TABLE OF CONTENTS The basic equation governing the propagation of pulses in optical fibers is known as the nonlinear Schr dinger equation, or NLS equation for short. It is of fundamental importance to almost everything we shall discuss in this book. In this chapter we shall derive that equation and examine some of its most immediate consequences. Before beginning a detailed study, however, it is useful to have a first look at this innocent-looking equation and its most significant properties. The NLS equation is
As its name suggests, Eq. (1.1) is similar to the well-known Schr dinger equation of quantum mechanics. Here, of course, it has nothing to do with quantum mechanics. Rather, it is just Maxwell's equations, adapted to field propagation in single-mode optical fiber. However, the analogy to quantum mechanics may be instructive to some, as the nonlinear term (the second on the right) is analogous to a negative potential energy, which allows the possibility of self-trapped pulse solutions. These are the solitons, which are the central concern of this book.
In a single-mode fiber, there is only one possible spatial behavior in the transverse dimensions x and y, so that we need to deal only with appropriate averages of the field quantities over those dimensions. Thus, the NLS equation involves only distance along the propagation direction, z, and time, t. The complex quantity u( z, t) is proportional to the light field, with the "central optical frequency" (a frequency arbitrarily chosen somewhere near the...
