Antonio Picozzi

Condensation of Classical Nonlinear Waves

We study the formation of a large-scale coherent structure (a condensate) in classical wave equations by considering the defocusing nonlinear Schrödinger equation as a representative model. We formulate a thermodynamic description of the classical condensation process by using a wave turbulence theory with ultraviolet cutoff. In three dimensions the equilibrium state undergoes a phase transition for sufficiently low energy density, while no transition occurs in two dimensions, in complete analogy with standard Bose-Einstein condensation in quantum systems. On the basis of a modified wave turbulence theory, we show that the nonlinear interaction makes the transition to condensation subcritical. The theory is in quantitative agreement with the numerical integration of the nonlinear Schrödinger equation.

Self-pulsing and dynamic bistability in cw-pumped Brillouin fiber ring lasers

The nonlinear dynamics of cw-pumped Brillouin long-fiber ring lasers that contain a large number of longitudinal modes N beneath the Brillouin gain curve is controlled by a single parameter, namely, the Stokes feedback R. Below Rcrit, a stable train of dissipative solitonic pulses is spontaneously structured at the round-trip frequency fr without any additional intracavity mode locking. Experimental observations in cw-pumped fiber ring cavities, supported by numerical simulation in a coherent space–time three-wave model that includes the optical Kerr effect, prove the universality of the self-pulsing mechanism. Stability analysis shows that below Rcrit the steady Brillouin mirror regime is destabilized through a Hopf bifurcation. For R<Rcrit<R0 the bifurcation is supercritical and exhibits an asymptotically monostable oscillatory regime at twice fr for high enough N or at fr for lower N, in a finite transition region. For R0<R<Rcrit, the bifurcation is subcritical and exhibits dynamic bistability between the steady and the pulsed regimes in a finite hysteresis region whose width is proportional to the Kerr parameter. For R small enough, the cavity longitudinal modes merge into a dissipative solitonic Brillouin pulse: the dynamic three-wave model yields self-structured asymptotically stable trains of pulses for any initial conditions, in fair quantitative agreement (for pulse width, intensity, shape, and period) with the experiments in the entire self-pulsing domain. Amplification of spontaneous emission breaks down the stable-pulse regime in long devices (i.e., high N), so the fiber noise amplitude is higher than the coherent amplitude that separates two consecutive pulses.

A universal optical all-fiber omnipolarizer

Wherever the polarization properties of a light beam are of concern, polarizers and polarizing beamsplitters (PBS) are indispensable devices in linear-, nonlinear- and quantum-optical schemes. By the very nature of their operation principle, transformation of incoming unpolarized or partially polarized beams through these devices introduces large intensity variations in the fully polarized outcoming beam(s). Such intensity fluctuations are often detrimental, particularly when light is post-processed by nonlinear crystals or other polarization-sensitive optic elements. Here we demonstrate the unexpected capability of light to self-organize its own state-of-polarization, upon propagation in optical fibers, into universal and environmentally robust states, namely right and left circular polarizations. We experimentally validate a novel polarizing device - the Omnipolarizer, which is understood as a nonlinear dual-mode polarizing optical element capable of operating in two modes - as a digital PBS and as an ideal polarizer. Switching between the two modes of operation requires changing beams intensity.

Incoherent modulation instability in instantaneous nonlinear Kerr media

We demonstrate theoretically and experimentally in an optical fiber system that partially temporally incoherent light exhibits modulational instability during its propagation in an instantaneous response nonlinear medium. We show that the modulation frequency and gain are substantially increased with respect to the corresponding values of coherent modulational instability.

Experimental signature of optical wave thermalization through supercontinuum generation in photonic crystal fiber

We report an experimental, numerical and theoretical study of the incoherent regime of supercontinuum generation in a two zero-dispersion wavelengths fiber. By using a simple experimental setup, we show that the phenomenon of spectral broadening inherent to supercontinuum generation can be described as a thermalization process, which is characterized by an irreversible evolution of the optical field towards a thermal equilibrium state. In particular, the thermodynamic equilibrium spectrum predicted by the kinetic wave theory is characterized by a double peak structure, which has been found in quantitative agreement with the numerical simulations without adjustable parameters. We also confirm that stimulated Raman scattering leads to the generation of an incoherent structure in the normal dispersion regime which is reminiscent of a spectral incoherent soliton.

Complete nonlinear polarization control in an optical fiber system

We consider the counterpropagating interaction of a signal and a pump beam in an isotropic optical fiber. On the basis of recently developed mathematical techniques, we show that an arbitrary state of polarization of the signal beam can be converted into any other desired state of polarization. On the other hand, an unpolarized signal beam may be repolarized into two specific states of polarization, without loss of energy. Both processes of repolarization and polarization conversion may be controlled by adjusting the polarization state of the backward pump.

Toward a thermodynamic description of supercontinuum generation.

Based on the kinetic wave theory, we describe continuous-wave supercontinuum generation as a thermalization process, i.e., an irreversible evolution of the optical field towards a state of maximum nonequilibrium entropy.

Spontaneous polarization induced by natural thermalization of incoherent light

We analyze theoretically the polarization properties of a partially coherent optical field that propagates in a nonlinear Kerr medium. We consider the standard model of two resonantly coupled nonlinear Schrödinger equations, which account for a wave-vector mismatch between the orthogonal polarization components. We show that such a phase-mismatch is responsible for the existence of a spontaneous repolarization process of the partially incoherent optical field during its nonlinear propagation. The repolarization process is characterized by an irreversible evolution of the unpolarized beam towards a highly polarized state, without any loss of energy. This unexpected result contrasts with the commonly accepted idea that an optical field undergoes a depolarization process under nonlinear evolution. The repolarization effect can be described in details by simple thermodynamic arguments based on the kinetic wave theory: It is shown to result from the natural tendency of the optical field to approach its thermal equilibrium state. The theory then reveals that it is thermodynamically advantageous for the optical field to evolve towards a highly polarized state, because this permits the optical field to reach the ???most disordered state???, i.e., the state of maximum (nonequilibrium) entropy. The theory is in quantitative agreement with the numerical simulations, without adjustable parameters. The physics underlying the reversible property of the repolarization process is briefly discussed in analogy with the celebrated Joule???s experiment of free expansion of a gas. Besides its fundamental interest, the repolarization effect may be exploited to achieve complete polarization of unpolarized incoherent light without loss of energy.

Hamiltonian tools for the analysis of optical polarization control

The study of the polarization dynamics of two counterpropagating beams in optical fibers has recently been the subject of a growing renewed interest, from both the theoretical and experimental points of view. This system exhibits a phenomenon of polarization attraction, which can be used to achieve a complete polarization of an initially unpolarized signal beam, almost without any loss of energy. Along the same way, an arbitrary polarization state of the signal beam can be controlled and converted into any other desired state of polarization, by adjusting the polarization state of the counterpropagating pump beam. These properties have been demonstrated in various different types of optical fibers, i.e., isotropic fibers, spun fibers, and telecommunication optical fibers. This article is aimed at providing a rather complete understanding of this phenomenon of polarization attraction on the basis of new mathematical techniques recently developed for the study of Hamiltonian singularities. In particular, we show the essential role that play the peculiar topological properties of singular tori in the process of polarization attraction. We provide here a pedagogical introduction to this geometric approach of Hamiltonian singularities and give a unified description of the polarization attraction phenomenon in various types of optical fiber systems.

Polarization control in spun and telecommunication optical fibers

We consider the counterpropagating interaction of a signal and a pump beam in a spun fiber and in a randomly birefringent fiber, the latter being relevant to optical telecommunication systems. On the basis of a geometrical analysis of the Hamiltonian singularities of the system, we provide a complete understanding of the phenomenon of polarization attraction in these two systems, which allows to achieve a control of the polarization state of the signal beam by adjusting the polarization of the pump. In spun fibers, all polarization states of the signal beam are attracted toward a specific line of polarization states on the Poincaré sphere, whose characteristics are determined by the polarization state of the injected backward pump. In randomly birefringent telecommunication fibers, we show that an unpolarized signal beam can be repolarized into any particular polarization state, without loss of energy.