Theoretical Cutoff Frequencies in Optical Fiber Using a Variational Technique

A numerical method for calculating the cutoff frequencies of modes in optical fibers with arbitrary refractive index profile is presented. Using a variational technique, the cutoff problem is transformed into a generalized eigenvalue problem whose eigenvalues are the cutoff frequencies. A similar variational technique has already been used for determining both the propagation constants and fields of guided modes of matched-clad optical fibers. In this technique, a series expansion of Laguerre-Gauss functions and a modified Bessel function have been used for describing the field in the fiber core and in the uniform cladding respectively. Here we adapt this technique for computing the cutoff frequencies using the limiting form for small argument of the modified Bessel function. Cutoff frequencies have been calculated for optical fibers with power-law refractive index profiles for which either exact or approximate reference solutions are available. A comparison with other published data is also reported.