Application of Davidenko's Method to the Solution of Dispersion Relations in Lossy Waveguiding Systems

Systematic and efficient root finder for computing the modal spectrum of planar layered waveguides

“…Although much attention has been devoted previously to the zero-searching procedure [7,10,13,17,19,32], the relevance of this task in many electromagnetic problems still requires the development of new strategies to enhance the efficiency of the overall procedure. To this end, we propose a systematic integral method to find all the real/complex roots of any analytic function within a given region (in the present context, the term analytic means free of both poles and branch points) and without any previous knowledge of the approximate location of the roots (although, if this information were available, it could be used advantageously).…”

Magnetostatic volume waves in lossy YIG film backed by a metal of finite conductivity

“…The complex dispersion relations given by (16) and (18), whose real and imaginary parts are denoted by M and N, can be expressed in Davidenko's form as given by Talisa [7] d dt = 0J 01 M N :…”

“…Thus, iteration procedures are not necessary. This method is very useful for the solution of dispersion relations of electromagnetic waves propagating in lossy waveguiding structures, particularly layered structures containing one or more gyrotropic layers [7]. It is to be noted that M , M , etc., although complicated expressions, need not be found explicitly since they will be calculated numerically.…”

Pseudo-Analytical Modeling for Electromagnetic Well-Logging Tools in Complex Geophysical Formations

“…The above is known as the scalar Davidenko differential equation [85, p. 162], [84,[86][87][88], whose solution can be written as…”

“…We can solve γ and γ with the help of the Runge-Kutta algorithm [84], by observing the convergence of both real and imaginary parts of γ as s becomes large [84,86,[88][89][90].…”