Kerr Medium Research Articles

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.

Entanglement between two charge qubits taking account the Kerr media

Background. The need to implement controlled coupling between qubits, which are the logical elements of quantum devices such as quantum computers and quantum networks, requires, along with the use of traditional methods, the development of new, more effective ways to organize the interaction of qubits with the microwave fields of resonators used to generate and control the entanglement of qubits. As one of these methods, a method based on the influence of frequency-regulated radio frequency signals on a superconducting Josephson qubit connected by a large Josephson junction to a free qubit has been proposed. Aim. The influence of the Kerr medium of the resonator, in which one of the two qubits is placed, on their entanglement induced by the coherent or thermal frequency-regulated radio frequency field of the resonator is considered. Methods. To analyze the dynamics of the system under consideration, the solution of the quantum Liouville equation for the full density matrix is studied. An exact solution o this equation is found in the case of initial separable and entangled states of qubits. The exact solution of the evolution equation is used to calculate the criterion of qubit-qubit entanglement – cconcurrence. Numerical modeling of the concurrence was carried out for various states of qubits, coherent and thermal fields of the resonator, as well as various values of the intensity of the resonator field and the Kerr nonlinearity parameter. Results. It is shown that for separable initial states of qubits, the inclusion of Kerr nonlinearity reduces the maximum degree of entanglement of qubits. For an entangled initial state of qubits, the possibility of creating long-lived entangled states in the presence of Kerr nonlinearity is shown. Conclusion. The type of initial states of qubits and the range of values of the intensities of the resonator fields and the Kerr nonlinearity parameters have been established, for which the most effective control and operation of the evolution of qubits, as well as the degree of their entanglement, in the physical system under consideration, is possible.

Ultrafast random polarization beam smoothing driven by counter-rotating wavefronts via the optical Kerr effect

We propose an ultrafast random polarization smoothing scheme to achieve ultrafast speckle movement and polarization randomization of the focal spot. In the scheme, each beamlet in a laser quad is driven by a rotating petal-like wavefront, giving rise to the ultrafast redistribution of the speckles within the focal spot. The rotating wavefront is induced by an optical Kerr medium pumped by a laser beam with rotating intensity distribution that is generated by the superposition of two Laguerre–Gaussian beams carrying conjugate vortex phase and frequency shift. In addition, by properly selecting the topological charges of the pump beams and polarization states of the beamlets, the beamlets in a quad can be divided into two sets with counter-rotating wavefronts and orthogonal polarizations, which further randomizes the polarization of the focal spot. Results indicate that the proposed scheme can reduce the contrast by more than 70% and the degree of polarization by more than 75% within several picoseconds, by utilizing the rotating phase pumped by two Laguerre-Gaussian beams with a peak intensity of 0.18GW/cm2 and a frequency shift of 1 THz. The ultrafast random polarization smoothing scheme is expected to suppress the growth of Laser Plasma Instabilities (LPIs) including the filamentation and backscatter in indirect-drive inertial confinement fusion (ICF) facilities.

Analytical investigations of propagation of ultra-broad nonparaxial pulses in a birefringent optical waveguide by three computational ideas

This paper mainly concentrates on obtaining solutions and other exact traveling wave solutions using the generalized G-expansion method. Some new exact solutions of the coupled nonlinear Schrödinger system using the mentioned method are extracted. This method is based on the general properties of the nonlinear model of expansion method with the support of the complete discrimination system for polynomial method and computer algebraic system (AS) such as Maple or Mathematica. The nonparaxial solitons with the propagation of ultra-broad nonparaxial pulses in a birefringent optical waveguide is studied. To attain this, an illustrative case of the coupled nonlinear Helmholtz (CNLH) system is given to illustrate the possibility and unwavering quality of the strategy utilized in this research. These solutions can be significant in the use of understanding the behavior of wave guides when studying Kerr medium, optical computing and optical beams in Kerr like nonlinear media. Physical meanings of solutions are simulated by various Figures in 2D and 3D along with density graphs. The constraint conditions of the existence of solutions are also reported in detail. Finally, the modulation instability analysis of the CNLH equation is presented in detail.

The Propagation Dynamics of the Symmetric Pearcey Gaussian Beam in the Kerr Medium

AbstractIn this paper, symmetric Pearcey Gaussian beams (SPGBs) are studied in a Kerr medium. By varying the initial input power, the autofocusing ability of the beams is investigated, to find a clear restrictive relationship between the breath‐like structure and the initial input power. The critical collapse power is investigated when SPGBs change from discrete beams to regular breath‐like structure. Finally, the transmission of SPGBs is discussed under different phase modulation when SPGBs are affected by astigmatic, the whole beam is rotated and the angle of rotation can be controlled.

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.

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.

Entanglemnt in nonlinear three-qubits Jaynes — Cummings

In this paper, we investigated the dynamics of entanglement of pairs of qubits in a system of three identical qubits that interact non-resonantly with the selected mode of a microwave resonator without loss with the Kerr medium by means of single-photon transitions. We have found solutions to the quantum time Schrodinger equation for the total wave function of the system for the initial separable, biseparable and true entangled states of qubits and the Fock initial state of the resonator field. Based on these solutions, the criterion of entanglement of qubit pairs — negativity is calculated. The results of numerical simulation of the negativity of qubit pairs have shown that the presence of disorder and Kerr nonlinearity in the case of an initial non-entangled state of a pair of qubits can lead to a significant increase in the degree of their entanglement. In the case of an initial entangled state of a pair of qubits, the disorder and the Kerr medium can lead to a significant stabilization of the initial entanglement.

Controlling nonlinear collapse of ellipticity and orientation of a co-variant vector optical field.

A vector optical field with inhomogeneous spatial polarization distribution offers what we believe to be a new paradigm to form controllable filaments. However, it is challenging to steer multiple performances (e.g. number, orientation, and interval) of filaments in transparent nonlinear media at one time. Herein, we theoretically self-design and generate a kind of believed to be novel ellipticity and orientation co-variant vector optical field to interact with Kerr medium to solve this issue. The collapsing behaviors of such a new hybrid vector optical field reveal that, by judiciously adjusting the inherent topological charge and initial phase of incident optical field, we are able to give access to stable collapsing filamentation with tunable numbers, orientations and interval. Additionally, the collapsing patterns presented are immune nearly to the extra random noise. The relevant mechanism behind the collapse of the vector optical field is elucidated as well. The findings in this work may have huge potential in optical signal processing, laser machining, and other related applications.

Multi-soliton solutions for the positive coherently coupled NLS in the Kerr media via the Riemann–Hilbert approach

Multi-soliton solutions for the positive coherently coupled NLS in the Kerr media via the Riemann–Hilbert approach

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.

Suppression of soliton collapses, modulational instability and rogue-wave excitation in two-Lévy-index fractional Kerr media

We introduce a generalized fractional nonlinear Schrödinger (FNLS) equation for the propagation of optical pulses in laser systems with two fractional-dispersion/diffraction terms, quantified by their Lévy indices, α 1   α 2 ∈ ( 1 , 2 ] , and self-focusing or defocusing Kerr nonlinearity. Some fundamental solitons are obtained by means of the variational approximation, which are verified by comparison with numerical results. We find that the soliton collapse, exhibited by the one-dimensional cubic FNLS equation with only one Lévy index (LI) α = 1 , can be suppressed in the two-LI FNLS system. Stability of the solitons is also explored against collisions with Gaussian pulses and adiabatic variation of the system parameters. Modulation instability (MI) of continuous waves is investigated in the two-LI system too. In particular, the MI may occur in the case of the defocusing nonlinearity when two diffraction coefficients have opposite signs. Using results for the MI, we produce first- and second-order rogue waves on top of continuous waves, for both signs of the Kerr nonlinearity.

Exact Solutions of the Paraxial Wave Dynamical Model in Kerr Media with Truncated M-fractional Derivative using the (G′/G, 1/G)-Expansion Method

Exact Solutions of the Paraxial Wave Dynamical Model in Kerr Media with Truncated M-fractional Derivative using the (G′/G, 1/G)-Expansion Method

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.

Single-shot observation of nonlinear pulse splitting in a Kerr medium.

We report single-shot, time-resolved observation of self-steepening and temporal splitting of near-infrared, 50 fs, micro-joule pulses propagating nonlinearly in flint (SF11) glass. A coherent, smooth-profiled, 60-nm-bandwidth probe pulse that propagated obliquely to the main pulse through the Kerr medium recorded a time sequence of longitudinal projections of the main pulse's induced refractive index profile in the form of a phase-shift "streak," in which frequency-domain interferometry recovered with ∼10 fs temporal resolution. A three-dimensional simulation based on a unidirectional pulse propagation equation reproduced observed pulse profiles.

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.