Nonlinear Medium Research Articles

Vectorial manipulation of twisted vector vortex optical fields in strongly nonlocal nonlinear media

Abstract We theoretically investigate the propagation properties and vectorial manipulation of twisted vector vortex beams (TVVB) with a cross-phase in a strongly nonlocal nonlinear medium (SNNM). The root mean square beam-width (RMS-BW) and the critical power required to retain the invariant RMS-BM of the TVVB in an SNNM are derived using the coupled nonlocal nonlinear Schrödinger equation. Numerical calculations reveal novel characteristics of the evolution of the state of polarization (SoP) and the optical intensity distributions during the TVVB propagating in an SNNM. It is found that mode conversions between a Laguerre Gaussian and a Hermite Gaussian mode take place during propagation in an SNNM, and the topological charge of the TVVB can be accurately measured by observing the interference intensity structure in the cross-section. Manipulation of the beam shape, SoP, and rotation of the TVVB is achieved by controlling factors such as the initial power, twisting coefficient, initial beam-width, and topological charge. These findings hold promise for applications in optical micro-manipulation, optical communication, and material processing.

Modeling beam propagation in a moving nonlinear medium

Modeling beam propagation in a moving nonlinear medium

Biological effect of dual-frequency laser pulse radiation during pre-sowing treatment of rice seeds at early stages of development under stressful environmental conditions

The biological effect of two-frequency laser pulsed radiation produced on copper vapor during pre-sowing treatment of rice seeds of Veles and Leader varieties at early stages of development in extreme stressful environmental conditions has been studied. The copper vapor laser used in the experiment had the following output characteristics: wavelengths of 510.6 nm (green radiation line) and 578.2 nm (yellow radiation line), pulse duration of 15 ns, repetition frequency of 10 kHz, total pulse power of 10 kW, energy-power ratio between the green and yellow radiation lines 3/1 The interaction of laser radiation with wavelengths of 510.6 and 578.2 nm in the nonlinear medium of the seed caused the formation of additional wavelengths: a total wavelength of 271 nm (ultraviolet radiation) and a difference wavelength of 4.37 microns. Exposure to each of the four wavelengths in its spectral range could lead to the initiation of at least four radiation-induced biochemical reactions. It is shown that pre-sowing treatment of rice seeds with two-frequency laser pulsed radiation for 5–20 seconds had a stimulating effect on the growth and development of rice (the greatest effect was when exposed to 5–10 seconds), and also increased its stability when grown in extreme stressful environmental conditions (moisture deficiency, depleted soil) at early stages of development.

An unconditional stable modified finite element methods for Maxwell’s equation in Kerr-type nonlinear media

The purpose of this paper is to construct a newly efficient finite element method which named as modified finite element method, for Maxwell’s equation in Kerr-type nonlinear media. Because the efficient unconditional stable alternative direction implicit method can’t extend to the Maxwell’s equations in Kerr-type nonlinear media (the difficulty will be discussed in section 3.1), we design the modified method to construct an efficient unconditional stable scheme for Maxwell’s equations in Kerr-type nonlinear media. Furthermore, combined with the direct method, we construct a more efficient direct modified scheme. Comparisons of the efficiency, stability, convergence rate for our modified method and classical explicit leapfrog method were done by theoretical analysis and numerical experiments. The modified method is unconditional stable and its efficiency is not less than leapfrog method.

Inverse Scattering Integrability and Fractional Soliton Solutions of a Variable-Coefficient Fractional-Order KdV-Type Equation

In the field of nonlinear mathematical physics, Ablowitz et al.’s algorithm has recently made significant progress in the inverse scattering transform (IST) of fractional-order nonlinear evolution equations (fNLEEs). However, the solved fNLEEs are all constant-coefficient models. In this study, we establish a fractional-order KdV (fKdV)-type equation with variable coefficients and show that the IST is capable of solving the variable-coefficient fKdV (vcfKdV)-type equation. Firstly, according to Ablowitz et al.’s fractional-order algorithm and the anomalous dispersion relation, we derive the vcfKdV-type equation contained in a new class of integrable fNLEEs, which can be used to describe the dispersion transport in fractal media. Secondly, we reconstruct the potential function based on the time-dependent scattering data, and rewrite the explicit form of the vcfKdV-type equation using the completeness of eigenfunctions. Thirdly, under the assumption of reflectionless potential, we obtain an explicit expression for the fractional n-soliton solution of the vcfKdV-type equation. Finally, as specific examples, we study the spatial structures of the obtained fractional one- and two-soliton solutions. We find that the fractional soliton solutions and their linear, X-shaped, parabolic, sine/cosine, and semi-sine/semi-cosine trajectories formed on the coordinate plane have power–law dependence on discrete spectral parameters and are also affected by variable coefficients, which may have research value for the related hyperdispersion transport in fractional-order nonlinear media.

Higher-order vortex solitons in Kerr nonlinear media with a flat-bottom potential

Higher-order vortex solitons in Kerr nonlinear media with a flat-bottom potential

An efficient reduced order model for nonlinear transient porous media flow with time-varying injection rates

An intrusive Reduced Order Model (ROM) is developed for nonlinear porous media flow problems with transient and time-discontinuous fluid injection rates. The proposed ROM is significantly more computationally efficient than the Full Order Model (FOM). The training regime is generated using the FOM with constant injection rates during the offline stage. The trained ROM exhibits high accuracy for complex pumping schedules (rate vs time) simulated online. The proposed ROM uses the combination of Proper Orthogonal Decomposition and Discrete Empirical Interpolation Method (POD-DEIM), which is compared with the classical POD-Galerkin. The use of an approximated column-reduced Jacobian is shown to be vital to achieving a substantial speedup of ROM vs FOM run-times. An analysis of the trade-off between accuracy and run-time is conducted for ROMs of different sizes and hyper-parameters. The impact of the training regime on the performance of the presented ROM is assessed. The performance of the ROM is studied in the context of a two-dimensional analysis of time-varying injection into a two-well system in a layered porous media reservoir. The accuracy and efficiency of POD-DEIM motivate its potential use as a surrogate model in the real-time control and monitoring of fluid injection processes.

Interaction of Solitons with Inhomogeneous Defects in Nonlocal Nonlinear Media

Interaction of Solitons with Inhomogeneous Defects in Nonlocal Nonlinear Media

Multiple rogue wave, double-periodic soliton and breather wave solutions for a generalized breaking soliton system in (3 + 1)-dimensions

We focused on solitonic phenomena in wave propagation which was extracted from a generalized breaking soliton system in (3 + 1)-dimensions. The model describes the interaction phenomena between Riemann wave and long wave via two space variable in nonlinear media. Abundant double-periodic soliton, breather wave and the multiple rogue wave solutions to a generalized breaking soliton system by the Hirota bilinear form and a mixture of exponentials and trigonometric functions are presented. Periodic-soliton, breather wave and periodic are studied with the usage of symbolic computation. In addition, the symbolic computation and the applied methods for governing model are investigated. Through three-dimensional graph, density graph, and two-dimensional design using Maple, the physical features of double-periodic soliton and breather wave solutions are explained all right. The findings demonstrate the investigated model’s broad variety of explicit solutions. All outcomes in this work are necessary to understand the physical meaning and behavior of the explored results and shed light on the significance of the investigation of several nonlinear wave phenomena in sciences and engineering.

Features of the surface wave propagation along the interface between the hyperbolic graded-index layer and nonlinear medium with a step change in the dielectric constant

A new exact analytical solution describing the transverse profile of the surface wave in the case of contact with nonlinear medium with the step-wise nonlinearity and the hyperbolic index profile and describing new features of the light localization near such an interface are found. The formation of the near interface cladding layer with the dielectric constant different from its value in the rest nonlinear medium is described. It is found that light localization can be effectively controlled by the parameters of the hyperbolic profile such as the interface dielectric constant and the effective refractive index. The depth of field penetration decreases inside the hyperbolic graded-index layer and it increases in the nonlinear medium with an increase in the effective refractive index. The depth of field penetration in the hyperbolic graded-index layer increases and it decreases in the nonlinear medium with an increase in the value of the dielectric constant at the medium interface. Thickness of the formed cladding layer decreases with increase in the interface dielectric constant and it increases with increase in the effective refractive index.

A synthetic moving-envelope metasurface antenna for independent control of arbitrary harmonic orders

Flexible frequency controls are crucial in many photonic and electronic applications, ranging from communications systems, spectroscopy, and metrology to quantum information processing. However, the state-of-the-art solutions based on nonlinear bulk media, electro-optic effect, and nonlinear metasurfaces incur very limited spectral controllability, and merely a couple of harmonic orders can be independently manipulated. Here, we theoretically propose and experimentally demonstrate synthetic moving-envelope metasurface antennas capable of simultaneously generating arbitrary harmonic orders and independently manipulating their wave properties in a software-defined manner. As proof-of-principle examples, we demonstrate unidirectional frequency transition, frequency comb generation, arbitrary harmonic orders independent control, and their applications in frequency-division multiplexing communications. All these complicated functionalities are achieved by the 1-bit spatiotemporally ON-OFF switching of meta-atoms of the waveguide-integrated metasurface antenna. Our proposed synthetic metasurface antenna solution greatly expands the frontiers of wave engineering and information manipulation, showing promising potential in wireless communications, spectroscopy, metrology, and quantum science.

Manipulating photonic spin Hall split based on nonlinear effect and surface plasmon resonance

In this work, we present a surface plasmon resonance (SPR) structure containing AuAl2 and a nonlinear Kerr medium. Based on the modulation of the refractive index of the Kerr medium by pumped light, we analyze the effects of the SPR structure and pumped light on the photonic spin Hall effect (PSHE). The numerical results indicate that the thickness of the AuAl2 exerts a profound impact on the SPR, while the intensity of the pump light (Ip) exerts a significant influence on the resonance angle. The transverse shift (TS) is very sensitive to the refractive index (RI) of the sensing layer after increasing through the SPR. Furthermore, it is observed that the sign of the TS of the PSHE can be modulated according to Ip within a specific angle of incidence. In light of these findings, we put forth a novel optical signal modulation and RI sensing scheme based on PSHE. Our study provides a new mechanism for practical applications of PSHE in optical communication and precision measurement.

Observation of off-axis solitary waves propagating along a specific trajectory in photorefractive crystals.

We report the propagation dynamics of swallowtail beams (SBs) within a photorefractive crystal. In the nonlinear regime, the self-accelerating and secondary self-focusing features of the swallowtail beams are influenced, and a solitary wave is generated. The main lobe energy of the swallowtail beams is guided to a specific inclined trajectory, leading to a stable solitary wave, and we control the output position of the solitary wave by changing the launch angle. Our results are supported by the corresponding experiments. In addition, we demonstrate that a Gaussian beam can be effectively guided in swallowtail optical waveguide structures. Our research represents an interesting interaction between the swallowtail beams and nonlinear medium, which may find potential applications in photonic integrated devices and optical information transmission.

Painlevé analysis and Hirota direct method for analyzing three novel physical fluid extended KP, Boussinesq, and KP-Boussinesq equations: Multi-solitons/shocks and lumps

Due to the extensive and diverse connections of the Kadomtsev-Petviashvili (KP) equation with various physical phenomena, such as the propagation of waves in sea and ocean water and the propagation of nonlinear waves in plasmas when two-dimensional perturbations are considered, thus in this study and based on the original KP equation, we construct and investigate three extended models, which are called the extended KP (eKP) equation, the extended Boussinesq (eBO) equation, and the extended KP-Boussinesq (eKP-BO) equation. These equations are commonly observed in many physical contexts involving nonlinear and dissipative media. Our research begins with thoroughly verifying the complete integrability of the three extended models. Once this crucial step is accomplished, we will examine these three extended models using the simplified Hirota approach (SHA), leading us to derive multiple soliton/shock solutions. Furthermore, the Hirota bilinear form of each model will be employed to derive a set of lump solutions for these three extended models, utilizing different parameter values. We also analyze some derived solutions graphically by presenting some two- and three-dimensional graphics to understand the dynamic behavior of the waves described by these solutions. The obtained results are anticipated to benefit a broad spectrum of academics interested in studying fluid mechanics, water wave characterization, and other interdisciplinary domains. Additionally, these models are anticipated to be essential in describing and understanding the dynamics of several nonlinear phenomena that arise and propagate in different plasma systems when perturbations are considered in multidimensions.

Analytical solution for Ξ-type qutrit interacting nonlinearly with a cavity field through Kerr-like medium with intrinsic noise present

This paper presents an analytical solution for the Milburn equation describing the interaction between a 3-level atom in a [Formula: see text]-configuration, a cavity field, and a nonlinear Kerr-like medium. The Hamiltonian of the model is presented in the rotating wave approximation (RWA) under specific conditions. The obtained analytical solution accounts for the impact of intrinsic decoherence and nonlinear terms on the dynamics of various physical phenomena. Specifically, we explore the behavior of atomic population, entropy functions, entanglement, negativity, and correlation, highlighting their dependence on the physical parameters of the [Formula: see text]-level atom-cavity system.

Excitation control of bright-bright vector ghost waves with ring structures in an inhomogeneous partially nonlocal nonlinear medium

The similar structures of coupled solitons for two-component systems were extensively discussed in literature. In this paper, the excitation management of different two-component structures for bright-bright vector ghost waves with ring structures of the inhomogeneous partially nonlocal nonlinear Schrödinger vector models under a parabolic potential is paid close attention. Considering the comparison between the maximum value of the accumulated time and the excited value of bright-bright ghost waves, the inhibition and maintenance of excitations for bright-bright ghost waves with ring structures are studied in the exponential system with the periodic modulation, and the periodical completion and periodical inhibition of excitations for bright-bright ghost waves with ring structures are discussed in the periodic modulation system. Moreover, the effect of different values of two transverse diffractions, and ring radius and thickness parameters on bright-bright ghost waves with ring structures is investigated. This study generalizes the excitation management of vector ghost waves into the partially nonlocal properties of nonlinear waves.

Self-Focused Pulse Propagation Is Mediated by Spatiotemporal Optical Vortices.

We show that the dynamics of high-intensity laser pulses undergoing self-focused propagation in a nonlinear medium can be understood in terms of the topological constraints imposed by the formation and evolution of spatiotemporal optical vortices (STOVs). STOVs are born from pointlike phase defects on the sides of the pulse nucleated by spatiotemporal phase shear. These defects grow into closed loops of spatiotemporal vorticity that initially exclude the pulse propagation axis, but then reconnect to form a pair of toroidal vortex rings that wrap around it. STOVs constrain the intrapulse flow of electromagnetic energy, controlling the focusing-defocusing cycles and pulse splitting inherent to nonlinear pulse propagation. We illustrate this in two widely studied but very different regimes, relativistic self-focusing in plasma and nonrelativistic self-focusing in gas, demonstrating that STOVs mediate nonlinear propagation irrespective of the detailed physics.

Non-linear media in weakly curved spacetime: optical solitons and probe pulses for gravimetry

That light propagating in a gravitational field gets frequency-shifted is one of the basic consequences of any metric theory of gravity rooted in the equivalence principle. At the same time, also a time dependent material’s refractive index can frequency-shift light propagating in it. The mathematical analogy between the two effects is such that the latter has been used to study the optical analogue of a black-hole spacetime. Here, we combine these two effects by showing that light propagation in non-linear media in the presence of a moving refractive index perturbation can lead to a gravity-dependent blueshift. We find that the predicted blueshift surpasses the gravitational redshift even if the medium is considered to be perfectly stiff. In realistic scenarios, by far the strongest frequency shift arises due to the deformation of the dielectric medium and the corresponding photoelastic change of refractive index. This has the potential to facilitate optical sensing of small gravity gradients.

Design of an Optimized Terahertz Time-Domain Spectroscopy System Pumped by a 30 W Yb:KGW Source at a 100 kHz Repetition Rate with 245 fs Pulse Duration

Ytterbium laser sources are state-of-the-art systems that are increasingly replacing Ti:Sapphire lasers in most applications requiring high repetition rate pulse trains. However, extending these laser sources to THz Time-Domain Spectroscopy (THz-TDS) poses several challenges not encountered in conventional, lower-power systems. These challenges include pump rejection, thermal lensing in nonlinear media, and pulse durations exceeding 100 fs, which consequently limit the detection bandwidth in TDS applications. In this article, we describe our design of a THz-TDS beamline that seeks to address these issues. We report on the effectiveness of temperature controlling the Gallium Phosphide (GaP) used to generate the THz radiation and its impact on increasing the generation efficiency and aiding pump rejection while avoiding thermal distortions of the residual pump laser beam. We detail our approach to pump rejection, which can be implemented with off-the-shelf products and minimal customization. Finally, we describe our solution based on a commercial optical parametric amplifier to obtain a temporally compressed probe pulse of 55 fs duration. Our study will prove useful to the increasing number of laboratories seeking to move from the high-energy, low-power THz time-domain spectroscopy systems based on Ti:Sapphire lasers, to medium-energy, high-power systems driven by Yb-doped lasers.

Non-self-similar light transport in scattering media

Transport processes underpin a wide variety of phenomena, ranging from chemistry, to physics and ecology. Despite their pervasiveness, however, several distinctive features of these processes are still elusive, making it difficult to recognize and classify the associated transport regimes. Using light scattering as a probe to explore different propagation regimes, we report on the experimental observation of non-self-similar light transport through turbid membranes. Our results show that a breakdown of self-similarity can arise for light waves even in the presence of isotropic and homogeneous disorder, and can be tuned by varying the turbidity of the system. By introducing the concept of self-similarity for light propagation, we provide a unified framework for the classification of light transport regimes—overcoming the dichotomy between normal and anomalous diffusion—and show that non-self-similar propagation is a common and experimentally accessible phenomenon. This insight can help to understand and model other scenarios where light transport is dominated by rare propagation events, such as in nonlinear and active media, but also in other fields of research beyond optics. Published by the American Physical Society 2024