Bessel Lattices Research Articles

Soliton dynamics in partially PT -symmetric two-dimensional Bessel lattices

We study the dynamics of two-dimensional spatial solitons supported by partially-parity-time ( PPT )-symmetric optical Bessel lattices. We show that these solitons with an imposed tilt can follow an oscillating or even a whole rotary trajectory in the transverse plane guided by a Bessel optical lattice. Due to the complex optical potential, these rotary solitons can also suffer from amplification or attenuation. Interestingly, we found that it is possible to find quasi-stability regions of parameters where there is a balance between the imposed tilt and the PPT -symmetric potential, allowing the launched spatial dissipative solitons to complete several rotations in their propagation.

Soliton cluster solutions of nonlinear Schrödinger equations with variable coefficients in Bessel lattice

The goal of this article is to obtain soliton cluster solutions of (2 + 1)-dimensional nonlinear variable coefficient Schrödinger equations through computerized symbolic computation. By applying the self-similarity method, one soliton solution is constructed for the NLS equations with variable coefficient, which provide a model of the propagation of the soliton waves. Consequently, the solitonary cluster solution is achieved in different structures. Additionally, the propagation of the obtaining solitonary cluster solutions is analyzed and discussed. The results are useful to explain the soliton phenomena in nonlinear optics.

Two-dimensional spatial optical solitons in Rydberg cold atomic system under the action of optical lattice

Realizing stable high-dimensional light solitons is a long-standing goal in the study of nonlinear optical physics. However, in high-dimensional space, the light field will inevitably be distorted due to diffraction. In order to solve the diffraction effect in nonlinear Kerr media and achieve the spatial localization of light fields, we propose a scheme to generate stable two-dimensional (2D) solitons in a cold Rydberg atomic system with a Bessel optical lattice, where a three-level atomic structure, a weak probe laser field, and a strong control field constitute the Rydberg-dressed atomic system. When the local nonlinearity, Bessel potential, and nonlocal nonlinearity which is caused by the long-range Rydberg-Rydberg interaction (RRI) between Rydberg atoms are balanced, the probe field can be localized. Under the approximation of electric dipole and rotating wave, the stable solution of probe field is obtained by solving Maxwell-Bloch equations numerically. A cluster of 2D spatial solitons, including fundamental, two-pole, quadrupole and vortex solitons, is found in this system. Among them, the fundamental, dipole and quadrupole have, one, two, and four intensity centers, respectively. Vortex solitons, on the other hand, exhibit vertical characters in profiles and phase structures. The formation and transmission of these solitons can be controlled by system parameters, such as the propagation coefficient, the degree of nonlocal nonlinearity, and Bessel lattice strength. The stable regions of these solitons are determined by anti Vakhitov Kolokolov (anti-VK) criterion and linear stability analysis method. It is found that four kinds of solitons can be generated and stably propagate in space with proper parameters. Owing to the different structures of the poles, the fundamental state and vortex state remain stable, while the quadrupole ones are unstable. In the modulation of solitons, there is a cutoff value of propagation constant <inline-formula><tex-math id="M1">\begin{document}${b_{{\text{co}}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20230096_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20230096_M1.png"/></alternatives></inline-formula>, only below which value, the solitons can propagate stably. The light intensity of soliton shows a periodic behavior by tuning Bessel lattice strength. The period of the intensity decreases with the order of the solitons as a result of the interaction between the poles. It is also found that the solitons are more stable with weak nonlocal nonlinearity coefficient. This study provides a new idea for the generation and regulation of optical solitons in high dimensional space.

Stationary structures of spin-orbit coupled polariton condensates in Bessel lattices

<sec>Bessel optical lattice yields a non-spatially periodic column-symmetric optical lattice potential field, which has the characteristics of both infinite deep potential well and the ring-shaped potential well. A deep potential is formed in the center of the 0-order Bessel optical lattice. In the non-zero-order Beseel optical lattice, a ring-shaped shallow potential well with a central barrier can be formed. Exciton-polariton is a semi-light and semi-matter quasi-particle, which can achieve the Bose-Einstein condensate phase transition even at room temperature to form a polariton condensate. In addition, the polariton condensate is likely to realize sufficiently strong spin-orbit coupling due to the cavity-induced TE-TM splitting of the polariton energy levels. The polariton condensate can be realized at room temperature, and there can be spin-orbit coupling in it, which provides a new platform for the studying of quantum physics. </sec><sec>In this paper, the Bessel optical lattice is introduced into a polariton condensate. The stationary state structure of spinor two-component polariton condensate with spin-orbit coupling is investigated. By solving the Gross-Pitaevskii equation, we first give a stationary state structures of the polariton condensate both in the laboratory coordinate frame and in the rotating coordinate frame. Owing to the introduction of the Bessel optical lattice, the stationary state structures of polariton condensate are diverse. We dispaly the stationary state structures of the basic Gaussian solitons and multipole solitons in the central deep potential well in the laboratory coordinate frame, and the ring solitons and multipole solitons in the central shallow potential well. We also dispaly the vortex ring soliton that exists in the rotating coordinate frame, and the stationary state structure of the component separation caused by the spin-orbit interaction. We analyze not only the influences of the spin-orbit coupling on the stationary state structures in the two coordinate frames, but also the stability of the multipole solitons in the rotating coordinate frame. It is found that the multipole solitons formed in the ring-shaped shallow potential well have better stability than in the central deep potential well, and they can maintain the relative structure and spatial distribution for a long time in the rotation process. In the rotating coordinate frame, even if the two-component separation conditions are not satisfied, the introduction of spin-orbit coupling can cause the two components to separate.</sec>

The Propagation Characteristics of the Third and Fourth Order Vortex Beams in Bessel Lattice

The Propagation Characteristics of the Third and Fourth Order Vortex Beams in Bessel Lattice

Bessel beam approach for photovoltaic trapping of micro- and nanoparticles on Fe-doped lithium niobate crystal

The non-diffracting Bessel beam approach was used for the first time for the elaboration of photovoltaic tweezers. We report the trapping of dielectric microparticles of chalk (CaCO3), as well as silver nanoparticles in glycerin suspension via dielectrophoretic forces on the surface of Fe doped LiNbO3 (LN:Fe) crystal with recorded volume holographic grating by the non-diffracting Bessel beam technique. The photorefractive Y-cut LN:Fe crystal was illuminated by 20–40 mW power Bessel beam at 532 nm wavelength which generates refractive Bessel lattice with ~40 μm periodicity via induction of photovoltaic space-charge fields. The Bessel beam approach provides the induction of high contrast 2D quasi-periodic distribution of space-charge electric field in the crystal volume and proximity of the crystal surface and high quality 2D patterning of the particles. Experiments showed that CaCO3 microparticles are trapped by attractive forces on the crystal surface in the areas of refractive index maxima of the Bessel lattice, while the trapping of Ag nanoparticles dispersed in glycerin takes places at the borderlines of lattice rings due to the repulsive forces. A physical model was developed to explain the experimental results. The photovoltaic approach of trapping and manipulation of micro- and nanoparticles is promising for applications in photonics, integrated optics and biotechnology.

Stationary structures of spin-orbit coupled polariton condensates in the Bessel lattices

Stationary structures of spin-orbit coupled polariton condensates in the Bessel lattices

Spatiotemporal solitons in cold Rydberg atomic gases with Bessel optical lattices

A scheme is proposed to generate stable spatiotemporal solitons (STs) in a cold Rydberg atomic system with a Bessel Lattice (BL) potential, by utilizing electromagnetically induced transparency (EIT). We investigate the existence and stability of these three-dimensional (3D) STs supported by BL in nonlocal nonlinear media. The results show that the system can support slow STs with low light intensity. We also find that the BL strength and the degree of nonlocality of the nonlinearity, which can be tuned in the system, can be used to control these STs and their propagation behaviors.

Two-dimensional vector solitons in a cold atomic gas via electromagnetically induced transparency

We investigate the formation and propagation of vector vortex solitons (VSs) and unipolar solitons (USs) in a cold coherent atomic gas with a Bessel lattice (BL). The system considered is a gas with a tripod level configuration. Owing to the big enhancement of Kerr nonlinearity contributed by the electromagnetically induced transparency (EIT), a weak vector vortex soliton can be effectively formed with ultraslow propagation velocity. We also demonstrate that the characteristics of two-dimensional VSs and USs can be controlled and manipulated by adjusting the parameters of BL. Results obtained may be useful for designing all-optical switches at low light levels.

Refractive Bessel lattice in azobenzene liquid crystal

ABSTRACTA refractive Bessel lattice with micrometric periodicity is induced optically in a photosensitive azobenzene liquid crystal cell of 3 µm thickness by a green 532 nm, 30 mW Bessel beam and with simultaneous illumination by a red 632.8 nm, 15 mW Gaussian beam. The uninterrupted action of both beams plays a key role in the complete mechanism of the refractive lattice formation. The lattice formation is investigated in real-time by the measurement of forward diffracted ring powers from both the red Gaussian and the green Bessel beams. The diffraction efficiency is investigated depending on the green Bessel beam intensity and on the mutual relation between the green beam polarization and the rubbing direction of the cell. A maximum diffraction efficiency of 1.1% is obtained which corresponds to a refractive index change of 6 × 10−3. Simulations are performed and a physical model to explain the experimental results is discussed.

The solitons in Bessel lattice potential with nonlocal nonlinearity

The existence and stability of fundamental and multipole solitons in Bessel potential are studied, including linear case, and nonlocal nonlinearity cases. For linear case, the eigenvalues and eigenfunction for different modulated depths of Bessel potential are obtained numerically. For nonlocal nonlinear cases, the existence and stability of fundamental and multipole solitons are studied. The results show that there exists a critical propagation constant b c of solitons, below which the solitons vanish. The value of b c is associated with the eigenvalue for linear case. It is found that nonlocality can expand the stability region of solitons. Fundamental and dipole solitons are stable in the whole region and the stable range of multipole solitons increase with increasing of the nonlocal degree.

Light bullets in spatially modulated Laguerre–Gauss optical lattices

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.

Optical lattice solitons in nonlinear media under the condition of hollow cylinder boundary

By using the self-similar method to solve the nonlinear Schrödinger eguation with distributed coefficients, the self-similar solitons in Bessel lattice are studied under the hollow cylinder boundary conditions and the analytical solutions are obtained. Analytical solutions and numerical solutions are found to be identical. The result indicates that optical lattices induced by non-diffractive Bessel beams are possible to support stable self-similar soliton clusters.

Discrete solitons in azimuthally modulated Bessel lattices: An introduction to solitons in quasi-periodic structure

The investigation of discrete solitons in quasi-periodic structure, namely azimuthally modulated Bessel lattices imprinted in photorefractive crystal, is introduced. It is shown that the discrete solitons centralize more energy in the internal layers than the Bessel lattice and moreover, the effect of centralization of discrete solitons in focusing media is stronger than that in defocusing media. The discrete solitons are unstable in some propagation constant windows and they are absolutely stable when the propagation constant is large enough. The stable solitons perform long-distance and periodic oscillation of intensity and shape under the perturbation of intrinsic excitation.

Solitary Waves in Spherical Bessel Lattice

The analytical solitary waves solution to (3+1)-dimensional Gross-Pitaevskii equation with varying coefficients and an spherical Bessel lattice potential is obtained, which is in the form of self-similar solitary waves. The properties and the stability of the solitary waves family are discussed in detail.

Self-similar solitary wave family in Bessel lattice

We focus on the formation and propagation of self-similar solitary wave family in Kerr nonlinear media with external Bessel lattice. A novel analytical solitary wave solution to (3+1)-dimensional Gross-Pitaevskii equation with varying coefficients and an external potential is obtained. The components of solitary wave family are differentiated by three quantum parameters. The properties and the stability of the solitary wave family are discussed in detail.

Multipeaked fundamental and vortex solitons in azimuthally modulated Bessel lattices

We demonstrate the existence of multipeaked fundamental and vortex solitons in defocusing Kerr media with an imprinted azimuthally modulated Bessel lattice. Multipeaked solitons emanating from the fundamental linear lattice modes are stable in their entire existence domains. The number of soliton peaks is determined by the azimuthal index. Multipeaked vortex solitons with high topological charges in lattices exhibit special amplitude and phase distributions that resemble those of azimuthons. We reveal that the “stability rule” for vortex solitons in defocusing Kerr media is exactly opposite to that in focusing media. Multipeaked vortex solitons we obtained may provide a missing link between the radially symmetric vortices and nonrotating soliton clusters.

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.

Soliton dynamics in modulated Bessel photonic lattices

We address the existence and the controlled stability of two-dimensional solitons in modulated Bessel lattices (MBL) induced by a superposition of nondiffracting Bessel beams. We show that variation of the modulation parameter of the lattice and the initial transverse momentum of the soliton significantly modify the behavior of the solitons. We find that, under suitable and well-identified conditions, solitons propagating in the MBL exhibit six regimes of transverse mobility: stationary, oscillatory, rotating, unbounded or escape, transitional, and unstable. These results report propagating solitons that can develop these dynamics of transverse motion.

Internal oscillation of vector solitons and necklace solitons

Internal modes and internal oscillation of vector solitons associated with photoisomerization and necklace solitons in Bessel lattices are researched. While white noise gives rise to the unsmoothness of the vector solitons, the perturbation of internal modes results in the long-distance quasi-periodic oscillation of soliton shape. Internal modes of two-dimensional necklace solitons in Bessel lattices have both real and imaginary parts, which is different with the internal modes of one-dimensional solitons which have only real part.