorem and plane wave expansion. Two eigen-solvers are employed. One is matrix-based and another is iterative. Calculated results show that both methods are effective for 2-D PBG structure, but the iterative eigen-solver is more attractive in both CPU-time and memory requirement. A sample of 2-D PBG structure, with Chiral medium as host and air cylinders arranged in triangular lattice as inclusion, is analyzed using both methods. It is found that the introduction of chirality increases the band gap width significantly.
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