Mighty morphing spatial solitons and bullets

Optical elliptic breathers in isotropic nonlocal nonlinear media

We investigate the propagation dynamics of elliptic Gaussian breathers without and with orbital angular momentum (OAM) in thermal nonlocal nonlinear media with both linear and nonlinear isotropy. The beamwidths and intensity of the elliptic breather without OAM, and the beamwidths and rotation angle of the elliptic breather with the critical OAM are analytically discussed in details. In experiment, the OAM-free elliptic beam is observed to oscillate and cannot form an elliptic soliton for any input power. By contrast, the elliptic beam carrying the critical OAM can keep its ellipticity changeless during the propagation and evolve into a spiralling elliptic soliton at the critical power. Specifically, in the vicinity of the critical power, the rotation angle of the spiralling elliptic beam can be controlled linearly by the input power and exceed π/2, while its beamwidths and ellipticity remain unchanged. Such a power-controllable, profile-preserving spiralling elliptic beam may provide potential applications in all-optical manipulation.

Solitons in PT-symmetric periodic systems with the logarithmically saturable nonlinearity

We report on the formation and stability of induced solitons in parity-time (PT) symmetric periodic systems with the logarithmically saturable nonlinearity. Both on-site and off-site lattice solitons exist for the self-focusing nonlinearity. The most intriguing result is that the above solitons can also be realized inside the several higher-order bands of the band structure, due to the change of nonlinear type with the soliton power. Stability analysis shows that on-site solitons are linearly stably, and off-site solitons are unstable in their existence domain.

Suppression of collapse for spiraling elliptic solitons

We reveal that orbital angular momentum can suppress catastrophic self-focusing in nonlinear Kerr media supporting stable spiraling solitons with an elliptic cross section. We discuss the necessary requirements for observation of this effect with coherent optical and matter waves.

Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons

We present an experimental study on wave propagation in highly nonlocal optically nonlinear media, for which far-away boundary conditions significantly affect the evolution of localized beams. As an example, we set the boundary conditions to be anisotropic and demonstrate the first experimental observation of coherent elliptic solitons. Furthermore, exploiting the natural ability of such nonlinearities to eliminate azimuthal instabilities, we perform the first observation of stable vortex-ring solitons. These features of highly nonlocal nonlinearities affected by far-away boundary conditions open new directions in nonlinear science by facilitating remote control over soliton propagation.

Nonlocal incoherent solitons

We investigate the propagation of partially coherent beams in spatially nonlocal nonlinear media with a logarithmic type of nonlinearity. We derive analytical formulas for the evolution of the beam parameters and conditions for the formation of nonlocal incoherent solitons.

Observation of elliptic incoherent spatial solitons

We present the first experimental observation of spatially incoherent elliptic solitons. We use partially spatially incoherent light with anisotropic correlation statistics and observe elliptic solitons supported by the photorefractive screening nonlinearity.

Observation of optical spatial solitons in a highly nonlocal medium

We report on the observation and quantitative assessment of self-trapped pulsating beams in a highly nonlocal nonlinear regime. The experiments were conducted in nematic liquid crystals and allow a meaningful comparison with the prediction of a scalar theory in the perturbative limit, while addressing the need for beyond-paraxial analytical treatments.

Asymmetric incoherent vector solitons

We introduce a wide class of partially coherent, partially polarized solitons whose second-order statistical properties include a certain type of reflectional symmetry to be referred to as the specularity. We describe generic properties of such solitons in any noninstantaneous saturable nonlinear media. We derive closed form analytical expressions for the intensity profiles as well as the degree of polarization of specular and antispecular partially coherent solitons supported by logarithmically saturable nonlinear media.

Incoherent white light solitons in logarithmically saturable noninstantaneous nonlinear media

We analytically demonstrate the existence of white light solitons in logarithmically saturable noninstantaneous nonlinear media. This incoherent soliton has elliptic Gaussian intensity profile, and elliptic Gaussian spatial correlation statistics. The existence curve of the soliton connects the strength of the nonlinearity, the spatial correlation distance as a function of frequency, and the characteristic width of the soliton. For this soliton to exist, the spatial correlation distance must be smaller for larger temporal frequency constituents of the beam.

Twisted Gaussian Schell-model solitons

We show that a certain class of spatially partially coherent solitons, namely, twisted Gaussian Schell-model solitons, exists in a logarithmically saturable nonlinear medium with a noninstantaneous temporal response. Unlike previously reported Gaussian Schell-model solitons, those discussed here carry a position-dependent twist phase, which vanishes in the fully coherent limit. We demonstrate that the presence of the twist phase provides an opportunity for controlling the degree of spatial coherence of such solitons without affecting their intensity.

Hamiltonian-versus-energy diagrams in soliton theory

Parametric curves featuring Hamiltonian versus energy are useful in the theory of solitons in conservative nonintegrable systems with local nonlinearities. These curves can be constructed in various ways. We show here that it is possible to find the Hamiltonian (H) and energy (Q) for solitons of non-Kerr-law media with local nonlinearities without specific knowledge of the functional form of the soliton itself. More importantly, we show that the stability criterion for solitons can be formulated in terms of H and Q only. This allows us to derive all the essential properties of solitons based only on the concavity of the curve H vs Q. We give examples of these curves for various nonlinearity laws and show that they confirm the general principle. We also show that solitons of an unstable branch can transform into solitons of a stable branch by emitting small amplitude waves. As a result, we show that simple dynamics like the transformation of a soliton of an unstable branch into a soliton of a stable branch can also be predicted from the H-Q diagram.

Observation of mighty morphing spatial solitons

The experimental observation of bright spatial solitons in the form of mighty morphing solitons is reported for the first time to the author's knowledge. These are Gaussian-like beams of elliptical cross section, which appear to change their shape constantly as they propagate. Saturation of the nonlinear medium is shown to progress logarithmically.

Beam splitting on weak illumination

We demonstrate, in both two and three dimensions, how a self-guided beam in a non-Kerr medium is split into two beams on weak illumination. We also provide an elegant physical explanation that predicts the universal character of the observed phenomenon. Possible applications of our findings to guiding light with light are also discussed.

Breathing spatial solitons in non-Kerr media

The concept of soliton internal mode is introduced to explain quantitatively the long-lived oscillations of self-guided beams, or breathing spatial solitons. Cubic-quintic nonlinearity is considered in detail, and it is shown that the existence of the internal mode affects strongly the beam propagation in non-Kerr media, leading to oscillatory dependence of the output width of the beam versus its input power.

Incoherent spatial solitons in saturable nonlinear media

It is shown that partially incoherent spatial solitons are possible in saturable nonlinear media. This is demonstrated by means of an exact Gaussian solution in the case when the saturable nonlinearity is of the logarithmic type. The conditions necessary to establish these soliton states as well as their associated characteristics are discussed in detail. Pertinent examples are provided to elucidate their behavior further.