Lez #13+14 Propagation in non-linear media, Kerr effect

 We discussed non linear effects. At first, we observed as in the very common case of centro symmetric materials even susceptibilities must be zero (only odd restoring forces, i.e. even potential energy). Therefore, the most general, lowest order non linear effect is the third order (Boyd 1.5.10 and this link). Such an effect can be introduced in terms of a non linear, intensity dependent refractive index. We solved the equation in time domain, obtaining a z-independent temporal profile and a z dependent phase term. It can be shown (numerically) how the resulting spectrum broadens with z. We then combined the two effects and derived the soliton solution arising when (anomalous) GVD and Kerr compensate for LD=Lnl. We also discussed wave breaking phenomenon, in presence of non linearity with small normal dispersion.