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2 The Total Field Guided Modes Six Vector Modeg
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adjoint eigenvector anisotropic Appendix appropriate boundary conditions California Attn characteristic impedances closed sheath wall completeness relations conjugate eigenvectors contributions conventional waveguides defined with respect degenerate eigenvalues discussion eigen eigenvalue problem eigenvectors associated electric and magnetic element employed equations 20 equivalent evident exhibit reflection symmetry extraordinary modes field components gonality Green's function H modes hermitian inner product homogeneous identical identifications imaginary eigenvalues implies Introduction isotropic media longitudinal power flow magnetic fields modal representations non-degenerate normalization constants Note obtain odd ordinary modes open waveguides operator dyads orthogonality properties orthogonality statements pair parallel plate waveguide projection operators readily verified real and imaginary real eigenvalue satisfy scalar mode functions Section solutions standing wave summation symmetric inner product Table tion transpose eigenvector transverse electric transverse modal indices uniform cylindrical waveguide vector waveguides bounded yields York Attn zero