Temporal Fresnel diffraction induced by phase jumps in linear and nonlinear optical fibres

We analytically and numerically study the temporal intensity pattern emerging from the linear or nonlinear evolutions of a single or double phase jump in an optical fiber. The results are interpreted in terms of interferences of the well-known diffractive patterns of a straight edge, strip and slit and a complete analytical framework is derived in terms of Fresnel integrals for the case of purely dispersive evolution. When Kerr non linearity affects the propagation, various coherent nonlinear structures emerge according to the regime of dispersion.