Resolución Numérica de la Ecuación de Dispersión para los Modos Normales de una Red de Alambres Metálicos

Abstract

The aim of this work is to calculate the complex roots of the equations that appear when we impose boundary conditions to the magnetic and electric fields, products of the light on the wire grating.
Solve this problem is a central point in the quality control of the low energy transmission grating designed for NASA's mission AXAF, and it is also useful in similar problems.
First in this work it is proved analitically that the roots don't depend on the angle of incidence of the radiation on the wire grating, a fact not known before this moment. Then numerical methods based on power series of the trigonometric functions are tried, it is analyzed the relation between roots and physical parameters of the problem, and alternative methods based on sums and subtractions of roots which have been alredy worked out are tried.
The definitive algorithm is very quick and general, being apropiate to the physical parameters of current interest as well as for other ones which could appear in the future.