Variational Approximations for ${\rm LP}_{l1}$ Modes of Graded-Index Few-Mode Fibers

Two parameter variational fields for the
${\rm LP}_{l1}$
modes of a graded index few-mode fiber have been proposed. Using these, the propagation constant, the normalized group delay and the normalized dispersion parameter have been calculated for few representative modes. The accuracies of the results have been calculated by comparison with the exact results obtained from the numerical solution of the scalar wave equation. As expected, the two parameter fields give better accuracies than the single-parameter fields available in the literature. Furthermore, it is observed that the accuracy decreases for higher order
${\rm LP}_{l1}$
modes. Thus, these fields may be used in few-mode fiber-based photonic devices, which utilize lower order
${\rm LP}_{l1}$
modes.