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.

Optimum design of NOLM-driven mode-locked fiber lasers.

Most of the saturable absorbers commonly used to perform mode locking in laser cavities affect the trigger conditions of laser oscillation, which requires manually forcing the laser start-up by various means such as polarization controllers. We present a procedure for designing a laser cavity driven by a nonlinear optical loop mirror, which allows the laser to operate optimally without interfering with the oscillation triggering conditions, thus opening up possibilities for integration of this type of laser.

3D time-domain beam mapping for studying nonlinear dynamics in multimode optical fibers.

Characterization of the complex spatiotemporal dynamics of optical beam propagation in nonlinear multimode fibers requires the development of advanced measurement methods, capable of capturing the real-time evolution of beam images. We present a new space-time mapping technique, permitting the direct detection, with picosecond temporal resolution, of the intensity from repetitive laser pulses over a grid of spatial samples from a magnified image of the output beam. By using this time-resolved mapping, we provide, to the best of our knowledge, the first unambiguous experimental observation of instantaneous intrapulse nonlinear coupling processes among the modes of a graded index fiber.

Highly efficient few-mode spatial beam self-cleaning at 1.5µm.

We experimentally demonstrate that spatial beam self-cleaning can be highly efficient when obtained with a few-mode excitation in graded-index multimode optical fibers. By using 160 ps long, highly chirped (6 nm bandwidth at -3dB) optical pulses at 1562 nm, we demonstrate a one-decade reduction of the power threshold for spatial beam self-cleaning, with respect to previous experiments using pulses with laser wavelengths at 1030-1064 nm. Self-cleaned beams remain spatio-temporally stable for more than a decade of their peak power variation. The impact of input pulse temporal duration is also studied.

Spatial Beam Self-Cleaning in Second-Harmonic Generation.

We experimentally demonstrate the spatial self-cleaning of a highly multimode optical beam, in the process of second-harmonic generation in a quadratic nonlinear potassium titanyl phosphate crystal. As the beam energy grows larger, the output beam from the crystal evolves from a highly speckled intensity pattern into a single, bell-shaped spot, sitting on a low energy background. We demonstrate that quadratic beam cleanup is accompanied by significant self-focusing of the fundamental beam, for both positive and negative signs of the linear phase mismatch close to the phase-matching condition.

Classical Rayleigh-Jeans Condensation of Light Waves: Observation and Thermodynamic Characterization.

Theoretical studies on wave turbulence predict that a purely classical system of random waves can exhibit a process of condensation, which originates in the singularity of the Rayleigh-Jeans equilibrium distribution. We report the experimental observation of the transition to condensation of classical optical waves propagating in a multimode fiber, i.e., in a conservative Hamiltonian system without thermal heat bath. In contrast to conventional self-organization processes featured by the nonequilibrium formation of nonlinear coherent structures (solitons, vortices,…), here the self-organization originates in the equilibrium Rayleigh-Jeans statistics of classical waves. The experimental results show that the chemical potential reaches the lowest energy level at the transition to condensation, which leads to the macroscopic population of the fundamental mode of the optical fiber. The near-field and far-field measurements of the condensate fraction across the transition to condensation are in quantitative agreement with the Rayleigh-Jeans theory. The thermodynamics of classical wave condensation reveals that the heat capacity takes a constant value in the condensed state and tends to vanish above the transition in the normal state. Our experiments provide the first demonstration of a coherent phenomenon of self-organization that is exclusively driven by optical thermalization toward the Rayleigh-Jeans equilibrium.

Spatial beam self-cleaning and supercontinuum generation with Yb-doped multimode graded-index fiber taper based on accelerating self-imaging and dissipative landscape.

We experimentally demonstrate spatial beam self-cleaning and supercontinuum generation in a tapered Ytterbium-doped multimode optical fiber with parabolic core refractive index profile when 1064 nm pulsed beams propagate from wider (122 µm) into smaller (37 µm) diameter. In the passive mode, increasing the input beam peak power above 20 kW leads to a bell-shaped output beam profile. In the active configuration, gain from the pump laser diode permits to combine beam self-cleaning with supercontinuum generation between 520-2600 nm. By taper cut-back, we observed that the dissipative landscape, i.e., a non-monotonic variation of the average beam power along the MMF, leads to modal transitions of self-cleaned beams along the taper length.

Wavefront shaping for optimized many-mode Kerr beam self-cleaning in graded-index multimode fiber.

We report experimental results, showing that the Kerr beam self-cleaning of many low-order modes in a graded-index multimode fiber can be controlled thanks to optimized wavefront shaping of the coherent excitation beam. Adaptive profiling of the transverse input phase was utilized for channeling the launched power towards a specific low-order fiber mode, by exploiting nonlinear coupling among all guided modes. Experiments were carried out with 7 ps pulses at 1064 nm injected in a five meters long multimode fiber operating in the normal dispersion regime. Optimized Kerr beam self-cleaning of five different LP modes is reported, with a power threshold that increases with the mode order.

Selective generation of Kerr combs induced by asymmetrically phase-detuned dual pumping of a fiber ring cavity.

We numerically and experimentally investigate the asymmetrically phase-detuned dual pumping of a passive inhomogeneous fiber ring cavity. This configuration originates from the fine control of frequency mismatch between the frequency spacing of the bichromatic pump and the free spectral range of the cavity. Multicomb states at offset frequencies can be selectively generated by means of the mismatch parameter and the coexistence of Turing and Faraday instabilities.

Interplay of Kerr and Raman beam cleaning with a multimode microstructure fiber.

We experimentally study the competition between Kerr beam self-cleaning and Raman beam cleanup in a multimode air-silica microstructure optical fiber. Kerr beam self-cleaning of the pump is observed for a certain range of input powers only. Stokes Raman beam generation and cleanup lead to both depletion and degradation of beam quality for the pump. The interplay of modal four-wave mixing and Raman scattering in the infrared domain leads to the generation of a multimode supercontinuum ranging from 500 nm up to 1800 nm.

Nonlinear beam self-cleaning in a coupled cavity composite laser based on multimode fiber.

We study a coupled cavity laser configuration where a passively Q-switched Nd:YAG microchip laser is combined with an extended cavity, including a doped multimode fiber. For appropriate coupling levels with the extended cavity, we observed that beam self-cleaning was induced in the multimode fiber thanks to nonlinear modal coupling, leading to a quasi-single mode laser output. In the regime of beam self-cleaning, laser pulse duration was reduced from 525 to 225 ps. We also observed a Q-switched mode-locked operation, where spatial self-cleaning was accompanied by far-detuned nonlinear frequency conversion in the active multimode fiber.

Intermodal modulational instability in graded-index multimode optical fibers.

We report on the experimental observation of an intermodal noise-seeded modulational instability process (MI) taking place in the normal dispersion regime of a few-mode graded-index optical fiber. Strong power dependence of the MI spectra is observed, with a peak gain modulation frequency that scales as the square root of the injected light power. These observations are in excellent agreement with the predictions of a bimodal-MI model.

Spectral broadening of picosecond pulses forming dispersive shock waves in optical fibers.

We investigate analytically, numerically, and experimentally the spectral broadening of pulses that undergo the formation of dispersive shocks, addressing in particular pulses in the range of tens of ps generated via electro-optic modulation of a continuous-wave laser. We give an analytical estimate of the maximal spectral extension and show that super-Gaussian waveforms favor the generation of flat-topped spectra. We also show that the weak residual background of the modulator produces undesired spectral ripples. Spectral measurements confirm our estimates and agree well with numerical integration of the nonlinear Schrödinger equation.

Far-detuned cascaded intermodal four-wave mixing in a multimode fiber.

We demonstrate far-detuned parametric frequency conversion processes in a few mode graded-index optical fibers pumped by a Q-switched picosecond laser at 1064 nm. Through a detailed analytical and numerical analysis, we show that the multiple sidebands are generated through a complex cascaded process involving inter-modal four-wave mixing. The resulting parametric wavelength detuning spans in the visible down to 405 nm and in the near-infrared up to 1355 nm.

Kerr self-cleaning of pulsed beam in an ytterbium doped multimode fiber.

We experimentally demonstrate that Kerr spatial self-cleaning of a pulsed beam can be obtained in an amplifying multimode optical fiber. An input peak power of 500 W only was sufficient to produce a quasi-single-mode emission from the double-clad ytterbium doped multimode fiber (YMMF) with non-parabolic refractive index profile. We compare the self-cleaning behavior observed in the same fiber with loss and with gain. Laser gain introduces new opportunities to achieve spatial self-cleaning of light in multimode fibers at a relatively low power threshold.

Second harmonic generation in multimode graded-index fibers: spatial beam cleaning and multiple harmonic sideband generation.

We study experimentally and numerically the spectral and spatial dynamics of second harmonic generation in an all-optically poled multimode graded-index fiber. In contrast with poled single-mode fibers, in a multimode graded-index fiber a pump can generate a series of sharp sidebands around its second harmonic (SH) that originate from the sub-millimetric periodic evolution of the intensity at the fundamental frequency. The mutual interaction between the fundamental and its SH may also strongly affect the spatial distribution of guided light for both colors: when increasing the pump power, both fundamental and SH output beams evolve from disordered multimode speckles into two bell-shaped beams.

Coherent and incoherent seeding of dissipative modulation instability in a nonlinear fiber ring cavity.

We investigate the coherent or incoherent seeding of dissipative modulation instability (MI) in a nonlinear fiber ring cavity. By varying wavelength and degree of coherence of the seed signal across the MI gain band, we observe a strong sensitivity of the resulting MI sidebands in terms of bandwidth and amplification. Both spectral and temporal characterizations are performed to reveal intensity coherence properties (over a single round-trip) of the generated temporal patterns. Experimental observations are well confirmed by numerical simulations. Our results provide new insights into the control of dissipative MI through a specific seeding in optical resonators with a moderate free-spectral range. In particular, a large tunability of the subsequent Kerr comb spacing is achieved by means of the early transient stage of seeded MI growth.

Spatiotemporal characterization of supercontinuum extending from the visible to the mid-infrared in a multimode graded-index optical fiber.

We experimentally demonstrate that pumping a graded-index multimode fiber with sub-ns pulses from a microchip Nd:YAG laser leads to spectrally flat supercontinuum generation with a uniform bell-shaped spatial beam profile extending from the visible to the mid-infrared at 2500 nm. We study the development of the supercontinuum along the multimode fiber by the cut-back method, which permits us to analyze the competition between the Kerr-induced geometric parametric instability and stimulated Raman scattering. We also performed a spectrally resolved temporal analysis of the supercontinuum emission.

Multiple four-wave mixing and Kerr combs in a bichromatically pumped nonlinear fiber ring cavity.

We report numerical and experimental studies of multiple four-wave mixing processes emerging from dual-frequency pumping of a passive nonlinear fiber ring cavity. We observe the formation of a periodic train of nearly background-free soliton pulses associated with Kerr frequency combs. The generation of resonant dispersive waves is also reported.

Comparison of a semiautomated commercial repetitive-sequence-based PCR method with spoligotyping, 24-locus mycobacterial interspersed repetitive-unit-variable-number tandem-repeat typing, and restriction fragment length polymorphism-based analysis of IS6110 for Mycobacterium tuberculosis typing.

Fifty-two multidrug-resistant isolates of Mycobacterium tuberculosis representative of the currently predominant lineages in France were analyzed using repetitive-sequence-based PCR (rep-PCR) DiversiLab (DL), spoligotyping, 24-locus mycobacterial interspersed repetitive-unit-variable-number tandem-repeat typing (MIRU-VNTR), and restriction fragment length polymorphism of IS6110 (IS6110-RFLP). DL, as opposed to MIRU-VNTR and IS6110-RFLP analysis, did not allow discrimination among half of the isolates, an indication of comparatively lower resolving power.