Nonlinear rotation of three-dimensional dark spatial solitons in a Gaussian laser beam

Adjustable rotation of multiple vortices produced by diode-pumped Nd:YVO4 lasers using intracavity second harmonic generation

The criteria for achieving adjustable rotation of optical vortices are analyzed and used to design a diode-pumped solid-state laser that incorporates intracavity second harmonic generation within a concave-flat cavity to produce frequency-doubled Hermite-Gaussian (FDHG) modes. These FDHG modes are subsequently employed to generate various structured lights containing 2, 4, and 6 nested vortices using an external cylindrical mode converter. Through theoretical exploration, we propose that increasing the radius of curvature of the concave mirror and extending the cavity length can enhance the rotational angles of multiple vortices by expanding the adjustable range of phase shift for FDHG modes. Moreover, theoretical analyses assess vortex rotation concerning the positions of a nonlinear medium, successfully validating the experimental observations and elucidating the phase structures of the transformed beams.

Observation of self-induced optical vortex precession

We report on the observation of self-induced precession of an optical vortex as a result of the nonlinear interaction between light and liquid crystals. The phenomenon corresponds to an instability for the spin-orbit interaction of light that manifests as a spontaneous axial symmetry breaking, which leads to the orbital motion of the optical vortex around the beam propagation. A nonlinear spin Hall effect of light is experimentally identified, thereby unveiling an original demonstration of spin to extrinsic orbital light angular momentum self-conversion.

Optical spatial solitons: historical overview and recent advances

Solitons, nonlinear self-trapped wavepackets, have been extensively studied in many and diverse branches of physics such as optics, plasmas, condensed matter physics, fluid mechanics, particle physics and even astrophysics. Interestingly, over the past two decades, the field of solitons and related nonlinear phenomena has been substantially advanced and enriched by research and discoveries in nonlinear optics. While optical solitons have been vigorously investigated in both spatial and temporal domains, it is now fair to say that much soliton research has been mainly driven by the work on optical spatial solitons. This is partly due to the fact that although temporal solitons as realized in fiber optic systems are fundamentally one-dimensional entities, the high dimensionality associated with their spatial counterparts has opened up altogether new scientific possibilities in soliton research. Another reason is related to the response time of the nonlinearity. Unlike temporal optical solitons, spatial solitons have been realized by employing a variety of noninstantaneous nonlinearities, ranging from the nonlinearities in photorefractive materials and liquid crystals to the nonlinearities mediated by the thermal effect, thermophoresis and the gradient force in colloidal suspensions. Such a diversity of nonlinear effects has given rise to numerous soliton phenomena that could otherwise not be envisioned, because for decades scientists were of the mindset that solitons must strictly be the exact solutions of the cubic nonlinear Schrödinger equation as established for ideal Kerr nonlinear media. As such, the discoveries of optical spatial solitons in different systems and associated new phenomena have stimulated broad interest in soliton research. In particular, the study of incoherent solitons and discrete spatial solitons in optical periodic media not only led to advances in our understanding of fundamental processes in nonlinear optics and photonics, but also had a very important impact on a variety of other disciplines in nonlinear science. In this paper, we provide a brief overview of optical spatial solitons. This review will cover a variety of issues pertaining to self-trapped waves supported by different types of nonlinearities, as well as various families of spatial solitons such as optical lattice solitons and surface solitons. Recent developments in the area of optical spatial solitons, such as 3D light bullets, subwavelength solitons, self-trapping in soft condensed matter and spatial solitons in systems with parity-time symmetry will also be discussed briefly.

Gray solitons in parity-time symmetric potentials

We numerically study the gray solitons in parity-time (PT) symmetric potentials. Simulated results show that there are two kinds of gray solitons, the dip-shaped gray solitons and the hump-shaped solitons, and both of them can be stable. Hump-shaped solitons can always exist, but the grayness of a stable dip-shaped gray soliton should exceed a threshold value. More interesting, it is discovered that when propagating in PT symmetric potentials, the gray solitons have no transverse deviation, and this is a phenomenon different from the usual gray solitons.

Vortex revivals with trapped light

We predict that vortex dipoles nested in light beams trapped in graded-index media can undergo closed Berry trajectories, yielding periodic vortex annihilations and revivals along the light-propagation direction. The vortex revivals from vortex-free wave fronts are mediated by Freund stationary point bundles that carry the necessary Poincaré-Hopf indices. Vortex spiraling and spontaneous generation of circular-edge dislocations are also found to occur.

Propagation and control of noncanonical optical vortices

We predict new features for the evolution of noncanonical screw wave-front dislocations nested in diffracting light beams. The evolution equations for the location of single-charge dislocations are derived, and their consequences are elaborated by use of illustrative examples. It is shown that the dynamic trajectories of the vortices can be controlled by adjustment of the noncanonical strength of the input dislocations.

Integer and fractional angular momentum borne on self-trapped necklace-ring beams

We present self-trapped necklace-ring beams that carry and conserve angular momentum. Such beams can have a fractional ratio of angular momentum to energy, and they exhibit a series of phenomena typically associated with rotation of rigid bodies and centrifugal force effects.

The curious arithmetic of optical vortices

The superposition of noncoaxial light beams containing screw wave-front dislocations is shown to create light patterns with a richer vortex content than that given by the arithmetic of the topological charges of the individual beams. We report the experimental observation of this phenomenon.

Observation of quadratic optical vortex solitons

We report on the generation of stable dark-vortex solitons in large-phase-mismatched second-harmonic generation of self-defocusing type, sustained by a combined effect of transverse walk-off and finite beam size.

Observed rotational enhancement of nonlinear optical vortices

The propagation dynamics of an optical vortex pair is experimentally confirmed to experience enhanced rotation in a self-defocusing medium. We measured this effect to be 3.5 times larger than in linear media. The enhancement is attributed to nonlinear refraction within the dark vortex cores, permitting the vortices to propagate as vortex filaments.

Modulational instability of multiple-charged optical vortex solitons under saturation of the nonlinearity

We present a linear analysis and numerical simulations of the instability of optical vortex solitons (OVSs) of arbitrary topological charge. They show a rich variety of instability scenarios depending on the type of perturbation. The saturation of the nonlinearity is shown to be able to slow down the decay of multiple charged dark beams at an intermediate evolution stage and to prevent their ultimate decay into charge-1 OVSs. This concept is experimentally verified by the observation of a partial decay of a triple-charged OV beam and by comparing this dynamic with the behavior of OV beams of topological charges m=1, 2, 3, and 4.

Generation of multiple-charged optical vortex solitons in a saturable nonlinear medium

Multiply charged optical vortex solitons (OVS) (m=1,...,4) are generated in a thermal nonlinear medium with saturation. The respective soliton constants are found to be linearly proportional to the topological charges. Special attention is paid to the modulational instability, which is effectively suppressed by a moderate saturation but still remains an increasing function of the topological charge. For the particular experimental conditions, the recorded OVS profiles are found to be in good qualitative agreement with the numerical stationary solutions of the generalized nonlinear Schrödinger equation.

Self-trapping of dark incoherent light beams

"Dark beams" are nonuniform optical beams that contain either a one-dimensional (1D) dark stripe or a two-dimensional (2D) dark hole resulting from a phase singularity or an amplitude depression in their optical field. Thus far, self-trapped dark beams (dark solitons) have been observed using coherent light only. Here, self-trapped dark incoherent light beams (self-trapped dark incoherent wavepackets) were observed. Both dark stripes and dark holes nested in a broad partially spatially incoherent wavefront were self-trapped to form dark solitons in a host photorefractive medium. These self-trapped 1D and 2D dark beams induced refractive-index changes akin to planar and circular dielectric waveguides. The experiments introduce the possibility of controlling high-power coherent laser beams with low-power incoherent light sources such as light emitting diodes.

Steady-state vortex-screening solitons formed in biased photorefractive media

We report the observation of steady-state photorefractive vortex-screening solitons. As a singly charged circular vortex nested on a broad beam propagates through a biased strontium barium niobate crystal, it self-traps in both transverse dimensions despite the inherent anisotropy of the photorefractive nonlinearity. When the vortex beam is a doughnut-shaped narrow beam, it breaks up into two elongated slices (with a self-defocusing nonlinearity) or into two focused filaments (with a self-focusing nonlinearity). We demonstrate the optical guidance of a probe beam in a circular waveguide induced by the self-trapped vortex.

Vortex soliton motion and steering

Experimental demonstration of the steering of an optical vortex soliton by the superposition of a weak coherent background field is presented. A model to account for vortex motion is derived, and its validity is verified experimentally and numerically.

Drift instability of dark solitons in saturable media

It is shown that dark solitons display an inherent instability for a strong saturation of the nonlinear refractive index provided that the background intensity exceeds a certain critical value. Such an instability manifests itself as a drift of a black soliton that transform into a gray soliton and radiation.

Observation of vortex solitons created by the instability of dark soliton stripes

The first experimental observation to the authors' knowledge is reported of the generation of optical vortex solitons from instability and breakup of a dark soliton stripe propagating through a saturable self-defocusing nonlinear medium.