G. De Angelis et al., A variational method to approximate the field of weakly guiding optical fibers by Laguerre-Gauss/Bessel expansion, J LIGHTW T, 17(12), 1999, pp. 2665-2674
In the analysis of weakly guiding single-mode optical fibers, Gaussian and
modified-Gaussian approximations appear inadequate to obtain accurate resul
ts at low normalized frequency for general refractive index profiles. To ov
ercome such limitations we propose an expansion in terms of Laguerre-Gauss
functions to represent the field in the fiber core. A modified Bessel funct
ion is instead used to describe the field in the cladding. All parameters d
efining the approximate field are evaluated by a variational method. We sho
w that the proposed approximation is very accurate in the low normalized fr
equency limit too and can be particularly valuable to analyze dispersion-sh
ifted fibers with triangular refractive index profile.