Analysis of general geometric scaling perturbations in a transmitting waveguide: fundamental connection between polarization-mode dispersion and group-velocity dispersion

Abstract

We develop a novel perturbation theory formulation to evaluate polarization-mode dispersion (PMD) for a general class of scaling perturbations of a waveguide profile based on generalized Hermitian Hamiltonian formulation of Maxwell’s equations. Such perturbations include elipticity and uniform scaling of a fiber cross section, as well as changes in the horizontal or vertical sizes of a planar waveguide. Our theory is valid even for discontinuous high-index contrast variations of the refractive index across a waveguide cross section. We establish that, if at some frequencies a particular mode behaves like pure TE or TM polarized mode (polarization is judged by the relative amounts of the electric and magnetic longitudinal energies in the waveguide cross section), then at such frequencies for fibers under elliptical deformation its PMD as defined by an intermode dispersion parameter τ becomes proportional to group-velocity dispersion D such that τ=λδ|D|, where δ is a measure of the fiber elipticity and λ is a wavelength of operation. As an example, we investigate a relation between PMD and group-velocity dispersion of a multiple-core step-index fiber as a function of the core–clad index contrast. We establish that in this case the positions of the maximum PMD and maximum absolute value of group-velocity dispersion are strongly correlated, with the ratio of PMD to group-velocity dispersion being proportional to the core–clad dielectric contrast.