Fast-Varying and Transient Nonlinear Equation for Microstructure Fibers

Abstract

The transient nonlinear equation that describes the fast varying field in microstructure fibers (photonic crystal fibers) is established. In this equation, the frequency and wavenumber are functions of time. It is solved using two methods (the Volterra series integration and the Laplace transformation) and validated by comparing its simulation results with those of reported experiments and published theories. It is demonstrated that due to the introduction of the functions $\omega (t)$ and $\beta (t)$ in the Maxwell's equations, new frequencies are continually induced and amplified by the nonlinear effect (supercontinuum generation). The second-order differential of the field to transmission distance ( ${\partial ^2}A{\rm{/}}\partial {z^2}$ ) cannot be deleted, and in the resonance condition, this field exhibits a periodic oscillation along z . This property can be utilized to interpret the principle of photonic crystal fiber metamaterials.