A new derivation of the nonlinear Schrodinger equation for physically realistic optical fibers

Summary form only given. Almost all published derivations of the nonlinear Schrodinger equation and certainly all those in commonly used textbooks are based on the assumption that optical fibers are perfectly circular and that fiber birefringence can be neglected. In fact, a study of the key length scales that exist in optical fibers shows that optical fiber birefringence-far from being negligible-is a large effect relative to dispersion and nonlinearity since it appears on a shorter length scale. Any physically correct derivation should take this essential fact into account. It is remarkable that no really complete derivation of the nonlinear Schrodinger equation for physically realistic fibers exists in the literature, although pieces can be found scattered throughout it. For example, Kodama (1985) has published a mathematically elegant and correct derivation that neglects birefringence. Others have taken into account birefringence but have made other simplifications like the plane wave approximation. In the contribution, an approach is outlined that allows one to derive the nonlinear Schrodinger equation from first principles in a step-by-step procedure using multiple scale length techniques. This approach not only arrives at the nonlinear Schrodinger equation but elucidates when it is valid and when it is expected to fail.