Group velocity of modes and pulse distortion in dielectric optical waveguides

Abstract

After a brief summary of the main factors causing pulse distortion in optical fibres, expressions are derived for phase velocity, group velocity and dispersion, that is velocity variation with frequency, of each mode. The analysis is carried out by making extensive use of the functiony(x) (y andx being the arguments of the first and second kind Bessel functions that appear in the solutions of Maxwell equations), that we call characteristic function. By using this function we obtain particularly simple and compact formulas that make easier the analysis of the behaviour of velocity and dispersion near and far from cut-off. It will also be seen that the ratio between the power propagating in the core,W ₁, and the power in the cladding,W ₂, for each mode takes a very simple form if expressed by means of the characteristic function: this fact permits a direct relation to be found between group velocity and power flow in an optical fibre. The study of the ratioW ₁/W ₂ will show that, contrary to expectation, for some modes, a substantial fraction of energy travels inside the core, even near cut-off. Expressions are given forW ₁/W ₂ at cut-off, and far from cut-off. Plots of velocity and dispersion are shown. On the grounds of the obtained results pulse distortion in optical fibres is discussed.