Unformatted text preview: 776 Pulse Propagation in Optical Fiber in [Agr95]. The qualitative description of these solutions in both the normal and anomalous chromatic dispersion regimes is discussed in Section 2.5.5. We can use (E.13) to estimate the SPMinduced chirp for Gaussian pulses. To do this, we neglect the chromatic dispersion term and consider the equation ∂A ∂z + β 1 ∂A ∂t = iγ  A  2 A. (E.16) By using the variables τ and U introduced in (E.14) instead of t and A , and L NL = (γ P ) − 1 , this reduces to ∂U ∂z = i L NL  U  2 U. (E.17) Note that we have not used the change of variable ξ for z since L D is infinite when chromatic dispersion is neglected. This equation has the solution U(z, τ) = U( , τ)e iz  U( ,τ)  2 /L NL . (E.18) Thus the SPM causes a phase change but no change in the envelope of the pulse. Note that the initial pulse envelope U( , τ) is arbitrary; so this is true for all pulse shapes. Thus SPM by itself leads only to chirping, regardless of the pulse shape...
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 Spring '09
 Boussert
 ξ, Chirp, chromatic dispersion, anomalous chromatic dispersion

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