Calculating Dispersion Derivatives in Fiber-Optic Design

Maxwell's equation for modeling the guided waves in a circularly symmetric fiber leads to a family of partial differential-equation-eigenvalue systems. In fiber design, one would like to determine the index profile, which is involved in Maxwell's equation so that certain optical properties, which sometimes involve derivatives of the eigenvalues, are satisfied. In this paper, we will discuss how to determine derivatives of the eigenvalue problem and the gradients of the dispersion with respect to design parameters in the model