Nonlinear Medium Research Articles

Soliton-like solutions supported by refined hydrodynamic-type model of an elastic medium with soft inclusions

A nonlinear elastic medium containing sharp inhomogeneities is considered. The properties of a modified model of such a medium are investigated. The modification consists in including in the asymptotic equation of state those terms that were discarded in the previously considered models. The main purpose of the ongoing research is to analyze the existence, stability, and dynamic properties of soliton-like solutions within the modified model, as well as to compare these solutions with analogous solutions obtained in the previously considered models.

Rotationally symmetric transverse magnetic vector wave propagation for nonlinear optics

In this paper the theory and simulation results are presented for 3D cylindrical rotationally symmetric spatial soliton propagation in a nonlinear medium using a modified finite-difference time-domain general vector auxiliary differential equation method for transverse magnetic polarization. The theory of 3D rotationally symmetric spatial solitons is discussed, and compared with two (1 + 1)D, termed “2D” for this paper, hyperbolic secant spatial solitons, with a phase difference of π (antiphase). The simulated behavior of the 3D rotationally symmetric soliton was compared with the interaction of the two antiphase 2D solitons for different source hyperbolic secant separation distances. Lastly, we offer some possible explanations for the simulated soliton behavior.

Circular dichroism in nonlinear topological Weyl semimetals

In recent years, the field of topological photonics has emerged as a promising area of research due to its potential for the development of new photonic devices with unique properties. Topological Weyl semimetals (TWSs), which are characterized by the presence of Weyl points in their electronic band structure, are one such example of a material with interesting topological properties. In this study, Kerr and Faraday rotations were used to determine the nonlinear characteristics of TWSs. We focused on surfaces where no Fermi arcs are involved, so that Maxwell’s equations would contain some peculiar topological terms. In Weyl semimetals with a specific topology, the distance between Weyl nodes aligned along the z-direction functions as a magnet. This results in a significant polar Kerr/Faraday rotation effect that is proportional to the separation distance, when light is directed onto the surface of the TWS that lacks Fermi arc states. Conversely, when the light is directed onto a surface with Fermi arc states, the Voigt effect is quadratically proportional to the separation distance. We considered electromagnetic wave propagation in a nonlinear Kerr-type medium. We have derived and solved the linear and nonlinear Helmholtz equations for TWSs using the tanh method. Our findings reveal that wave solutions could have some potentially significant implications for the design and optimization of photonic devices based on TWSs.

Influence of the focusing parameter on the SHG efficiency at a wavelength of 968 nm in a ZnSe polycrystal

A theoretical model for determine the optimal focusing parameter for second harmonic generation (SHG) process in a polycrystalline nonlinear medium has been constructed. Theoretical calculations were confirmed by an experiment to obtain SHG at a wavelength of 968[Formula: see text]nm in a zinc selenide polycrystal using a thulium laser.

Modulation instability in nonlinear media with sine-oscillatory nonlocal response function and pure quartic diffraction.

Modulation instability of one-dimensional plane wave is demonstrated in nonlinear Kerr media with sine-oscillatory nonlocal response function and pure quartic diffraction. The growth rate of modulation instability, which depends on the degree of nonlocality, coefficient of quartic diffraction, type of the nonlinearity and the power of plane wave, is analytically obtained with linear-stability analysis. Different from other nonlocal response functions, the maximum of the growth rate in media with sine-oscillatory nonlocal response function occurs always at a particular wave number. Theoretical results of modulation instability are confirmed numerically with split-step Fourier transform. Modulation instability can be controlled flexibly by adjusting the degree of nonlocality and quartic diffraction.

Multi-vortex beams in nonlinear media with harmonic potential wells

As is well known, the vortex beams have significant potential applications in both quantum and classical communication systems. In this paper, we study the existence and robustness to propagation of families of multi-vortex waveforms, namely multi-vortex optical beams in nonlinear self-focusing cubic (Kerr) media with harmonic potential wells. The intensity patterns, phase structures, transverse energy flow, and gradient forces (upon micro-particles) of those multi-vortex beams are presented and we found that they are all different from those of the ordinary vortex beams. The evolution during propagation of the intensities and widths of the multi-vortex beams is investigated in detail. The obtained results show that the one-vortex beams have asymmetric patterns and spiral propagation trajectories, depending on the off-axis parameter of the vortices. The two-vortex beams and the higher than two-vortex waveforms have symmetric patterns, which rotate during propagation, and the rotation direction can be controlled by the sign of the topological charge.

Analytical solution to second-harmonic generation of ultrashort laser pulse

We present an analytical method to evaluate the second-harmonic generation (SHG) process of ultrashort laser pulses in a nonlinear medium within the small-signal regime. Building upon the broadband nonlinear coupled wave theory, we derive an analytical solution that allows one to investigate the fundamental physics and detailed dynamics of the nonlinear interaction between ultrashort laser pulses. We find that SHG for ultrashort laser pulses in a nonlinear crystal arises from a series of self-SHG and self sum-frequency generation processes involving different frequency components. We have applied the analytical method to investigate specific pulse profiles with Gaussian and sech functions and found good agreement between analytical theory and numerical simulations, validating the accuracy of the analytical approach. The analytical method enables one to explore the evolution of the second-harmonic wave under various pulse profiles, pulse widths, and crystal thicknesses, and offers a more efficient and insightful approach to study the nonlinear optical dynamics of ultrashort laser pulses.

Multipole solitons and vortex solitons in nonlocal nonlinear media

The nonlinear Schrödinger equation (NLSE) under nonlocal nonlinear media (NNM) is described and the approximate analytical solutions of the vector multipole solitons and vortex optical soliton clusters are obtained via the variational method. The results show that the structure of the optical solitons is determined by modulation depth and topological charge. In the propagation process, the spatial soliton has an observable rotation property. Under certain conditions, the rotating space modulated vortex optical solitons degenerate into circular symmetric vortex optical solitons. The results can be extended to other physical systems.

Entangling entanglement: coupling frequency and polarization of biphotons on demand

Quantum information is often carried in the frequency and polarization degrees of freedom (DoFs) in single photons and entangled photons. We demonstrate an approach to couple and decouple the frequency and polarization DoFs of broadband biphotons. Our approach is based on a nonlinear interferometer consisting of a linear dispersive medium and a polarization controller in between the two biphoton sources (nonlinear media). When the two DoFs are decoupled, maximally polarization-entangled biphotons are observed in the polarization DoF, while interference fringes are observed in the spectrum of the biphotons. When the two DoFs are coupled, by adjusting the polarization controller, interference fringes disappear from the spectrum and instead appear in the degree of polarization entanglement, varying between 0 and 1, depending on the signal and idler frequencies. Our approach offers a convenient means of tuning the polarization entanglement and can be employed for arbitrary biphoton polarization state generation.

Stable Patterns in the Lugiato–Lefever Equation with a Confined Vortex Pump

We introduce a model of a passive optical cavity based on a novel variety of the two-dimensional Lugiato–Lefever equation, with a localized pump carrying intrinsic vorticity S, and the cubic or cubic–quintic nonlinearity. Up to S=5, stable confined vortex ring states (vortex pixels) are produced by means of a variational approximation and in a numerical form. Surprisingly, vast stability areas of the vortex states are found, for both the self-focusing and defocusing signs of the nonlinearity, in the plane of the pump and loss parameters. When the vortex rings are unstable, they are destroyed by azimuthal perturbations, which break the axial symmetry. The results suggest new possibilities for mode manipulations in passive nonlinear photonic media by means of appropriately designed pump beams.

Extraction of optical wave structures to the coupled fractional system in magneto-optic waveguides

In this article, truncated M-fractional coupled nonlinear Schrodinger equation (NLSE) with quadratic–cubic nonlinearity is under observation. The studied model is composed of chromatic dispersion, magneto-optic parameter and inter-modal dispersion. The NLSE is the most significant physical model to explain the fluctuations of optical soliton proliferation. The NLSEs have become more popular because of the clarity with which they explain a wide range of complex physical phenomena and the depth with which they display dynamical patterns via localized wave solutions. Optical soliton propagation in magneto-optic is currently a subject of great interest due to the multiple prospects for ultrafast signal routing systems and short light pulses in communications. The optical solitons are secured in the forms of bright, dark, singular and combo solitons. In addition, hyperbolic, periodic and exponential function solutions have been recovered. The modified Sardar subequation and enhanced modified extended tanh-expansion approaches recently developed integration tools are adopted in this study for securing the solutions. In nonlinear dispersive media, optical solitons are stretched electromagnetic waves that maintain their intensity due to a balance between the effects of dispersion and nonlinearity. The effect of parameters have been observed by allotting suitable values and sketching the different shapes of the graphs.

New soliton solutions of fractional Biswas–Milovic equation with Kerr, parabolic and cubic-quartic nonlinearities

This paper presents new explicit solutions of hyperbolic and trigonometric functions, obtained from the conformable fractional Biswas–Milovic equation, characterizing the long distance optical communications with three types nonlinearities: Kerr law, parabolic law and cubic-quartic ones. The Sardar sub-equation method is used, which gives the results that are of significant potential in a nonlinear system, providing a clear physical interpretation of the model under study. The resulting solutions are novel for the fractional Biswas–Milovic equation with the help of the method used, a powerful instrument for exploring precise solitary wave solutions for various other nonlinear equations in a nonlinear medium.

Collapse Dynamics of Vector Vortex Beams in Kerr Medium with Parity–Time-Symmetric Lattice Modulation

Based on the two-dimensional (2D) nonlinear Schrödinger equation, we investigate the collapse dynamics of a vector vortex optical field (VVOF) in nonlinear Kerr media with parity–time (PT)-symmetric modulation. The critical power for the collapse of a VVOF in a Kerr-ROLP medium (Kerr medium with a real optical lattice potential) is derived. Numerical simulations indicate that the number, position, propagation distance, and collapse profile of the collapse of a VVOF in sine and cosine parity–time-symmetric potential (SCPT) Kerr media are closely related to the modulation depth, initial powers, and the topological charge number of a VVOF. The VVOF collapses into symmetric shapes during propagation in a Kerr-ROLP medium, and collapse shapes are sensitively related to the density of the PT-symmetric optical lattice potential. In addition, due to gain–loss, the VVOF will be distorted during propagation in the Kerr-SCPT medium, forming an asymmetric shape of collapse. The power evolution of the VVOF in a Kerr-SCPT medium as a function of the transmission distance with different modulating parameters and topological numbers is analyzed in detail. The introduction of PT-symmetric optical lattice potentials into nonlinear Kerr materials may provide a new approach to manipulate the collapse of the VVOF.

On the optical wave structures to the fractional nonlinear integrable coupled Kuralay equation

This paper is mainly concerning the study of truncated M-fractional Kuralay equations that have applications in numerous fields, including nonlinear optics, ferromagnetic materials, signal processing, engineering fields and optical fibers. Due to its ability to clarify a wide range of sophisticated physical phenomena and reveal more dynamic structures of localized wave solutions, the Kuralay equation has captured a lot of attention in the research field. The newly designed integration methods, known as the modified Sardar subequation method and enhanced modified extended tanh expansion method are used as solving tools to validate the solutions. The goal of this study is to extract several kinds of optical solitons, such as mixed, dark, singular, bright-dark, bright, complex and combined solitons. Due to the many potential applications for superfast signal routing techniques and shorter light pulses in communications, the optical propagation of soliton in optical fibers is now a topic of significant interest. In nonlinear dispersive media, optical solitons are stretched electromagnetic waves that maintain their intensity due to a balance between the effects of dispersion and nonlinearity. In addition, exponential, periodic, hyperbolic solutions are generated. The applied approaches are efficient in explaining fractional nonlinear partial differential equations by providing pre-existing solutions and also producing new solutions by combining results from multiple processes. Additionally, we plot the contour, 2D, and 3D graphs with the associated parameter values to visualize the solutions. The results of this study show the effectiveness of the approaches adopted and help enhance comprehension of the nonlinear dynamical behavior of specific systems. We expect that a substantial amount of engineering model specialists will greatly benefit from our work. The findings demonstrate the efficacy, efficiency, and applicability of the computational method employed, particularly in dealing with intricate systems.

Spatial optical soliton cluster solutions in strongly nonlocal nonlinear media

A (2+1)-dimensional variable coefficient nonlinear Schrödinger equation (NLSE) is described under strongly nonlocal nonlinear media. The soliton cluster solutions are obtained by using the improved self-similar reduction and F-expansion method. The regulation of nonlinear coefficients on the dynamics of spatial optical solitons and the self-similar propagation characteristics of the optical soliton clusters are investigated. It is observed that dark solitons transmitted in nonlinear media show two different spatial distributions. It is also found that the peak intensity of the soliton cluster only fluctuates in a small range during the propagation process, but the soliton cluster after harmonic potential modulation has some loss during the propagation process. But the loss is not as dramatic as when bright solitons are modulated. A new kind of soliton cluster is formed after the modulation of dark solitons, which has great practical significance such as application in logic gates, all-optical devices.

Development and possible applications of tunable elements based on composite materials

This work is devoted to the synthesis of nano-sized weakly agglomerated magnetic particles with different crystal structures, which were used in the development of nonlinear composite structures, in particular, nonlinear resonant microwave elements, left-handed media, and nonlinear magnetoelectric systems.

The Janus layered metamaterial modulated by liquid crystal with multitasking of different logic gates and mode-switching biosensing

A Janus layered metamaterial (JLM) operating in the terahertz (THz) region is proposed, which increases the direction dimension to manipulate the propagation of electromagnetic waves (EWs) through the introduction of nonlinear Kerr media. It achieves multi-scale multitasking with different logic gates and mode-switching biosensing, making a breakthrough on traditional single-function and single-scale THz devices. Due to the electro-optical effect, the liquid crystal (LC) is adjusted by the electric field, and the sharp transmission peak generated by the located defect mode resonance can be used to realize the forward scale logic product gate and the backward scale exclusive NOR gate. In addition, by locking the sharp transmission peak, the biosensing can have different detection ranges under the LC modulation. Therefore, when EWs propagate forward and backward, the mode switching of different biosensing categories with a glucose concentration of 300–550 g/l, creatinine concentration of 80.9–85.28 μmol/l, and the blood component in refractive index of 1.33–1.38 can be realized. The JLM proposed provides a possibility for the design of the chip-level compact optical integrated circuit and offers a new idea for multi-purpose biomedical detection, owning certain research value.

Bifurcations and Exact Solutions of Optical Soliton Models in Fifth-Order Weakly Nonlocal Nonlinear Media

For the optical soliton model in fifth-order weakly nonlocal nonlinear media, to find its exact explicit solutions, the corresponding traveling wave system is formulated as a planar dynamical system with a singular straight line. Then, by using techniques from dynamical systems and singular traveling wave theory developed by [Li & Chen, 2007] to analyze the planar system and find the corresponding phase portraits, the dynamical behavior of the amplitude component can be assessed. Under different parameter conditions, exact explicit solitary wave solutions, periodic wave solutions, kink, and anti-kink wave solutions, compacton solutions, as well as peakons and periodic peakons are found with precise formulations.

RÓWNANIA POLA ELEKTROMAGNETYCZNEGO W ŚRODOWISKU NIELINIOWYM

The paper proposes electromagnetic field equations from the point of view of their adaptation to numerical methods. Maxwell's equations with partial derivatives are used, written concerning field vectors, which most fully reproduce the picture of physical processes in electrical engineering devices. The values of these vectors provide comprehensive information about the field at any spatio-temporal point. The concept of creating mathematical models of electrical devices adequate to physical processes has been developed. Mathematical transformations are carried out according to the rules of differential calculus. Dynamic processes in the elements of electrotechnical devices were analyzed using the apparatus of mathematical modeling. An algorithm for implementing differential equations with partial derivative numerical methods using computer simulation was implemented. The obtained results made it possible to understand the nature of electromagnetic phenomena in nonlinear media. The paper provides calculations of the field parameters in a flat ferromagnetic plate and the groove of the rotor of an electric machine.

Transverse electric waves in three-layered waveguide structure with a parabolic spatial profile of the dielectric constant, optical linear and nonlinear layers

A three-layered waveguide structure containing the Kerr nonlinear medium separated by an optical linear interlayer from a parabolic graded-index layer is considered. Exact solutions of the wave equation corresponding to several types of transverse electric waves existing in different ranges of values of the effective refractive index are found. The types of waves differ from each other by the presence or absence of oscillations in the interlayer and in the graded-index layer, as well as the form of attenuation in a nonlinear medium. The wave types obtained can be divided into two main groups. The first group includes such waves that can propagate with an arbitrarily varying effective refractive index in the allowable range of values. The second one includes such waves that can propagate at certain discrete values of the effective refractive index. Such values of the effective refractive index of waveguide modes are determined by the wavelength of the incident ray, difference between the dielectric constants of a parabolic graded-index layer, and its width. Even and odd waveguide modes are described separately. Field oscillations can be observed only in the interlayer for waves of the first group. Field oscillations can also be observed in the graded-index layer for waves of the second group. The field profile is a self-focusing nonlinear medium flatter than in a defocusing one for all types of waves. An increase in the same parameters has a different effect on the profiles of the different types of waves. The possibility of controlling the distribution of the wave energy between the layers of the waveguide structure by changing the angle of incidence is shown.