Electromagnetic wave propagation in non-homogeneous waveguides
Published inJyväskylä studies in computing
We investigate an electromagnetic waveguide, having several cylindrical ends. The waveguide is assumed to be empty and to have a perfectly conductive boundary. We study the electromagnetic ﬁeld, excited in the waveguide in the presence of charges and currents. The ﬁeld can be described as a solution of the stationary Maxwell system with conductive boundary conditions and “intrinsic” radiation conditions at inﬁnity. We prove the problem to be well-posed. Electromagnetic waves propagation in the waveguide can be described by means of a scattering matrix. We introduce such a matrix for all values of the spectral parameter k in the waveguide continuous spectrum and study its properties. Moreover, we propose and justify a method for approximating the scattering matrix for all k in the continuous spectrum, including thresholds; the presence of waveguide eigenvalues does not inﬂuence the method statement. The results of the thesis extend the area of electromagnetic waveguide theory and have numerous applications. Particularly, the asymptotic and numerical methods, developed in the thesis, can be used for design and analysis of complex waveguides with resonators, SHF splitters, etc. To prove the results, we extend the over-determined Maxwell system to an elliptic problem and study the latter in detail. The information on the Maxwell system comes from that, obtained for the elliptic problem. ...
PublisherUniversity of Jyväskylä
aaltojohtimet Maxwellin yhtälöt elliptiset raja-arvo-ongelmat sirontamatriisit the stationary Maxwell system waveguides elliptic extension intrinsic radiation conditions radiation principle scattering matrix method for approximating the scattering matrix minimizer of a quadratic functional exponential convergence rate thresholds stable basis extended scattering matrix limits of the scattering matrix at thresholds sähkömagneettinen säteily sähkömagneettiset kentät sironta osittaisdifferentiaaliyhtälöt matriisilaskenta numeeriset menetelmät
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