Application of multiple-length-scale methods to the study of optical fiber transmission

It is natural to apply multiple-length-scale methods to the study of optical-fiber transmission because the key length scales span 13 orders of magnitude and cluster in three main groups. At the lowest scale, corresponding to micrometers, the full set of Maxwell’s equations should be used. At the intermediate scale, corresponding to the range from one centimeter to tens of meters, the coupled nonlinear Schrödinger equation should be used. Finally, at the longest length scale, corresponding to the range from tens to thousands of kilometers, the ManakovPMD equation should be used, and, when polarization mode dispersion can be neglected and the fiber gain and loss can be averaged out, one arrives at the scalar nonlinear Schrödinger equation. As an illustrative example of multiple-scale-length techniques, the nonlinear Schrödinger equation will be derived, carefully taking into account the actual length scales that are important in optical-fiber transmission.