Variational analysis of matched-clad optical fibers

A variational analysis of weakly guiding optical fibers is described. A series expansion of Laguerre-Gauss functions and a modified Bessel function have been used to describe the field in the fiber core and in the uniform cladding, respectively. A numerical procedure optimizing the field parameters (the expansion coefficients, the Gaussian spot-size and the normalized transverse propagation constant) has been developed which allowed highly accurate field representations to be obtained through few-term expansions. Low-order LP modes have been analyzed for refractive index profiles with a power-law variation in the core for which reference solutions (either exact or approximate) are available. A modified profile exhibiting a high index ring around the core has also been analyzed. For power-law profiles, the results are in excellent agreement with the reference solutions and show that the proposed variational analysis also appears to be appropriate for determining the field at wavelengths near to cutoff. Moreover, the comparison with other field representations which use series expansions, shows that our solution needs a noticeably lower number of terms. The analysis of the modified profile, for which only numerical solutions are available, highlights that the developed method provides very accurate field representations.