Spatiotemporal pulse-train solitons

An Introduction to Nonlinear Integrated Photonics Devices: Nonlinear Effects and Materials

The combination of integrated optics technologies with nonlinear photonics, which has led to the growth of nonlinear integrated photonics, has also opened the way to groundbreaking new devices and applications. Here we introduce the main physical processes involved in nonlinear photonics applications, and we discuss the fundaments of this research area, starting from traditional second-order and third-order phenomena and going to ultrafast phenomena. The applications, on the other hand, have been made possible by the availability of suitable materials, with high nonlinear coefficients, and/or by the design of guided-wave structures, which can enhance the material's nonlinear properties. A summary of the most common nonlinear materials is presented, together with a discussion of the innovative ones. The discussion of fabrication processes and integration platforms is the subject of a companion article, also submitted for publication in this journal. There, several examples of nonlinear photonic integrated devices to be employed in optical communications, all-optical signal processing and computing, or quantum optics are shown, too. We aimed at offering a broad overview, even if, certainly, not exhaustive. We hope that the overall work could provide guidance for those who are newcomers to this field and some hints to the interested researchers for a more detailed investigation of the present and future development of this hot and rapidly growing field.

Vortex revivals and Fermi-Pasta-Ulam-Tsingou recurrence

We study the self-trapped vortex-ring eigenstates of the two-dimensional Schrödinger equation with focusing Poisson and cubic nonlinearities. For each value of the topological charge l, there is a family of solutions depending on a parameter that can be understood as the relative importance of the cubic term. We analyze the perturbative stability of the solutions and simulate the fate of the unstable ones. For l=1 and l=2, there is an interval of the family of eigenstates for which the initial profile breaks apart but subsequently reconstructs itself, a process that can be interpreted as a nontrivial nonlinear oscillation between the vortex and an azimuthon. This revival provides a compelling realization of a recurrence of the Fermi-Pasta-Ulam-Tsingou type. Outside this interval, the vortices can be stable (for small cubic terms) or unstable and nonrecurrent (for large cubic terms). We argue that there is a crossover between these regimes that resembles a strong stochasticity threshold. For l≥3, all solutions are unstable and nonrecurrent. Finally, we comment on the possible experimental implementation of this phenomenon in the context of nonlinear laser beam propagation in thermo-optical media.

Self-trapped leaky waves in lattices: discrete and Bragg soleakons

We propose lattice soleakons: self-trapped waves that self-consistently populate slowly-attenuating leaky modes of their self-induced defects in periodic potentials. Two types, discrete and Bragg, lattice soleakons are predicted. Discrete soleakons that are supported by combination of self-focusing and self-defocusing nonlinearities propagate robustly for long propagation distances. They eventually abruptly disintegrate because they emit power to infinity at an increasing pace. In contrast, Bragg soleakons self-trap by only self-focusing nonlinearity. Also, they do not disintegrate because they emit power at a decreasing rate.

Self-phase modulation spectral broadening in two-dimensional spatial solitons: toward three-dimensional spatiotemporal pulse-train solitons

We demonstrate self-phase modulation (SPM) spectral broadening in two-dimensional solitons in homogeneous media using two different schemes. In the active mode, a train of pulses are collectively trapped and form a spatial soliton through a photorefractive, slowly responding, and electronically controlled self-focusing nonlinearity, and each pulse experiences spectral broadening by the fast SPM nonlinearity. In the passive mode, the pulse-train beam is guided in a waveguide that is optically induced by a continuous-wave thermal spatial soliton. The soliton formation increased the normalized spectral broadening factor from 0.5% up to 197%. This experiment presents significant progress toward the experimental demonstration of three-dimensional spatiotemporal pulse-train solitons.

Enhancement of third-harmonic generation in nonlocal spatial solitons

We report on the observation of Type I third-harmonic generation induced by a train of femtosecond laser pulses in nematic liquid crystals. We find that as the average power of the train is increased, the frequency conversion process is enhanced as a consequence of the tight confinement of the pulses into a nonlocal spatial soliton.

Space-time bullet trains via modulation instability and nonlocal solitons

We introduce the generation of dense trains of light-bullets in nonlocal nonlinear dielectrics. We exploit stable spatio-temporal self-trapped optical packets stemming from the interplay between local electronic and nonlocal reorientational nonlinearities, considering a seeded temporal modulation instability by specifically referring to nematic liquid crystals.