Abstract: Deducing from the variational principle, longitudinal component of electromagnetic waveguide is e- liminated and the transverse electric and magnetic components are treated as dual vectors to each other. Then the Maxwell equations for electromagnetic waveguide are derived to Hamilton system formulation and symplectic geomet- ric form. The finite element method is used to discretize the cross section of the waveguide structure, and a set of linear algebraic equations are obtained for calculating the cutoff frequency and propagation constant of electromag- netic wave in waveguide. Examples demonstrate the accuracy of the proposed method. This paper also provides a new approach to analyze and calculate the problem of electromagnetic waveguide.

Key words: symplectic system, electromagnetic waveguide, Maxwell equations, I-Iamilton system, finite ele-ment method