In general, the refractive index n ( ω ω ) , and therefore the wave vector k ( ω ω ) = n ( ω ω ) ω ω / c , can be an arbitrary function of ω ω , making it difficult to analytically perform the inverse Fourier transform back into the time domain. However, if the bandwidth of the pulse is narrow relative to the curvature of n , then good approximations of the impact of the refractive index can be obtained by replacing k ( ω ω ) with its Taylor expansion centered about ω ω 0 :