Observation of Light Thermalization to Negative-Temperature Rayleigh-Jeans Equilibrium States in Multimode Optical Fibers.

Although the temperature of a thermodynamic system is usually believed to be a positive quantity, under particular conditions, negative-temperature equilibrium states are also possible. Negative-temperature equilibriums have been observed with spin systems, cold atoms in optical lattices, and two-dimensional quantum superfluids. Here we report the observation of Rayleigh-Jeans thermalization of light waves to negative-temperature equilibrium states. The optical wave relaxes to the equilibrium state through its propagation in a multimode optical fiber-i.e., in a conservative Hamiltonian system. The bounded energy spectrum of the optical fiber enables negative-temperature equilibriums with high energy levels (high-order fiber modes) more populated than low energy levels (low-order modes). Our experiments show that negative-temperature speckle beams are featured, in average, by a nonmonotonic radial intensity profile. The experimental results are in quantitative agreement with the Rayleigh-Jeans theory without free parameters. Bringing negative temperatures to the field of optics opens the door to the investigation of fundamental issues of negative-temperature states in a flexible experimental environment.

Polarization chaos and random bit generation in nonlinear fiber optics induced by a time-delayed counter-propagating feedback loop.

In this manuscript, we experimentally and numerically investigate the chaotic dynamics of the state-of-polarization in a nonlinear optical fiber due to the cross-interaction between an incident signal and its intense backward replica generated at the fiber-end through an amplified reflective delayed loop. Thanks to the cross-polarization interaction between the two-delayed counter-propagating waves, the output polarization exhibits fast temporal chaotic dynamics, which enable a powerful scrambling process with moving speeds up to 600-krad/s. The performance of this all-optical scrambler was then evaluated on a 10-Gbit/s On/Off Keying telecom signal achieving an error-free transmission. We also describe how these temporal and chaotic polarization fluctuations can be exploited as an all-optical random number generator. To this aim, a billion-bit sequence was experimentally generated and successfully confronted to the dieharder benchmarking statistic tools. Our experimental analysis are supported by numerical simulations based on the resolution of counter-propagating coupled nonlinear propagation equations that confirm the observed behaviors.

Gas-Solid Phase Transition in Laser Multiple Filamentation.

While propagating in transparent media, near-infrared multiterawatt (TW) laser beams break up in a multitude of filaments of typically 100-200 um diameter with peak intensities as high as 10 to 100 TW/cm^{2}. We observe a phase transition at incident beam intensities of 0.4 TW/cm^{2}, where the interaction between filaments induce solidlike two-dimensional crystals with a 2.7 mm lattice constant, independent of the initial beam diameter. Below 0.4 TW/cm^{2}, we evidence a mixed phase state in which some filaments are closely packed in localized clusters, nucleated on inhomogeneities (seeds) in the transverse intensity profile of the beam, and other are sparse with almost no interaction with their neighbors, similar to a gas. This analogy with a thermodynamic gas-solid phase transition is confirmed by calculating the interaction Hamiltonian between neighboring filaments, which takes into account the effect of diffraction, Kerr self-focusing, and plasma generation. The shape of the effective potential is close to a Morse potential with an equilibrium bond length close to the observed value.

Reversibility of laser filamentation.

We investigate the reversibility of laser filamentation, a self-sustained, non-linear propagation regime including dissipation and time-retarded effects. We show that even losses related to ionization marginally affect the possibility of reverse propagating ultrashort pulses back to the initial conditions, although they make it prone to finite-distance blow-up susceptible to prevent backward propagation.

Melanosis cerebelli.

Melanosis cerebelli (melanic pigmentation involving the dentate nuclei and the granular layer of the cerebellar cortex) is described in three patients, aged between 72 and 99 years. In two cases atrophic changes of the Alzheimer type co-existed in the cerebral cortex. One patient had a history of tremors, possibly cerebellar in origin.