Analytical Modal Solutions on Optical Inhomogeneous Fibers: the Frobenius-Taylor Method (FTM)
Keywords:Inhomogeneous Optical Fibers, Modal Solutions, Dispersion, FTM
Analytical solutions for wave propagation in a general inhomogeneous optical fiber profile are built using serial expansions about regular points of differential equations for radial variation of field components, called as Frobeniusâ€™ and Taylorâ€™s, whose coefficients are evaluated recursively. Using both types of series expansion, a general and fast convergent algorithm for computing modal characteristics is presented: the Frobenius-Taylor Method (FTM), together with a set of alternative functions to the second-kind Bessel ones (used in the cladding), closely related but numerically more stables. The complete algorithm is presented and can be applied to both high and low values of the index difference, showing a fast convergence for frequencies just over, very near and far from cutoff.
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