The linearly polarized approximation (LPA) is employed for the analysis of the propagation characteristics of the guided modes in parabolic-index fibers. Characteristic equations for fibers in both the infinite- and finite-cladding configurations are derived and the conditions for the core-mode cutoffs are thereby deduced. In particular, it is shown that the effects of the finite cladding on the properties of the guided modes can be accounted for by a direct generalization of the LPA that has been used for the analysis of infinite-cladding fibers. Furthermore, it is demonstrated that the LPA is applicable even when the cladding layer is thin compared with the core radius and the refractive index of the surrounding medium is much smaller than that of the cladding, provided the weakly guiding condition for the core modes is fulfilled and the propagating radiation frequency is far from the cladding-mode cutoff. The good agreement between the results obtained by the LPA and those calculated by the vector wave analysis, which is overwhelmingly complex for the finite-cladding fibers, demonstrates the appeal of the LPA by providing simple and yet sufficiently accurate formulas for the practical design calculations for parabolic-index fibers. It is also pointed out that the mathematical procedure employed in this paper can be adapted for other types of graded-index fibers.
© 1980 Optical Society of America
Equations on this page are rendered with MathJax. Learn more.