System Analysis using the Split Operator Method K J Blow Aston University, Aston Triangle, Birmingham, B4 7ET, UK Abstract. The split step operator technique underlies both numerical and analytical approaches to optical communication system studies. In this paper I will show how these are related and how they give rise to real systems applications of the principles. The technique can also be related to other analytical methods such as the Lie transform. The predicted special points of systems are also equivalent to pre-chirping techniques. 1 Introduction The use of optical solitons in communication systems is now a well established field of research. Many techniques have been developed to study the complex propagation phenomena including numerical simulation [3] [5], perturbation theory, variational methods [2], transforms and inverse scattering theory. Here I will describe the split operator method that was originally used to derive a higher order numerical integration scheme but has since been used to derive an- alytic results in the average soliton regime [4]. The split operator method can be used to achieve two things. First, we can demonstrate that under certain con- ditions pulse propagation can be described by the lossless nonlinear Schrodinger equation [NLS]. Second, we can derive corrections to the NLS that give addi- tional information about system performance. The method is based on a formal operator representation of the nonlinear differential equations describing the propagation of light in a monomode optical fibre. 1.1 Operator Representations We begin with a brief review of operator representations of differential equations. The NLS can be written in the following form where u is the optical field and the two terms on the RHS represent the dispersion and nonlinearity respectively. i ∂u ∂z = 1 2 ∂ 2 u ∂t 2 + |u| 2 u (1) In order to simplify much of the following discussion we will represent this in the following way i ∂u ∂z = ˆ Du + ˆ Nu. (2)