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

Abstract

This paper presents two methods of analysis of the complex moving waveguide. One approach is a numerical technique based on Davidenko'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. Davidenko technique offers an alternative which is efficient and reliable and which relaxes the extent of the restriction placed on initial guess to be sufficiently close to the solution. The main idea of Davidenko's algorithm is to reduce Newton's method for the numerical solution of n-coupled nonlinear algebraic equations into n-coupled first-order differential equations in a dummy variable. The second one is a simple and accurate perturbation method, where the real part (beta) ' of the complex modal index (beta) equals (beta) ' + i(beta) '' is obtained by solving the corresponding real eigenvalue equation and the imaginary part (beta) '' is given by ((partial)(beta) '/(partial)(epsilon) ')(epsilon) '', where (epsilon) equals (epsilon) ' + i(epsilon) '' is the dielectric constant of the absorptive layer, and ((partial)(beta) '/(partial)(epsilon) ') 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 in our knowledge, the complex propagation characteristics are presented for moving waveguides. These results could be used in designing many optical moving sensors.