Optical Networks - _E_3 Soliton Pulse Propagation_157

Optical Networks - _E_3 Soliton Pulse Propagation_157 - 776...

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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 SPM-induced 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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