A Rapid Accurate Technique to Calculate the Group Delay, Dispersion and Dispersion Slope of Arbitrary Radial Refractive Index Profile Weakly-Guiding Optical Fibers

Abstract

Abstract-This paper introduces a new numerical method to calculate the group delay, chromatic dispersion and dispersion slope of weakly-guiding optical fibers with arbitrary radial refractive index profiles. It is based on the analytical differentiation of the propagation coefficient up to the third order. The simulation results are compared to experimental data, with those calculated by other approaches and exact data where possible. Due to the analytical differentiation of the matrix equation, the method is more accurate compared to other approaches, it is also much faster than numerical differentiation as allows avoiding repeated solution of the eigenvalue problem to calculate the derivatives of the propagation coefficient. The precision of the method is limited only by the approximation errors of the mode solver. The Galerkin method with Laguerre-Gauss basis functions is used to determine the propagation coefficients of weakly-guiding structures. The new method enables fiber manufacturers to rapidly design dispersion characteristics of graded index, step index, single-and multiple-clad fibers, as well as few-mode and bend insensitive fibers.

Design and Analysis of a Compact High Gain Wideband Monopole Patch Antenna for Future Handheld Gadgets

“…Group delay is used not only to compute the phase characteristics of filters/amplifiers but also to characterize the phase transfer function of UWB/SWB antenna. The average group delay is described as the ratio of phase derivative to its angular frequency [24,25]…”

Analysis of graded-index optical fibers by the spectral parameter power series method

“…The dispersion represents one of the main impairments for optical communications. The study and the tailoring of different refractive index profiles aim at a desirable manipulation of the dispersion (as well as of several other transmission characteristics, e.g., [25,28,29]). Fibers with the dispersion parameter reduced at a certain wavelength, flattened for a wide range of wavelengths or even made highly negative are used for applications concerning long-haul communications, wavelength division multiplexing and dispersion compensation, among others (see, e.g., [3], [26, chapter 4]).…”

Method of Angular Invariants: Experiment

“…The choice of a certain method is determined by a certain object under study and the aim of measurement with certain instruments and required accuracy. The precise measurement of refractive indices has been recently become of great interest [5][6][7] because of increasing productivity, as well as complex simulation and fabrication, currently required for waveguide-based devices [8,9]. The refractive indices of the materials used in these devices should be known with an accuracy of 10 −4 .…”