Analysis of the ellipticity induced PMD and general scaling perturbation in a transmitting fiber.

Presented is an analysis of general scaling perturbations in a transmitting fiber. For elliptical perturbations, under some conditions an intermode dispersion parameter characterizing modal PMD is shown to be directly proportional to the mode dispersion. c2008 Optical Society of America OCIS codes: (060.24000) Fiber properties ; 060.2280 Fiber design and fabrication In the following paper we derive a generalized Hermitian Hamiltonian approach for the treatment of Maxwell equations in waveguides as well as develop a perturbation theory for the general class of scaling perturbations that include ellipticity and a uniform scaling of an arbitrary index profile. Because of the Hermitian nature of the formulation most of the results from the well developed perturbation theory of quantum mechanical systems can be directly related to the light propagation in the waveguides. Such formulation provides for an intuitive way of understanding PMD and birefringence in the elliptically perturbed fiber profiles. Region of validity of our theory extends to the case of large variations of the dielectric constant across the fiber crossection and is limited only by an amount of re-scaling. Finally, we establish that if in some range of frequencies a particular mode behaves like a mode of pure polarization T E,T M (where polarization is judged by the relative amounts of the electric and magnetic longitudinal energies in a modal crossection) its inter-mode dispersion parameter τ = | ∂△β e ∂ω | is related to its dispersion D as τ = λδ|D|, where δ is a measure of the fiber ellipticity and △βe is a split in a wavevector of a linearly polarized doubly degenerate mode of interest due to an elliptical perturbation. While there has been a wide amount of work done on estimating such quantities as local birefringence induced by perturbations in the fiber profile most of the treatments were geared toward understanding the low contrast, weakly guiding systems such as ubiquitous silica waveguides and are not directly applicable to the high contrast systems such as Bragg fibers, photonic crystal fibers and integrated optics waveguides which are steadily emerging as an integral part of the state of the art transmission systems.