Analytical analysis of defect lines in two-dimensional photonic crystals based on polynomial expansion of electromagnetic fields

Analytical analysis of straight single-line defect optical waveguides in two dimensional photonic crystals based on expanding electromagnetic fields in terms of Hermite polynomials is reported. This novel electromagnetic field expression is substituted in Helmholtz equation, a new set of linear ordinary differential equations with variable coefficients are obtained, and by employing differential transfer matrix method; defect modes, i.e. the guided modes propagating in the line defect waveguide, are analytically derived. The validity of the results obtained by applying the proposed approach are confirmed by comparing them to those derived by using finite difference time domain method.

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