TABLE OF CONTENTS The field in an optical fiber transmission line that arrives at some location z can usefully be resolved into Fourier components. These may be called temporal modes of the field. The word mode is used in a number of ways. In a fiber with a large core, there may be several transverse modes, that is, different transverse field patterns that the fiber can support. We are concerned here only with fibers that support only one transverse mode. Such fibers are called single (transverse)-mode fibers, with the word transverse usually omitted. In addition, in the very nearly cylindrical fibers that are primarily in use, there are two independent polarization modes, which give rise to a defect called polarization-mode dispersion, as discussed in Chapter 7.
Consider the temporal modes of a single polarization mode. In some appropriately long time T (see below), the field u( t, z) that arrives at some location z can be resolved into a sum of orthogonal Fourier components
where a n is a complex coefficient and ? n is the frequency of the nth mode. The different modes are made orthogonal by imposing periodic boundary conditions, so that u n( t + T) = u n( t). This requirement is satisfied by ? n = n/T, so that we have
where ?( m, n) is the Kroneker...
