A novel approach to solve eigenvalue and forced response problems in waveguide theory by means of bi-orthogonality relations

L S Ledet, S V Sorokin
2019 Journal of Physics, Conference Series  
In this paper recent advances on solving challenging problems in dynamics of multimodal symmetric waveguides (having identical properties of positive/negative going waves) using bi-orthogonality are summarised. It has already been shown by the authors that bi-orthogonality, valid for arbitrarily complicated unbounded symmetric waveguides, greatly facilitates analysis of their forced response in any excitation conditions. Recent findings have shown that bi-orthogonality is a powerful tool also
more » ... r bounded waveguides and by direct use it resolves the classical Boundary Integral Equations (BIE) into a set of individual relations between modal amplitudes at the boundaries. Moreover, bi-orthogonality permits to uniquely identify special sets of boundary conditions for which the eigenfrequency spectra may be found directly from the dispersion diagrams. These solutions are available simply by drawing horizontal lines specifying an inverse of the wave length of interest in the (Ω, k)-dispersion diagram and so the eigenfrequency spectrum may be read directly as intersections of these lines with dispersion curves. This paper therefore serves to promote this method, discuss applications, new possibilities, physical interpretation and its generalisation to a broader class of waveguide problems.
doi:10.1088/1742-6596/1264/1/012058 fatcat:2fmtjtcv5nf5tmawog4qw5iqg4