Analytical solution for photorefractive screening solitons

We study formation and interaction of one-dimensional screening solitons in a photorefractive medium with sublinear dependence of the photoconductivity on light intensity. We find an exact analytical solution to the corresponding nonlinear Schrodinger equation. We show that these solitons are stable in propagation and their interaction is generic for solitons of saturable nonlinearity. In particular, they may fuse or "give birth" to new solitons upon collision.     

Surface defect gap solitons in superlattices with self-defocusing nonlinearity

We put forward the existence and stability of defect surface gap solitons at the interface between uniform media and an superlattice with self-defocusing nonlinearity. We reveal that the defect plays the significant role in controlling the region of solitons existing. Various solitons are found to be existed in different gaps for different defects. For positive defects, fundamental solitons can exist stably in the semi-infinite gap, and dipole solitons can exist stably in the first gap but they are unstable in the second gap. For zero or negative defects, fundamental and dipole solitons can exist stably in the first gap and the second gap, respectively.     

Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications

We present an overview of nonlinear phenomena related to optical quadratic solitons—intrinsically multi-component localized states of light, which can exist in media without inversion symmetry at the molecular level. Starting with presentation of a few derivation schemes of basic equations describing three-wave parametric wave mixing in diffractive and/or dispersive quadratic media, we discuss their continuous wave solutions and modulational instability phenomena, and then move to the classification and stability analysis of the parametric solitary waves. Not limiting ourselves to the simplest spatial and temporal quadratic solitons we also overview results related to the spatio-temporal solitons (light bullets), higher order quadratic solitons, solitons due to competing nonlinearities, dark solitons, gap solitons, cavity solitons and vortices. Special attention is paid to a comprehensive discussion of the recent experimental demonstrations of the parametric solitons including their interactions and switching. We also discuss connections of quadratic solitons with other types of solitons in optics and their interdisciplinary significance.     

Cavity soliton laser based on VCSEL with saturable absorber

We study theoretically a broad-area vertical cavity surface emitting laser (VCSEL) with a saturable absorber. We show numerically the presence of cavity solitons in the system: they exist as solitary structures formed through a modulationally unstable homogeneous lasing state that coexists with a background with zero intensity. Such a peculiar scenario endows the solitons with unique properties compared to cavity solitons in most previously studied optical systems. In particular, these solitons do not as such rely on a proper phase of the addressing pulses to be either created or deleted. We show that exciting and deleting the solitons depend crucially on whether a threshold in the soliton peak has been reached.     

Gap and dark solitons in discrete photorefractive media with?intensity-resonant nonlinearity

Light propagation in one-dimensional nonlinear waveguide arrays with self-defocusing intensity-resonant nonlinearity is investigated theoretically. We study thoroughly conditions for existence and stability of both gap and discrete dark solitons. According to the linear stability analysis both fundamental types (on-site and intersite) of gap solitons may be stable. Discrete dark solitons are unstable except in the low-power regime and, depending on system parameters, evolve into either gray solitons, breathers, or background radiation. Mobility of these solitons is analyzed by the free energy concept: gap solitons are immobile but dark solitons can be easily set in motion.     

Chirped Lambert W-kink solitons of the complex cubic-quintic Ginzburg-Landau equation with intrapulse Raman scattering

In this paper, an exact explicit solution for the complex cubic-quintic Ginzburg-Landau equation is obtained, by using Lambert W function or omega function. More pertinently, we term them as Lambert W-kink-type solitons, begotten under the influence of intrapulse Raman scattering. Parameter domains are delineated in which these optical solitons exit in the ensuing model. We report the effect of model coefficients on the amplitude of Lambert W-kink solitons, which enables us to control efficiently the pulse intensity and hence their subsequent evolution. Also, moving fronts or optical shock-type solitons are obtained as a byproduct of this model. We explicate the mechanism to control the intensity of these fronts, by fine tuning the spectral filtering or gain parameter. It is exhibited that the frequency chirp associated with these optical solitons depends on the intensity of the wave and saturates to a constant value as the retarded time approaches its asymptotic value.     

The linear and nonlinear optical effects of white light

An overview of our research group’s experimental and theoretical developments is provided on the linear and nonlinear optical effects of white light since 2003. Their work includes the experimental researches on the white light one-dimensional photovoltaic dark spatial solitons and the waveguides and directional couplers induced by them, the circular and elliptic white-light dark spatial solitons and the white-light photorefractive phase masks, two-dimensional white-light photonic lattices and the applicati...     

Polarization vortex spatial optical solitons in Bessel optical lattices

We investigate the formation of polarization vortex spatial optical solitons in optical lattice induced by a non-diffracting Bessel beam. The properties of these solitons in zeroth-order and first-order Bessel lattices with focusing and defocusing Kerr nonlinearity are discussed. It is found that these solitons have some analogies with phase vortex solitons carrying single positive or negative topological charge in these lattices. Besides, these polarization vortex solitons have complicated dynamical characteristic and can be stabilized in some parameter region.     

Spatial solitons in linearly and nonlinearly amplitude-modulated optical lattices

We demonstrated that linearly and nonlinearly amplitude-modulated (chirped) harmonic lattices can support odd and even solitons in both focusing and defocusing saturable media. The modulated lattice modifies the profiles and enlarges the stability domains of solitons, comparing with the unchirped one. Twisted solitons, or “soliton trains” whose profiles exhibit multi-peak structures can also be supported by linearly and nonlinearly chirped lattices. In sharp contrast with periodic lattices, chirped lattices remarkably broaden the existence and stability domains of twisted solitons, especially for solitons with more components. While even solitons in focusing media and twisted solitons in defocusing media are unstable, odd and twisted solitons in focusing media are stable in relatively wide parameter windows. Chirped lattice can be used as a linear guidance to realize the oscillation of solitons which is impossible in unchirped lattice.     

Incoherently coupled screening photovoltaic spatial solitons in biased photovoltaic photorefractive crystals

Propagation characteristics and stability properties of two-component composite screening photovoltaic spatial solitons have been analyzed in this paper. Employing paraxial ray approximation, we have identified a very large family of new two-component composite screening photovoltaic solitons in photovoltaic-photorefractive crystals. These composite solitons can exist only when the carrier beams have the same polarization, wavelength and are mutually incoherent. We have identified a wide parameter space involving spatial width and power where these composite solitons can exist as a stationary entity. The identified regions of existence of solitons give a deeper understanding of these solitons and reveal some interesting properties. We have shown that composite solitons with different widths cannot propagate as a stationary entity. A relevant example has been provided where the crystal is LiNbO₃ or BaTiO₃. In addition, we have shown that in the new family of solitons, a degenerate pair with equal peak power possesses bistable property. Both paraxial theory and numerical simulation show that the identified family of composite solitons is stable.     

Curvilinear motion of multivortex laser-soliton complexes with strong and weak coupling

We reveal the existence of stable dissipative soliton complexes with curvilinear motion of their center of mass. This type of motion results from the field distribution asymmetry and is well pronounced for asymmetric complexes of laser solitons with strong coupling. We present results of numerical simulations of such complexes in a model of wide-aperture lasers or laser amplifiers with saturable gain and absorption. The complex consists of a pair of strongly coupled vortex solitons weakly coupled with a number of other vortex solitons. Similar complexes are expected to exist in different spatially distributed nonlinear dissipative systems, including schemes with discrete dissipative solitons.     

Solitonic fullerene structures in light atomic nuclei

The Skyrme model is a classical field theory which has topological soliton solutions. These solitons are candidates for describing nuclei, with an identification between the numbers of solitons and nucleons. We have computed numerically, using two different minimization algorithms, minimum energy configurations for up to 22 solitons. We find, remarkably, that the solutions for seven or more solitons have nucleon density isosurfaces in the form of polyhedra made of hexagons and pentagons. Precisely these structures arise, though at the much larger molecular scale, in the chemistry of carbon shells, where they are known as fullerenes.     

Higher-order surface solitons in one-dimensional Bessel optical lattices

We demonstrate the existence of higher-order solitons occurring at an interface separating two one-dimensional (1D) Bessel optical lattices with different orders or modulation depths in a defocusing medium. We show that, in contrast to homogeneous waveguides where higher-order solitons are always unstable, the Bessel lattices with an interface support branches of higher-order structures bifurcating from the corresponding linear modes. The profiles of solitons depend remarkably on the lattice parameters and the stability can be enhanced by increasing the lattice depth and selecting higher-order lattices. We also reveal that the interface model with defocusing saturable Kerr nonlinearity can support stable multi-peaked solitons. The uncovered phenomena may open a new way for soliton control and manipulation.     

Asymmetrical surface soliton trains

We elucidate the existence, stability and propagation dynamics of multi-spot soliton packets in focusing saturable media. Such solitons are supported by an interface beside which two harmonically photonic lattices with different modulation depths are imprinted. We show that the surface model can support stable higher-order structures in the form of asymmetrical surface soliton trains, which is in sharp contrast to homogeneous media or uniform harmonic lattice modulations where stable asymmetrical multi-peaked solitons do not exist. Surface trains can be viewed as higher-order soliton states bound together by several different lowest order solitons with appropriate relative phases. Their existence as stable objects enriches the concept of compact manipulation of several different solitons as a single entity and offers additional freedom to control the shape of solitons by adjusting the modulation depths beside the interface.     

Passive harmonic mode locking of soliton bunches in a fiber ring laser

We report on the experimental observation of passive harmonic mode locking of bunches of single-pulse solitons or twin-pulse solitons in an Erbium-doped fiber ring laser. Experimental investigations on the phenomenon revealed that, although the soliton interaction between the adjacent single-/twin-pulse solitons in a bunch is weaker than that of the pulse interaction in the twin-pulse solitons, a soliton bunch could also function as a unit and form the state of passively harmonic mode-locking. Harmonic mode-locking is one of the intrinsic characteristics of soliton emission in passively mode-locked fiber ring lasers. It can be formed based on the single-pulse soliton, twin-pulse soliton, or bunch of solitons.     

Exact soliton solutions of spinor Bose-Einstein condensates

We study matter-wave solitons in Bose-Einstein condensates of ultracold gaseous atoms with spin degrees of freedom and present a class of exact solutions based on the inverse scattering method. The one-soliton solutions are classified with respect to the spin states. We analyze collisional effects between solitons in the same or different spin state(s), which reveals a very interesting possibility: we can manipulate the spin dynamics by controlling the parameters of colliding solitons.     

Composite multihump vector solitons carrying topological charge

We propose composite solitons carrying topological charge: multicomponent two dimensional [ (2+1)D] vector (Manakov-like) solitons for which at least one component carries topological charge. These multimode solitons can have a single hump or exhibit a multihump structure. The "spin" carried by these multimode composite solitons suggests 3D soliton interactions in which the particlelike behavior includes spin, in addition to effective mass, linear, and angular momenta.     

Observation of in-band lattice solitons

We report the first experimental and theoretical demonstrations of in-band (or embedded) lattice solitons. Such solitons appear in trains, and their propagation constants reside inside the first Bloch band of a square lattice, different from all previously observed solitons. We show that these solitons bifurcate from Bloch modes at the interior high-symmetry X points within the first band, where normal and anomalous diffractions coexist along two orthogonal directions. At high powers, the in-band soliton can move into the first band gap and turn into a gap soliton.     

Transverse instability of vector solitons and generation of dipole arrays

We develop a theory of modulational instability of multiparameter solitary waves and analyze the transverse instability of composite (or vector) optical solitons in a saturable nonlinear medium. We demonstrate theoretically and experimentally that a soliton stripe breaks up into an array of ( 2+1)-dimensional dipole-mode vector solitons, thus confirming the robust nature of those solitons as fundamental composite structures of incoherently coupled fields.     

Rotary dynamics of solitons in radially periodic optical lattices

We investigate the dynamics of strongly localized solitons trapped in remote troughs of radially periodic lattices with Kerr-type self-focusing nonlinearity. The rotary motion of solitons is found to be more stable for larger nonlinear wavenumbers, lower rotating velocity, and shorter radius of the trapping troughs. When the lattice is shrunk or expanded upon propagation, the solitons can be trapped in the original trough and move outward or inward, with their rotating linear velocity inversely proportional to the radius of the trapping troughs.