Calculation of Modes in an Optical Fiber Using the Finite Element Method and EISPACK

T h i s paper presents a method for calculating the propagation modes of a circular optical fiber. T h e modal quantities, essential for telecommunications, include the waveforms (which describe the radial distribution of propagating power), t h e propagation c o n s t a n t s (which determine cutoff conditions), and t h e delays per unit length (which *Bell Laboratories. °Copyright 1983, American Telephone & Telegraph Company. Photo reproduction for noncommercial use is permitted without payment of royalty provided that each reproduction is done without alteration and that the Journal reference and copyright notice are included on the first page. The title and abstract, but no other portions, of this paper may be copied or distributed royalty free by computer-based and other information-service systems without further permission. Permission to reproduce or republish any other portion of this paper must be obtained from the Editor. 2663 determine pulse dispersion along the fiber). T h e technique combines the Finite Element Method (FEM) and routines from the Eigensystem Package (EISPACK) 1 to achieve an efficient calculation of these modal quantities for both single and multimode fibers. T h e most popular approach to modal calculations for multimode fibers has been the Wentzel, Kramers, Brillouin (WKB) method, where Maxwell's equations are approximated by an easily integrated first-order differential equation. 2 W K B analysis provides a simple model for understanding optical transmission through a fiber 3 and has guided fiber design.