Nonlinear Kerr Medium Research Articles

Quantum correlations and parameter estimation for two superconducting qubits interacting with a quantized field

In the present manuscript, we introduce a quantum system of two superconducting qubits (S–Qs) interacting with a quantized field under the influence of the Kerr nonlinear medium and Ising interaction. We formulate the Hamiltonian of the quantum model and determine the density operator of whole quantum system as well as quantum subsystems. We examine the dynamics of the quantumness measures for subsequent times including the S–Qs entanglement, S–Qs-field entanglement and quantum Fisher information in relation to the system parameters. Finally, we display the connection among the measures of quantumness during the time evolution.

Generation and control of circular Airy solitons in fractional nonlinear optical systems under different modes

In this paper, the dynamics of the circular Airy beam (CAB) in the spatial fractional nonlinear Schrödinger equation (FNLSE) optical system are investigated. The propagation characteristics of CABs modulated by the quadratic phase modulation (QPM) in a Kerr (cubic) nonlinear medium under power function diffractive modulation modes and parabolic potentials are numerically simulated by using a step-by-step Fourier method. Specifically, the threshold for CABs to form solitons in the Kerr medium is controlled by the Lévy index and the QPM coefficient. Secondly, the parabolic potential has the ability to stabilize the FNLSE optical system, making it easier for the formation of CAB solitons. The addition of QPM allows the refocusing of the split beam caused by the Lévy index, and it can change the position and intensity of solitons. Finally, we also study the transmission evolution of QPM-modulated CABs in the Kerr medium under the power function diffraction modulation mode. We can obtain different types of solitons by varying the power function modulation coefficients. A dark soliton with high stability is formed, and we can control its size. Results show that it is possible to optimize the parameter settings (parabolic potential coefficients, power function modulation coefficients, QPM coefficients, Lévy indices, and nonlinear Kerr intensity coefficients) to obtain different types of solitons as well as to modulate the soliton transport. It provides more degrees of freedom for the study of CAB soliton propagation in the Kerr media, which is of great significance and application in fields of nonlinear optical transport, particle manipulation, and optical metrology.

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

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.

Nonlinear localized states near the interface with nonlinear response between the medium with a parabolic index spatial profile and Kerr-type medium

The interface with nonlinear response separating the parabolic graded-index and the Kerr nonlinear media are considered. Exact solutions to the nonlinear Schrödinger equation with nonlinear short-range potential and a parabolic spatial profile are found applying to the theoretical description of the stationary states localized near interface with nonlinear properties. Localized states with continuous/discrete energy spectrum are described by the Whittaker function/Hermite polynomials in the medium with a parabolic profile of characteristic and the hyperbolic cosine (sine) in the medium with a self-focusing/defocusing Kerr nonlinearity. The field localization length is wider in the case of a self-focusing nonlinearity than in the case of a defocusing one. The maximum of the wave function is located in a nonlinear medium in the case of a self-focusing nonlinearity and at the interface in the case of a defocusing one. It is shown the possibility of a motion closer to the interface (or away from it) the maximum intensity of the localized state by changing the values of the interface response parameters at the fixed localization energy. A growth of the width of the parabolic graded-index layer adduced an increase in the maximum height of localized states of discrete spectrum and theirs localization length in the graded-index layer, but it had almost no effect on the profile of localized states of the continuous spectrum.

Creating light-made waveguides with structured optical beams in nonlinear Kerr media

Creating light-made waveguides with structured optical beams in nonlinear Kerr media

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.

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.

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.

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.

Spatiotemporal dynamics of modulation instability in Kerr nonlinear media with pure-quartic dispersion

We present the analytical and numerical analysis on spatiotemporal dynamics of modulation instability (MI) in Kerr nonlinear media with pure-quartic dispersion. We apply a linear stability method to arrive at a universal expression for pure-quartic instability gain, which can simultaneously describe the temporal, spatial, and spatiotemporal cases. The results show that the condition of such three fundamental instability occurrence in pure-quartic dispersion media (PDM) is the same as that in conventional quadratic dispersion media (QDM). Another interesting observation is that the maximum gain is also the same in both cases. For temporal instability, there exists a critical power below which the instability bandwidth becomes wider than the corresponding case in QDM or otherwise. For spatiotemporal instability, the instability region depending on critical frequencies is found to show some remarkable difference when compared with the latter case. The analytical prediction resulting from linear stability analysis is confirmed by the numerical method.

Four-wave mixing based spectral Talbot amplifier for programmable purification of optical frequency combs

Optical frequency combs (OFCs) with programmable free spectral range and high optical carrier-to-noise ratio (CNR) play a crucial role in diverse research fields, including telecommunications, spectroscopy, quantum information, astronomy, sensing, and imaging. Unfortunately, the presence of stochastic noise often results in degraded optical CNR, leading to limited communication performance and measurement accuracy in comb-based systems. There is a lack of effective and flexible methods to improve the CNR of OFCs contaminated by broadband noise, hampering their widespread utilization. To address this challenge, we propose a four-wave mixing based spectral Talbot amplifier to purify OFCs flexibly. Our approach employs programmable spectral phase filters followed by a nonlinear Kerr medium to regenerate an OFC with superior CNR. In our experimental demonstration, we regenerated a 165-GHz spaced CNR enhanced OFC from a noise-dominated comb source spaced at 11 GHz, achieving up to ∼11-dB CNR improvement. The technique allows for a user-defined purification factor m to range from 7 to 15. Furthermore, our scheme demonstrates flexibility in adjusting the wavelengths of the regenerated comb lines via a tunable optical delay line without the need for a tunable seed laser. We also investigated the impact of the pump and signal on the regenerated comb experimentally and studied the influence of dispersion mismatch on the suppression of undesired sidebands numerically. Our proposed scheme presents a powerful alternative for programmable purification, manipulation, and detection of noise-dominated spectral waveforms.

Optical response properties and bipartite entanglement in a hybrid optomechanical system assisted by Kerr-nonlinearity and amplitude modulated drive field

We theoretically investigate the optomechanical interaction between an optical field and a mechanical mode mediated by a Kerr nonlinear medium inside an optical cavity and simultaneously driven by an external amplitude-modulated pump field and a probe field. We show that switching between bistability and multistability is influenced by the rocking parameter and Kerr nonlinearity. Further, we study the quantum fluctuation dynamics of the system, which shows the quantum coherence and interference effects resulting in the transmission of the probe field from opacity to amplification. We also find that the rocking parameter, Kerr nonlinearity, and the optomechanical coupling influence the transmission spectrum. In addition, we also show that the rocking parameter significantly enhances the optomechanical coupling, which can be a new handle to control the entanglement between the optical and mechanical modes. The results show that such a hybrid optomechanical system has potential application in designing and optimizing all-optical switching and optical sensors.

Shortcuts to adiabatic soliton compression in active nonlinear Kerr media.

We implement variational shortcuts to adiabaticity for optical pulse compression in an active nonlinear Kerr medium with distributed amplification and spatially varying dispersion and nonlinearity. Starting with the hyperbolic secant ansatz, we employ a variational approximation to systematically derive dynamical equations, establishing analytical relationships linking the amplitude, width, and chirp of the pulse. Through the inverse engineering approach, we manipulate the distributed gain/loss, nonlinearity and dispersion profiles to efficiently compress the optical pulse over a reduced distance with high fidelity. In addition, we explore the dynamical stability of the system to illustrate the advantage of our protocol over conventional adiabatic approaches. Finally, we analyze the impact of tailored higher-order dispersion on soliton self-compression and derive physical constraints on the final soliton width for the complementary case of soliton expansion. The broader implications of our findings extend beyond optical systems, encompassing areas such as cold-atom and magnetic systems highlighting the versatility and relevance of our approach in various physical contexts.

Interaction of a four-level atom with a quantized field in the presence of a nonlinear Kerr medium

Quantum entanglement and atomic coherence are examined for a system consisting of a four-level atom (FLA) interacted with a nonlinear quantum field. We assume that the FLA-field coupling, Kerr medium and quantified field are all f\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f$$\\end{document}-deformed with full nonlinear formalism. We consider N-configuration and cascade (C)-configuration of the FLA. We explore the impact of field deformation and Kerr medium on the dynamics of the quantumness measures when the quantized field is initially prepared in a deformed coherent state without and with Kerr medium effect. Moreover, we examine the statistical properties of the radiation field using the second order correlation function. The results indicate how the considered quantumness measures in the FLA–field system can be manipulated and controlled through the parameters of the quantum model.

Suppressing filamentation instability due to laser beam self-filtering

Abstract The development of small-scale self-focusing in a nonlinear Kerr medium after preliminary self-filtering of a laser beam propagating in free space is studied numerically. It is shown that, under definite conditions, due to self-filtering, filamentation instability (beam splitting into filaments) either occurs at significantly larger values of the B-integral, or does not occur at all. In the latter case, there develops the honeycomb instability revealed in this work. This instability is the formation of a random honeycomb structure in the beam cross-section. It is shown that self-filtering can significantly increase the permissible values of the B-integral, at which the beam quality remains acceptable.

Spatial self-phase modulation excited by fractional-order linearly polarized vector fields.

Compared to the integer-order vector field, the fractional-order vector field has an additional degree of control freedom, which will bring rich photophysical properties and what we believe to be novel nonlinear optical phenomena. In this work, we theoretically and experimentally investigate the focusing, propagation, and spatial self-phase modulation (SSPM) of fractional-order linearly polarized vector fields (FLPVFs). It is shown that the weak focusing field of FLPVF exhibits an asymmetric intensity distribution. Intriguingly, its state of polarization (SoP) has a hybrid polarization distribution. When this focused FLPVF propagates to the far field in free space, its SoP degenerates into a localized linearly polarization distribution. However, after the focused FLPVF passes through an isotropic nonlinear Kerr medium, its SoP exhibits a hybrid polarization distribution. Additionally, unlike the self-diffraction intensity pattern of integer-order linearly polarized vector field (ILPVF) with a concentric multi-ring structure, the SSPM pattern of FLPVF is a symmetry broken self-diffraction intensity pattern. The presented work provides a nonlinear optics approach for manipulating both the SoP and intensity distributions of the light field.

Geometric phase and Wehrl phase entropy for two superconducting qubits in a coherent field system under the effect of nonlinear medium

In this paper, we study the dynamical behavior of coherence, geometric phase, Wehrl entropy (WE) for a quantum model consisting of two superconducting qubits (SC–Qs) in the presence of multi-photon transition. We develop the Hamiltonian model and solve the Schrödinger equation that leads to evaluate the density matrix of whole system as well as subsystems. We introduce the effects of nonlinearity and subsystems interaction and display the temporal behavior of different quantumness measures in the existence and absence of nonlinear Kerr medium and Ising interaction.

Nonlinear evolution of modulational instability under the interaction of Kerr nonlinearity with pure higher, even-order dispersion

We investigate the nonlinear evolutions of modulation instability (MI) under the interaction of Kerr nonlinearity with pure higher, even-order dispersion (HEOD) by using the truncating method of three-wave mixing. For any HEOD, we find the phase-plane topological structure of the MI changes in three frequency regions whose ranges depend on the order of HEOD. And we present the novel types of nonlinear evolutions of the MI, which do not exist in the case of quadratic dispersion. Taking the pure-sextic dispersion as an example, the theoretical predictions of the MI evolutions are confirmed by numerically solving the modified nonlinear Schrödinger equation. Our results not only further deepen the understanding of MI, but also provide a universal guideline for experimental investigation of nonlinear waves, such as breather solitons or rogue waves excitation, in nonlinear Kerr media with pure HEOD.

Dynamical structures of wave front to the fractional generalized equal width-Burgers model via two analytic schemes: Effects of parameters and fractionality

Abstract This work focuses on the fractional general equal width-Burger model, which describes one-dimensional wave transmission in nonlinear Kerr media with combined dispersive and dissipative effects. The unified and a novel form of the modified Kudryashov approaches are employed in this study to investigate various analytical wave solutions of the model, considering different powers of nonlinearity in the Kerr media. As a result, a wide range of structural solutions, including trigonometric, hyperbolic, rational, and logarithmic functions, are formulated. The achieved solutions present a kink wave, a collision of kink and periodic peaked soliton, exponentially increasing wave profiles, and shock with a dark peaked wave. The obtained solutions are numerically demonstrated for specific parameter values and general parametric powers of nonlinearity. We analyzed the effect of existing parameters on the obtained wave solutions with numerical graphics. Moreover, the stability of the model is analyzed with a perturbed system. Furthermore, a comparison with published results in the literature is provided, highlighting the differences and similarities. The achieved results showcase the diversity of structural solutions obtained through the proposed approaches.