Efficient Photonic-Crystal Mode Solver: Eigenvalue Rather Than Generalized Eigenvalue Approach

We present an iterative scheme to obtain guided Bloch modes in lossy and dispersive photonic crystals. The formulation is based on the concept of sources and transforms the quadratic generalized eigenvalue problem of modes into simpler eigenvalue counterpart for iterations. This feature makes it particularly useful in computations with large matrix sizes. Fewer memories and less computation time than those of conventional methods are required in these cases. The robustness of iterations is rooted in the reciprocity theorem for periodic Bloch parts. Through repeated estimations of propagation constants, Bloch modes of periodic structures converge quickly. Using this method, we take sinusoidal metal gratings as examples and demonstrate advantages of the scheme.