3) Photonique

The Fermi-Pasta-Ulam (FPU) recurrence is a very well known phenomenon in non-linear optics. When several waves propagate in an optical fiber, the energy exchanges between the pump, the idler and the signal make that the pump first undergoes a depletion of its power for the benefit of the other components. The process is then reversed, and the pump recover its initial power. This is the FPU recurrence. This recurrence is known to have a trajectory in the phase space, which differs according to the initial phase difference between the pump and the signal. When crossing a characteristic value of this initial phase, there is a sudden change of phase-space trajectories induced by a symmetry breaking. This has been discovered forty years ago. However, it has never been experimentally observed. Indeed, it is not visible while looking only at the wave’s intensity. Furthermore, because of the loss, the system is not Hamiltonian, so that this symmetry breaking has not been either observed in hydrodynamics. Thanks to the expertise of vector Brillouin reflectometry from a previous project, we have develop a new vector reflectometer based on Rayleigh backscattered light. At first sight, the Rayleigh diffusion does not allow distributed phase measurements. As its name indicates, it is a diffusive process. The scatterers are the defects of the fiber. Of quasi-infinite number, they have a random location and size along the fiber. The backscattered light looks like noise with random phase. However, if one notice that the response of the system is potentially very complex, it remains linear! The fiber is thus probed with a sequence of two pulses. The first one is intense to excite the non-linear dynamics. The second is weak enough to only probe the linear response. Computing the ratio of the complex amplitudes of these two consecutive time of flight signals, we eliminate the huge Rayleigh fluctuations. We then recover the complex distributed non-linear evolution of each optical component. To finalize the experiment, we add a distributed Raman amplification along the fiber. It compensates for the inline fiber losses, making it transparent. This instrument allowed us to make the very first experimental observation of the FPU symmetry breaking.