Temporal Arago spot in optical fibers

The history of conceptions of light is among the most exciting scientific adventures. It was Fresnel's theoretical work that made it possible to establish the most solid theoretical basis of wave optics. Two centuries ago, his approach was validated by the observation of a counter-intuitive bright spot appearing at the center of the geometric shadow of an illuminated opaque circular object. This phenomenon has remained known as the Arago spot. We propose here to further extend the spatial/temporal analogy that exists between diffraction and dispersion by revisiting the Arago spot formation in the time domain through the temporal dispersive evolution of light after being briefly stopped by an obstacle. The analytical treatment that is possible for linear propagation as well as the experiments based on telecom optical fibers and fast optoelectronics confirm that we observe the emergence of light where it was initially absent. As the power increases and Kerr nonlinearity affects the propagation, the Arago spot intensity is affected by the sign of the dispersion.