Analysis of optical fibers with arbitrary refractive index profiles: accuracy, convergence, and effects of finite cladding

We have formulated a matrix eigenvalue problem for cylindrical optical fibers from a set of finite difference equations. Numerical solution of this problem yields the propagation constants for propagating modes. The method can be used for arbitrary index profiles, does not require the explicit evaluation of Bessel or modified Bessel functions, and does not use iterative methods to search for the propagation constants as was the case in earlier proposed methods using finite differences. The method is accurate, fast, and simple. We have established the convergence and stability of this method, and explored the effects of finite cladding width on the dispersion characteristics.