Linear and nonlinear propagation properties of Cosine-Gauss (CG) pulses in optical fibers

From a recent interpretation [A. Gajadharsingh, P.-A. Bélanger, Opt. Commun. 241 (2004) 377] of the formation of a dispersion managed soliton (DMS) in the zero-average dispersion regime, we have seen that the use of CG pulses to approximate such solutions proves to be very accurate in this regime. Hence the basic linear and nonlinear propagation properties of such distributions deserve a closer look and are one of the subjects of this paper. We study, through second-order moment (SOM) theory, the root-mean-square (RMS) properties of a general CG ansatz and discuss the possible applications of such distributions. We also derive, using a perturbative approach, new approximate propagation laws through the moment theory which prove to be very accurate when compared to exact numerical results therefore providing us with analytical tools that can be used for various design purposes.