Two methods (numerical and analytical) of the analysis of complex moving waveguides

Abstract

This paper presents two methods ofanalysis ofthe complex moving waveguide One approach is a numerical technique based on Davedinko's method , the other is a perturbation method. It is clear that if one wants to obtain more accurate results over a wide range it is necessary to develop numerical techniques capable for solving lossy waveguides that has a complex propagation constant or a complex dielectric constant. Newton's method is one of these methods which requires several iterations in the complex plane ,but this method fails in most cases in producing satisfactory results. Davedinko technique offers an alternative which is efficient and reliable and which relaxes the extent ofthe restriction placed on initial guess to be sufficiently close to the solution. The main idea ofDavidenko's algorithm is to reduce Newton's method for the numerical solution ofn-coupled nonlinear algebraic equations into ncoupled first-order differential equations in a dummy variable. The second one is a simple and accurate perturbation method, where the real part 13' ofthe complex modal index f3 = + if3' ' is obtained by solving the corresponding real eigenvalue equation and the imaginary part f3' ' is given by ( t3/ôf)' ' , where c c' + ic' ' is the dielectric constant ofthe absorptive layer, and ( a3'/c') is obtained by numerical differentiation.Numerical results by Davidenko's method are compared with these obtained from the perturbation method. It is found that the perturbation method is in a good agreement with the numerical one Furthermore ,for the first time to our knowledge, the complex propagation characteristics are presented for moving waveguides. These results could be used in designing many optical moving sensors.