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The optical Bloch oscillation (OBO) is an optical-quantum analogy effect that is significant for light field manipulations, such as light beam localization, oscillation and tunneling. As an intra-band oscillation, OBO was important for optical investigations in photonic lattices and atomic vapors over an extended period of time. However, OBO in reconfigurable platforms is still an open topic, even though tunability is highly desired in developing modern photonic techniques. Here we theoretically establish and experimentally demonstrate OBO in an electromagnetically induced photonic lattice with a ramping refractive index, established in a coherently-prepared three-level 85Rb atomic vapor under the electromagnetically induced transparency condition. This is achieved by interfering two coupling beams with Gaussian profiles and launching a probe beam that exhibits OBO within the resulting lattice. The induced reconfigurable photonic lattice possesses a transverse gradient, due to the innate edges of Gaussian beams, and sets a new stage for guiding the flow of light in periodic photonic environments. Our results should motivate better understanding of peculiar physical properties of an intriguing quantum-optical analogy in an atomic setting.

This paper numerically investigates the evolution of solitons in an optical lattice with gradual longitudinal manipulation. We find that the stationary solutions (with added noise to the amplitude) keep their width, profile, and intensity very well, although the propagation path is continuously changing during the modulated propagation. Discontinuities in the modulation functions cause the scattering of the beam that may end the stable propagation. Our results reveal a method to control the trajectory of solitons by designed variation of the optical lattice waveguides. Interesting examples presented include the snakelike and spiraling solitons that both can be adaptively induced in sinusoidally and helically shaped optical lattices. The controlled propagation paths provide an excellent opportunity for various applications, including optical switches and signal transmission, among others.

We demonstrate two new types of non-circularly-symmetric solitons, the elliptical and rectangular solitons, which can be sustained by the cubic–quintic nonlinearity in the nonlinear Schrödinger equation with a linear potential well. The characteristics of these solitons are investigated in some detail. Notably, the elliptical and circular solitons can transform into each other, and similarly the rectangular and square solitons can transform into each other. Interestingly, we find that elliptical and rectangular solitons can also transform into each other—a phenomenon not readily seen among different types of solitons. In addition, the rotation of elliptical and rectangular solitons is displayed as well. Finally, we find that stable vortex modes of elliptical and rectangular solitons can be also supported by our model. • Non-circularly-symmetric solitons, elliptical and rectangular solitons, are supported in cubic–quintic nonlinearity with the help of a linear potential. • The elliptical and circular solitons can transform into each other, and similarly the rectangular and square solitons can transform into each other. • The rotation of elliptical and rectangular solitons is also reported. • Vortex modes of the elliptical and rectangular solitons are also displayed in such model. [ABSTRACT FROM AUTHOR]

In small transition and noble metal particles, commonly used as active parts of heterogeneous industrial catalysts, only a tiny fraction of metal atoms at their surfaces are utilized in relevant chemical reactions. In an effort to use precious metal atoms much more efficiently, the idea of single-atom catalysts (SACs) emerged, where every metal atom would take place in a catalytic process. Applying density functional theory, we carried out a computational search for efficient SACs based on transition metal atoms embedded into monovacancies of graphene and hexagonal boron-nitride (h-BN), where the point defects were used to stabilize metal adatoms and prevent their aggregation into bigger clusters. The efficiency of the catalysts was examined by studying their ability to adsorb H atoms and recombine them into H2in a thermodynamically neutral manner. The critical steps in the process of the hydrogen evolution reaction (HER) were modeled over nine different metal adatoms embedded into three point defects of graphene and the h-BN, revealing several SACs with nearly flat potential energy landscape for HER, comparable to or even more favorable than the ones found at Pt surfaces.

We demonstrate a novel method for producing optically induced Lieb and super-honeycomb lattices, by employing the fractional Talbot effect of specific periodic beam structures. Our numerical and analytical results display the generation of Lieb and super-honeycomb lattices at fractional Talbot lengths effectively and with high beam quality. By adjusting the initial phase shifts of the interfering beams, the incident periodic beam structures, as well as the lattices with broken inversion symmetry, can be constructed in situ. This research suggests not only a possible practical utilization of the Talbot effect in the production of novel optically induced lattices but also in the studies of related optical topological phenomena.

The (2+1)-dimensional nonlinear asymmetric Nizhnik-Novikov-Veselov system is one of the extended versions of the Korteweg-de Vries equation, and as such of considerable significance in nonlinear wave dynamics. In this work, it is transformed into a bilinear form by using the Hirota transformation and then treated by the variable separation method. In particular, by separating variables in a specific manner, a class of solutions is obtained, which are constructed with the help of three auxiliary functions, P y , R y , and Q x t. By selecting the three functions conveniently, we obtain novel nonlinear excitations for the asymmetric Nizhnik-Novikov-Veselov system. To make our results more explicit and interesting, various types of nonlinear profiles were displayed, colloquially named as the parallelogram, walnut, dark breather, half-moon breather, and the top-compressed quadrilateral breather structures. It is found that these local wave packets can be well controlled by appropriately selecting the three auxiliary functions, and that the variable separation approach can be extended to other high-dimensional nonlinear systems. • We report on the new results involving nonlinear wave excitations in the (2+1)-D asymmetric NNV system. • Novel nonlinear structures of the (2+1)-D asymmetric NNV system are found in terms of the Hirota transformation. • We list several typical examples and analyze their profiles. [ABSTRACT FROM AUTHOR]

We performed density functional theory computations to study the structural and electronic properties as the basis of ethylene addition activity for [Ni(XC)4]n(X = Se, S)-extended lattices. We demonstrated that the mechanism of ethylene cycloaddition to a periodic [Ni(SeC)4]ntwo-dimensional (2D) network is analogous to that previously described for [Ni(SC)4]n2D sheets and similar to the metal bis(dithiolene) molecular complexes [M(S2C2R2)2] (M = Ni, Pd, Pt, Co, Cu). These nanosheet materials avoid decomposition upon olefin addition, which is one of the main limitations of the molecular metal bis(dithiolene) complexes, as we find the decomposition processes to be thermodynamically unfavorable. Our calculations also suggest that the preferred conformation of the [Ni(SeC)4]nbilayer lattice is parallel displaced, with the Se atoms positioned above the Ni atoms, which is different from the eclipsed conformation found for [Ni(SC)4]n. We also managed to optimize an adduct of [Ni(SC)4]nin the bilayer form, which exceed the ethylene coverage of molecular complexes. We calculate that the preferred three-dimensional geometry of the stacked sheets is eclipsed because of strong van der Waals interactions. Such an arrangement of the sheets indicates that these materials should be highly porous, pointing to the high capacity for olefin bindings. Indeed, a few moderately stable ethylene adducts have been located. Owing to their unique structures and chemical reactivity, these newly predicted materials can be potentially developed as electrocatalysts for olefin purification.

We discuss analytical localized soliton solutions to the generalized nonautonomous nonlinear Schrödinger equation (NLSE) in waveguides featuring transverse modulation of both the linear and nonlinear refractive index changes. We utilize the similarity transformation technique to obtain these solutions. It turns out that the generalized nonautonomous NLSE with space-dependent coefficients can be reduced to the stationary NLSE, provided certain constraints are placed on the linear and nonlinear refractive indices. Various shapes of exact vortex soliton solutions are studied theoretically and analytically. Finally, the stability analysis of the solutions is discussed numerically. Our findings address an alternative way for the realization of stable vortex solitons with higher topological charges and the radial quantum numbers.

Atomic media are important in optics research since they can be conveniently manipulated and controlled due to easy selection of atomic levels, laser fields, and the active adjustment of many system parameters. In this paper, we investigate optical Bloch oscillation, Zener tunneling, and Bloch–Zener oscillation in atomic media both theoretically and numerically. We use two coupling fields to prepare the dynamical optical lattice through interference. To induce a transverse force, we make the frequency difference between the two coupling fields increase linearly along the longitudinal coordinate. These phenomena have potential application for beam splitters and optical interconnects, and are helpful for investigating quantum analogies.

We show that media with inhomogeneous defocusing cubic nonlinearity growing toward the periphery can support a variety of stable vortex clusters nested in a common localized envelope. Nonrotating symmetric clusters are built from an even number of vortices with opposite topological charges, located at equal distances from the origin. Rotation makes the clusters strongly asymmetric, as the centrifugal force shifts some vortices to the periphery, while others approach the origin, depending on the topological charge. We obtain such asymmetric clusters as stationary states in the rotating coordinate frame, identify their existence domains, and show that the rotation may stabilize some of them.

We theoretically and numerically investigate the nonparaxial self-accelerating beams in a Λ-type three-level energy system of rubidium atomic vapor in the electromagnetically induced transparency (EIT) window. In the EIT window, the absorption of the atomic vapor is small, and robust nonparaxial self-accelerating beams can be generated. The reason is that the energy of the tail transfers to the main lobe, which then maintains its shape, owing to the self-healing effect. Media with large absorption would demand large energy to compensate, and the tail would be lifted too high to maintain the profile of an accelerating beam, so that self-accelerating beams cannot be obtained any longer. An atomic vapor with small absorption is the ideal medium to produce such self-accelerating beams and, in return, self-accelerating beams may inspire new ideas in the research associated with atomic vapors and atomic-like ensembles.

Nucleocytoplasmic transport of transcription factors is vital for normal cellular function, and its breakdown is a major contributing factor in many diseases. The glucocorticoid receptor (GR) is an evolutionarily conserved, ligand-dependent transcription factor that regulates homeostasis and response to stress and is an important target for therapeutics in inflammation and cancer. In unstimulated cells, the GR resides in the cytoplasm bound to other molecules in a large multiprotein complex. Upon stimulation with endogenous or synthetic ligands, GR translocation to the cell nucleus occurs, where the GR regulates the transcription of numerous genes by direct binding to glucocorticoid response elements or by physically associating with other transcription factors. While much is known about molecular mechanisms underlying GR function, the spatial organization of directionality of GR nucleocytoplasmic transport remains less well characterized, and it is not well understood how the bidirectional nucleocytoplasmic flow of GR is coordinated in stimulated cells. Here, we use two-foci cross-correlation in a massively parallel fluorescence correlation spectroscopy (mpFCS) system to map in live cells the directionality of GR translocation at different positions along the nuclear envelope. We show theoretically and experimentally that cross-correlation of signals from two nearby observation volume elements (OVEs) in an mpFCS setup presents a sharp peak when the OVEs are positioned along the trajectory of molecular motion and that the time position of the peak corresponds to the average time of flight of the molecule between the two OVEs. Hence, the direction and velocity of nucleocytoplasmic transport can be determined simultaneously at several locations along the nuclear envelope. We reveal that under ligand-induced GR translocation, nucleocytoplasmic import/export of GR proceeds simultaneously but at different locations in the cell nucleus. Our data show that mpFCS can characterize in detail the heterogeneity of directional nucleocytoplasmic transport in a live cell and may be invaluable for studies aiming to understand how the bidirectional flow of macromolecules through the nuclear pore complex (NPC) is coordinated to avoid intranuclear transcription factor accretion/abatement.

We demonstrate the fractional Talbot effect of nonparaxial accelerating beams, theoretically and numerically. It is based on the interference of nonparaxial accelerating solutions of the Helmholtz equation in two dimensions. The effect originates from the interfering lobes of a superposition of the solutions that accelerate along concentric semicircular trajectories with different radii. Talbot images form along certain central angles, which are referred to as Talbot angles. The fractional nonparaxial Talbot effect is obtained by choosing the coefficients of beam components properly. A single nonparaxial accelerating beam possesses duality—it can be viewed as a Talbot effect of itself with an infinite or zero Talbot angle. These results improve the understanding of the nonparaxial accelerating beams and of the Talbot effect among them.

We demonstrate the dual accelerating Airy–Talbot recurrence effect, i.e., the self-imaging of accelerating optical beams, by propagating a superposition of Airy beams with successively changing transverse displacements. The dual Airy–Talbot effect is a spontaneous recurring imaging of the input and of the input with alternating component signs. It results from the constructive interference of Airy wave functions, which is also responsible for other kinds of Airy beams, for example, Airy breathers. An input composed of finite-energy Airy beams also displays the dual Airy–Talbot effect, but it demands a large transverse displacement and diminishes fast along the propagation direction.

We analytically and numerically investigate an anharmonic propagation of two-dimensional beams in a harmonic potential. We pick noncentrosymmetric beams of common interest that carry orbital angular momentum. The examples studied include superposed Bessel–Gauss (BG), Laguerre–Gauss (LG), and circular Airy (CA) beams. For the BG beams, periodic inversion, phase transition, and rotation with periodic angular velocity are demonstrated during propagation. For the LG and CA beams, periodic inversion and variable rotation are still there but not the phase transition. On the whole, the “center of mass” and the orbital angular momentum of a beam exhibit harmonic motion, but the motion of the beam intensity distribution in detail is subject to external and internal torques and forces, causing it to be anharmonic. Our results are applicable to other superpositions of finite circularly asymmetric beams.

Using the balance principle and the F-expansion method, we find dark soliton solutions in a general nonlocal nonlinear optical model with a diffusive type of nonlinearity. These solutions are modeled by numerical simulation, in order to study how they propagate and interact with each other. Our results show that the multidimensional nonlocal solitary waves can be manipulated and controlled by changing the degree of nonlocality and the diffraction coefficient.

We numerically investigate interactions between two bright or dark incoherent localized beams in a strontium barium niobate photorefractive crystal in one dimension, using the coherent density method. For the case of bright beams, if the interacting beams are in-phase, they attract each other during propagation and form bound breathers; if out-of-phase, the beams repel each other and fly away. The bright incoherent beams do not radiate much and form long-lived, well-defined breathers or quasi-stable solitons. If the phase difference is π/2, the interacting beams may both attract or repel each other, depending on the interval between the two beams, the beam widths, and the degree of coherence. For the case of dark incoherent beams, in addition to the above, the interactions also depend on the symmetry of the incident beams. As already known, an even-symmetric incident beam tends to split into a doublet, whereas an odd-symmetric incident beam tends to split into a triplet. When launched in pairs, the dark beams display dynamics consistent with such a picture and in general obey soliton-like conservation laws, so that the collisions are mostly elastic, leading to little energy and momentum exchange. But they also radiate and breathe while propagating. In all the cases, the smaller the interval between the two interacting beams, the stronger the mutual interaction. On the other hand, the larger the degree of incoherence, the weaker the interaction.

We investigate numerically the interactions of two in-phase and out-of-phase Airy beams and nonlinear (NL) accelerating beams in Kerr and saturable NL media, in one transverse dimension. We find that bound and unbound soliton pairs, as well as single solitons, can form in such interactions. If the interval between two incident beams is large relative to the width of their first lobes, the generated soliton pairs just propagate individually and do not interact. However, if the interval is comparable to the widths of the maximum lobes, the pairs interact and display varied behavior. In the in-phase case, they attract each other and exhibit stable bound, oscillating, and unbound states, after shedding some radiation initially. In the out-of-phase case, they repel each other and, after an initial interaction, fly away as individual solitons. While the incident beams display acceleration, the solitons or soliton pairs generated from those beams do not.

We investigate the generation and stability of light bullets (LBs) in Laguerre–Gauss (LG) optical lattices, in which both linear and nonlinear changes in the refractive index are spatially modulated. We demonstrate that the linear and nonlinear contributions considerably affect the bullet shape and its range of stability; at the same time the nonlinear modulation depth, through the propagation constant, affects the width of the stability domain. We find that the energy of stable space-time solitons increases with the increase in the modulation depth. We discover that the behavior of LBs in LG optical lattices is substantially different from the behavior in the more familiar Bessel lattices.

We investigate the propagation of localized three-dimensional spatiotemporal Airy self-accelerating parabolic-cylinder light bullets in a linear medium. In particular, we consider the effects resulting from utilizing initial finite-energy Airy wave packets to accelerate these localized beams in the absence of any external potential. A general localized light bullet solution with the joint Airy pulse characteristics and parabolic-cylinder spatial characteristics is obtained in the Cartesian coordinates, using parabolic-cylinder and Airy functions. Our results show that the localized wave packets can retain their intensity features and still be accelerated over several Rayleigh lengths. [ABSTRACT FROM AUTHOR]

Using multivariate self-similarity transformation, we construct explicit spatial bright and dark solitary wave solutions of the generalized nonlinear Schrödinger equation with spatially Bessel-modulated nonlinearity and an external potential. Special kinds of explicit solutions, such as periodically breathing bright and dark solitary waves, are discussed in detail. The stability of these solutions is verified by means of direct numerical simulation.

We study numerically Anderson localization of light in a disordered photonic lattice containing vacancy defects of different length. The influence of Kerr nonlinearity and disorder level on the transverse localization of light in different triangular lattice geometries is discussed. We demonstrate both suppression and enhancement of light localization in the presence of defects of different size, depending on the disorder level and the strength of the nonlinearity. We find that, in the linear regime, localization is more pronounced in the lattice with the simplest defect type—the single vacancy. In a strongly focusing nonlinear regime, the presence of all defect kinds enhances localization, as compared to the case with no defects. In the defocusing nonlinear regime, a suppression of localization in the presence of all defect types is demonstrated, as compared to the localization in the lattice without defects. In the end, the effect of input beam width on various regimes of Anderson localization is discussed.

We investigate the existence and form of (2+1)-dimensional ground-state counterpropagating solitons in photorefractive media with saturable nonlinearity. General conditions for the existence of fundamental solitons in a local isotropic model that includes an intensity-dependent saturable nonlinearity are identified. We confirm our theoretical findings numerically and determine the ground-state profiles. We check their stability in propagation and identify the coupling constant threshold for their existence. Critical exponents of the power and beam width are determined as functions of the propagation constant at the threshold. We finally formulate a variational approach to the same problem, introduce an approximate fundamental Gaussian solution, and verify that this method leads to the same threshold and similar critical exponents as the theoretical and numerical methods.

We introduce three-dimensional (3D) spatiotemporal vector solitary waves in coupled (3+1)D nonlinear Schrödinger equations with variable diffraction and nonlinearity coefficients. The analysis is carried out in spherical coordinates, providing for novel localized solutions. Using the Hirota bilinear method, 3D approximate but analytical spatiotemporal vector solitary waves are built with the help of spherical harmonics, including multipole solutions and necklace rings. Variable diffraction and nonlinearity allow utilization of soliton management methods. The comparison with numerical solutions is provided and the behavior of relative error is displayed. It is demonstrated that the spatiotemporal soliton profiles found are stable in propagation.

In a numerical study, we observe Anderson localization of surface modes at the interface between a linear and a nonlinear dielectric medium, containing an optically induced disordered photonic lattice. We discover the threshold for the existence of such localized modes. The influence of Kerr nonlinearity and disorder levels on the transverse localization of light at such an interface is discussed. We demonstrate the suppression of localization for lower disorder levels, as compared to both completely linear and completely nonlinear medium. We also reveal Anderson localization at the linear-nonlinear interface in the presence of a phase-slip defect, and demonstrate the suppression of localization in that case as well. [ABSTRACT FROM AUTHOR]

In a numerical study, we demonstrate the dimensionality crossover in Anderson localization of light. We consider crossover from the two-dimensional (2D) to the one-dimensional (1D) lattice, optically induced in both linear and nonlinear dielectric media. The joint influence of nonlinearity and disorder on Anderson localization in such systems is discussed in some detail. We find that, in the linear regime, the localization is more pronounced in two dimensions than in one dimension. We also find that the localization in the intermediate cases of crossover is less pronounced than in both the pure 1D and 2D cases in the linear regime, whereas in the nonlinear regime this depends on the strength of the nonlinearity. There exist strongly nonlinear regimes in which 1D localization is more pronounced than the 2D localization, opposite to the case of the linear regime. We find that the dimensionality crossover is characterized by two different localization lengths, whose behavior is different along different transverse directions. [ABSTRACT FROM AUTHOR]

We report approximate analytical solutions to the (3+1)-dimensional spatiotemporal nonlinear Schrödinger equation, with the uniform self-focusing nonlinearity and a variable negative radial diffraction coefficient, in the form of three-dimensional solitons. The model may be realized in artificial optical media, such as left-handed materials and photonic crystals, with the anomalous sign of the group-velocity dispersion (GVD). The same setting may be realized through the interplay of the self-defocusing nonlinearity, normal GVD, and positive variable diffraction. The Hartree approximation is utilized to achieve a suitable separation of variables in the model. Then, an inverse procedure is introduced, with the aim to select a suitable profile of the modulated diffraction coefficient supporting desirable soliton solutions (such as dromions, single- and multilayer rings, and multisoliton clusters). The validity of the analytical approximation and stability of the solutions is tested by means of direct simulations. [ABSTRACT FROM AUTHOR]

We report solutions for expanding dipole-type optical solitary waves in two-dimensional Kerr media with the self-focusing nonlinearity, using exact analytical (Hirota) and numerical methods. Such localized beams carry intrinsic vorticity and exhibit symmetric shapes for both scalar and vector solitary modes. When vector beams are close to the scalar limit, simulations demonstrate their stability over propagation distances exceeding 50 diffraction lengths. In fact, the continuous expansion helps the vortical beams avoid the instability against the splitting, collapse, or decay, making them "convectively stable" patterns. [ABSTRACT FROM AUTHOR]

Despite ample studies devoted to single-atom catalysts (SACs) based on two-dimensional materials, their structural robustness under atmospheric conditions has not been addressed so far. Using density functional theory, we examined the structural stability of metal adatoms embedded into mono-atomic vacancies of graphene and hexagonal boron nitride (h-BN) in the presence of oxygen molecules. We considered 30 different elements from the periodic table, including early- and late transition as well as noble metals. We found that the highest stability occurs in SACs with a missing B atom in h-BN, utilized as the trapping site for metal adatoms. The structural stability is preserved for most of the transition metals embedded into mono-atomic vacancies of graphene. The least stable are SACs formed when metal binding occurs at the missing N atom in h-BN. We found that a general picture of the structural stability of SACs in the oxygen environment can be provided from the comparison of binding energies of O and metal atoms at three defected surfaces. A refined understanding of the structural stability of SACs requires coadsorption of metal and O atoms and a closer inspection of electronic properties of metal atoms and mono-atomic point defects at graphene and h-BN, which is also presented here.

• Fractional Schrödinger equation is an important extension of Schrödinger equation • Solitons in spin-orbit-coupled fractional Schrödinger equations are investigated • Such solitons can be supported with or without Zeeman splitting • The existence, stability and propagation of the obtained solitons are studied We demonstrate the existence of various types of solitons in the spin-orbit-coupled systems with the fractional dimension based on Lévy random flights, including the systems with or without Zeeman splitting. Specifically, the systems without Zeeman splitting can support families of symmetric solitons, whereas the systems with Zeeman splitting can support families of stable asymmetric solitons. These coupled solitons may come in the form of fundamental single solitons or dipole solitons. The Lévy index, the strength of self- and cross-phase modulation, and the propagation constant strongly affect the waveforms and stability domains of coupled solitons. The stability and instability domains of such single and dipole solitons are calculated by the method of linear stability analysis and are confirmed by the numerical simulation of perturbed propagation. The general conclusion is that for the Lévy index close to 2, corresponding to the normal nonlinear optics, the solitons tend to be stable, while in the opposite case of Lévy index close to 1, corresponding to Cauchy random flights, the solitons tend to become unstable. [ABSTRACT FROM AUTHOR]

We demonstrate that the two-component model of Bose–Einstein condensates (BECs) trapped in an optical lattice with the spin–orbit Rashba coupling and cubic repulsive interactions gives rise to gap solitary complexes of three types. The first type is the fundamental–fundamental soliton (FFS), with a fundamental soliton in both components; the second is the fundamental–dipole soliton (FDS), with a fundamental soliton in one component and a dipole soliton in the other; and the third is the dual-hump–dual-hump soliton (DHDHS), with a dual-hump soliton in both components. We study two types of fundamental solitons, namely, the single-hump and the three-hump ones. We establish that the first and second components of FFS and DHDHS in our model are mirror-symmetric about the y -axis. The first component of FDS displays the left–right symmetry, while the second component displays the rotational symmetry about the origin. We also discover that the stability domains of FFS and FDS in both the first and second band gaps are large, lending credence to their stability. This work advances the understanding of the rather complicated behavior of BECs in optical lattices and opens avenues for experimental verification of these gap soliton structures. • Gap solitons in spin-orbit-coupled Bose-Einstein condensates with optical lattices • Three types of coupled solitons are studied • Two types of fundamental solitons are surveyed • The two components of some solitons are mirror-symmetric about the y-axis. [ABSTRACT FROM AUTHOR]

Slowly varying envelope wave equations for cross-polarization two-wave mixing in cubic photorefractive crystals are solved exactly by a novel analytical method. The method allows both the transmission (codirectional) and the reflection (contradirectional) geometry of the process to be treated equally and yields simple explicit expressions.

A unified but simple method for solution of four-wave mixing equations in photorefractive crystals in both transmission and reflection geometries is presented. The method is applied to the problems of double phase conjugation and two-wave mixing with crossed polarizations in cubic crystals.

We consider the theory of photorefractive ring oscillators, using our unified solution method. Both unidirectional and bidirectional ring resonators are analyzed, based on the two-wave mixing process with crossed polarization and the four-wave mixing process with parallel polarization in photorefractive crystals. We highlight symmetries between the transmission and the reflection geometries of these processes and use them to write analytical expressions for oscillation conditions in all the cases. Symmetry breaking is noted in the four-wave mixing between the transmission and the reflection grating cases. An optical transistor based on photorefractive rings is proposed.

Multigrating optical phase conjugation in photorefractive media in the case of pump depletion and for arbitrary relationships among different coupling strengths is studied numerically. The role of linear absorption as well as the role of all the coupling mechanisms and their competition in the wave mixing process is examined. It is found that multigrating operation with accidental values of coupling constants leads to a decrease in the efficiency of the process. It is also shown that the presence of absorption, which is in principle detrimental, sometimes exerts a beneficial influence on multigrating phase conjugation.

We show that the standard model of four-wave mixing in a photorefractive crystal predicts the appearance of deterministic chaos. In this model there is a single (transmission) grating and no external or internal (intracavity) feedback. The intensity of the phase-conjugate wave is found to exhibit a period-doubling route to chaos on variation of the intensity of the probe beam and the linear absorption coefficient. The crucial elements in obtaining chaotic behavior are operation above the threshold for self-oscillation and the presence of an external electric field, which causes a shift in the optical frequency of the phase-conjugate wave.

In a numerical investigation, we demonstrate the existence and curious evolution of vortices in a ladder-type three-level nonlinear atomic vapor with linear, cubic, and quintic susceptibilities considered simultaneously with the dressing effect. We find that the number of beads and topological charge of the incident beam, as well as its size, greatly affect the formation and evolution of vortices. To determine the number of induced vortices and the corresponding rotation direction, we give common rules associated with the initial conditions coming from various incident beams.

Anderson localization (AL) of light is investigated numerically in a disordered parity-time (PT)-symmetric potential, in the form of an optical lattice. The lattice is recorded in a nonlinear medium with Kerr nonlinearity. We demonstrate enhancement of light localization in a PT-symmetric lattice, as compared to the localization in the corresponding real lattice. The effect of strength of the gain-loss component in the PT lattice on various regimes of AL is also discussed. It is found that the localization exists and is further enhanced above the threshold strength of the imaginary part of the potential. The influence of nonlinearity and disorder level on the transverse localization of light in such a complex-valued potential is addressed.

We study numerically the interaction of two counterpropagating (CP) optical beams near the boundary of a truncated one-dimensional photonic lattice. We demonstrate that the mutual coupling of beams suppresses the effective repulsion from the lattice edge, resulting in the formation of CP surface solitons. Such localized beams may propagate in the same, as well as in neighboring, waveguides. We also reveal that the lattice disorder reduces substantially the threshold power for the formation of CP surface states.

We obtain exact extended traveling-wave and spatiotemporal soliton solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equations for both the normal and the anomalous dispersion.

An exact solution to photorefractive four-wave mixing equations with complex couplings in reflection geometry is obtained. It is shown that the efficiency of the process of phase conjugation can be enhanced by introduction of a frequency shift between the pumps and the signal, similar to the case of transmission geometry. However, to obtain an improved agreement with experiment, the inclusion of transverse effects is found to be necessary.

Dirac points are special points in the energy band structure of various materials, around which the dispersion is linear. If the corresponding Fermi surface is projected as a pair of crossing lines—or touching cones in two dimensions, the Dirac point is known as the type-II; such points violate the Lorentz invariance. Until now, thanks to its unique characteristics, the Klein tunneling is successfully mimicked and the topological edge solitons are obtained in the type-II Dirac photonic lattices that naturally possess type-II Dirac points. However, the interplay between these points and corner states is still not investigated. Here, we report both linear and nonlinear corner states in the type-II Dirac photonic lattice with elaborate boundaries. The states, classified as in-phase and out-of-phase, hide in the extended bands that are similar to the bound states in the continuum (BIC). We find that the nonlinear BIC-like corner states are remarkably stable. In addition, by removing certain sites, we establish the fractal Sierpiński gasket structure in the type-II Dirac photonic lattice, in which the BIC-like corner states are also demonstrated. The differences between results in the fractal and nonfractal lattices are rather small. Last but not least, the corner breather states are proposed. Our results provide a novel view on the corner states and may inspire fresh ideas on how to manipulate/control the localized states in different photonic lattices. • Both linear and nonlinear corner states in the type-II Dirac photonic lattice are demonstrated. • The states hide in the extended bands that are similar to the bound states in the continuum (BIC). • The differences between the results in the fractal and nonfractal lattices are investigated. [ABSTRACT FROM AUTHOR]

In this paper we consider two-dimensional (2D) rogue waves that can be obtained from the approximate solution of the (2 + 1)-dimensional nonlinear Schrödinger (NLS) equation with Kerr nonlinearity. The approximate method proposed in this paper not only reduces complex operations needed for the solution of high-dimensional nonlinear partial differential equations, but also furnishes an effective mechanism for constructing stable high-dimensional rogue wave clusters, and also provides for more abundant local rogue wave excitations. Such an investigation is important in view of the known tendency for instability of localized solutions to the 2D and 3D NLS equations with focusing Kerr nonlinearity. We adopt the (2 + 1)-dimensional NLS equation in cylindrical coordinates as the basic model, and reduce the complexity of its solution by looking for the radially-symmetric ring-like solutions with the specific feature that the radius of the ring L is much greater than the ring thickness w. In this manner, we obtain an approximate analytical solution with the separated radial and angular functions which depend on the two integer parameters, the azimuthal mode number m and the rogue wave solution's order number n. With the two parameters L and w also included in the approximate solution, we show the profiles of the first-order and the second-order rogue waves, and discuss their characteristics. The method for finding approximate rogue wave solutions of the (2 + 1)-dimensional NLS equation proposed in this paper can be used as an effective way to obtain higher-order rogue wave excitations, and can be extended to other (2 + 1)-dimensional nonlinear systems. • Rogue wave cluster solutions of the (2 + 1)-D NLS equation are discussed. • Distributions of rogue waves with different ring radii are presented. • The dynamic behavior of and between first- and second-order rogue waves is analyzed. [ABSTRACT FROM AUTHOR]

We investigate the squeezing of two-component quantum optical solitons slowly moving in a tripod-type atomic system with double electromagnetically induced transparency (EIT). The evolution of the double probe-field envelopes is governed by a vector quantum nonlinear Schrödinger equation, derived from the coupled Heisenberg-Langevin and Maxwell equations. Quantum fluctuations of vector soliton pairs and atomic spin are analysed by means of a direct perturbation approach. Importantly, we find that the quantum squeezing of vector soliton pairs is generated by the giant Kerr nonlinearity, which is provided by EIT, and the outcome of the squeezing can be optimized by the selection of propagation distance and angle. The atomic spin squeezing is found for short propagation distances. The predicted results offer insights into soliton physics and may be useful for entanglement detection. • We report the study of quantum properties of stable vector slow-light solitons in a coherent atomic system. • A lifetime-broadened cold atomic gas system with a tripod type four-level configuration is constructed in this study. • A vector quantum nonlinear Schrödinger equation is derived from coupled Heisenberg-Langevin and Maxwell equations. • The quantum squeezing of the vector soliton pairs and spin squeezing are observed owing to the giant Kerr nonlinearity. • The quantum squeezing effect and can be optimized by the selection of propagation distance and angle. [ABSTRACT FROM AUTHOR]

We investigate numerically and theoretically solitons in highly nonlocal three-dimensional nematic liquid crystals. We calculate the fundamental soliton profiles using the modified Petviashvili method. We apply the variational method to the widely accepted scalar model of beam propagation in uniaxial nematic liquid crystals and compare the results with numerical simulations. To check the stability of such solutions, we propagate them in the presence of noise. We discover that the presence of any noise induces the fundamental solitons--the so-called nematicons--to breathe. Our results explain the difficulties in experimental observation of steady nematicons. [ABSTRACT FROM AUTHOR]

We study numerically the effect of boundaries on Anderson localization of light in truncated two-dimensional photonic lattices in a nonlinear medium. We demonstrate suppression of Anderson localization at the edges and corners, so that stronger disorder is needed near the boundaries to obtain the same localization as in the bulk. We find that the level of suppression depends on the location in the lattice (edge vs corner), as well as on the strength of disorder. We also discuss the effect of nonlinearity on various regimes of Anderson localization. [ABSTRACT FROM AUTHOR]