Fiber spot size: a simple method of calculation

The ability to integrate the Laguerre-Gauss functions in closed form is exploited to allow a simple but accurate evaluation of single-mode fiber spot size using Galerkin´s method. The method avoids the need for numerical integration in a broad class of refractive-index profiles. Its simplicity depends on the use of a pattern-matching algorithm to avoid the numerical integration normally called for. The algorithm is very fast and gives exact results. The development of symbolic computer languages makes this approach especially easy. A symbolic program was used to predict the spot size and the far-field radiation pattern, and the results are compared with the exact values, getting excellent results