Reciprocity and the scattering matrix of waveguide modes
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The implications of the Lorentz reciprocity theorem for a scatterer connected to waveguides with arbitrary modes, including degenerate, evanescent, and complex modes, are discussed. In general it turns out that a matrix CS is symmetric, where C is the matrix of generalized orthogonality coefficients and S is the scattering matrix. Examples are given, including a scatterer surrounded by waveguides or free space, and discontinuities of waveguides.
Svendsen, Guro Kristin; Haakestad, Magnus Willum; Skaar, Johannes. Reciprocity and the scattering matrix of waveguide modes. Physical Review A. Atomic, Molecular, and Optical Physics 2013 ;Volum 87.(1) s. -