Optical Networks - _E_3 Soliton Pulse Propagation_157

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online