A variational method to approximate the field of weakly guiding optical fibers by Laguerre-Gauss/Bessel expansion

In the analysis of weakly guiding single-mode optical fibers, Gaussian and modified-Gaussian approximations appear inadequate to obtain accurate results at low normalized frequency for general refractive index profiles. To overcome such limitations we propose an expansion in terms of Laguerre-Gauss functions to represent the field in the fiber core. A modified Bessel function is instead used to describe the field in the cladding. All parameters defining the approximate field are evaluated by a variational method. We show that the proposed approximation is very accurate in the low normalized frequency limit too and can be particularly valuable to analyze dispersion-shifted fibers with triangular refractive index profile.