Fundamental Equations of Nonlinear Fiber Optics

摘要

A set of nonlinear differential equations are derived from the first principles, namely the Maxwell's equations and the material responses to electromagnetic excitations. The derivation retains the mathematical exactitude down to details. Still in compact and convenient forms, the final equations include the effect of group-velocity dispersion down to an arbitrary order, and take into account the frequency variations of the optical loss as well as the transverse modal function. Also established is a new formulation of multi-component nonlinear differential equations, which is especially suitable for the study of wide-band wavelength-division multiplexed systems of optical communications. The formulations are applied to discuss the problem of compensating the optical nonlinearity of fiber transmission lines using optical phase conjugation. Two system configurations are identified suitable for nonlinearity compensation. One setup is mirror-symmetric and the other translationally symmetric about the optical phase conjugator, both being in a scaled sense.