nonlinear mixing Research Articles (Page 1)

Abstract Topological quantum plasmas provide a groundbreaking platform for high-efficiency terahertz generation through nonlinear wave mixing. A comprehensive theoretical framework is presented by combining quantum hydrodynamics with Maxwell’s equations to demonstrate that Dirac fermions in materials like graphene and topological insulators exhibit a giant third-order nonlinear susceptibility enhanced by linear band dispersion, Berry phase effects, and spin-momentum locking. The predicted terahertz emission efficiency exceeds conventional semiconductor plasmas by 2–3 orders of magnitude, reaching enhancement factors of 25–1250 times across different Dirac materials. The analysis reveals that the combination of quantum plasmon dispersion and intrinsic Dirac fermion nonlinearity enables exceptional spectral tunability through pump frequency and chemical potential control. This work establishes topological quantum plasmas as a superior platform for compact, efficient on-chip terahertz sources, providing a transformative pathway to bridge the longstanding ‘THz gap’ in photonic technology.

Frequency combs consist of a spectrum of evenly spaced spectral lines. Optical frequency combs enable technologies ranging from timing, LiDAR, and ultra-stable signal sources. Microwave frequency combs are analogous to optical frequency combs, but often leverage electronic nonlinearity for comb generation. Generating microwave frequency combs using piezoelectric mechanical resonators would enable this behavior in a more compact form factor, thanks to the shorter acoustic wavelengths. In this work, we demonstrate a microwave frequency comb leveraging thermal nonlinearity in high quality factor (Q), overmoded acoustic resonators in thin-film lithium niobate. By providing input power at 257 MHz, which is the sum frequency of two acoustic modes at 86 and 171 MHz, we generate parametric downconversion and comb generation. We explore the nonlinear mixing regimes and the associated conditions for comb generation. Comb spacing is observed to vary significantly with drive frequency and power, and its general behavior is found to rely heavily on initial conditions. This demonstration showcases the potential for further improvement in compact and efficient microwave frequency combs, leveraging nonlinear acoustic resonators.

Microcrack damage was detected in orthotropic carbon fiber-reinforced polymers (CFRPs) repaired with a single-sided patch during the tensile process via nonlinear mixing Lamb wave detection technology. An integrated numerical model of tensile displacement–devibration–nonlinear mixing Lamb wave detection was established to explore the relationship between the patch parameters and the nonlinear mixing Lamb wave response. A static tensile test and nonlinear mixing Lamb wave detection were designed to verify the exactness of the simulation model. On the basis of the optimal Latin hypercube design, a response surface mathematical model with the patch radius, patch thickness and patch rotation angle as independent variables and mixing relative acoustic nonlinearity parameters (MRANPs) as the response value was constructed. An archiving microgenetic algorithm was used to identify the optimal combination of patch design parameters. The results revealed that under the same tensile displacement conditions, the tensile load on the patch-repaired CFRP plate was significantly greater than that on the unrepaired sample, indicating a greater bearing capacity. The MRANPs initially decreased but then increased with increasing patch radius and patch thickness; they first increased but then decreased with increasing patch rotation angle. After multiobjective optimization, the sum RANP and difference RANP were 0.4754 and 0.2434, respectively, representing reductions of 8.29% and 30.75%, respectively, compared with the single–factor simulation results. This significant optimization effect provides reference value for CFRP structural health monitoring in aircraft safety engineering.

Many electrically active devices rely on nonlinear signal mixing (heterodyning) between two electrical signals. Heterodyning between electric and acoustic signals can allow for active control of typically passive components such as transmission lines, acoustic resonators, and electrical resonators built from piezoelectric materials. However, there are few techniques to characterize the nonlinear properties of materials that lead to heterodyning between electric and acoustic signals within the material. Here we demonstrate a proof-of-concept microwave interferometer that uses electromagnetic and acoustic waves to measure second-order mixing from electrical and acoustic signals in a piezoelectric material. The sum and difference frequencies of signal mixing can be detected in the electromagnetic spectrum in our measurement. We show the effect of frequency and power of the fundamental signals on the mixing products. We additionally characterize the heterodyne signal to show that it is electric-acoustic in nature, versus purely electric. Characterizing nonlinear electric-acoustic properties is important to the development of next generation piezoelectric materials models and devices.

Existence and multiplicity of normalized solutions for the quasi-linear Schrödinger equations with mixed nonlinearities

Shaping the structure of light with flat optical devices has driven significant advancements in our fundamental understanding of light and light-matter interactions, and enabled a broad range of applications, from image processing and microscopy to optical communication, quantum information processing, and the manipulation of microparticles. Yet, pushing the boundaries of structured light beyond the linear optical regime remains an open challenge. Nonlinear optical interactions, such as wave mixing in nonlinear flat optics, offer a powerful platform to unlock new degrees of freedom and functionalities for generating and detecting structured light. In this study, we experimentally demonstrate the non-trivial structuring of third-harmonic light enabled by the addition of total angular momentum projection in a nonlinear, isotropic flat optics element-a single thin film of amorphous silicon. We identify the total angular momentum projection and helicity as the most critical properties for analyzing the experimental results. The theoretical approach we propose, supported by numerical simulations, offers quantitative predictions for light structuring through nonlinear wave mixing under various pumping conditions, including vectorial and non-paraxial pump light. Notably, we reveal that the shape of third-harmonic light is highly sensitive to the polarization state of the pump. Our findings demonstrate that harnessing the addition of total angular momentum projection in nonlinear wave mixing can be a powerful strategy for generating and detecting precisely controlled structured light.

Multiple normalized solutions for Schrödinger-Maxwell equation with Sobolev critical exponent and mixed nonlinearities

ABSTRACT This paper is dedicated to investigating the existence of normalized ground state solutions to a class of Kirchhoff problems, where the mixed nonlinearity exhibits critical exponential growth of the Trudinger–Moser type. By utilizing an abstract critical point theorem, we have obtained several new existence results. Our conclusions extend and complement some known results in previous papers.

Nonlinear Internal Wave Mixing Observations Within the Interior of a River Plume

By using OPFs to transmit data in the form of light, fiber-optic communication has completely changed the way in-formation is transmitted. This technology's remarkable benefits, such as much lower attenuation, increased band-width capacity, and decreased crosstalk over extended distances, make it superior to conventional electrical trans-mission techniques. The deployment of Wavelength Division Multiplexing (WDM), which maximizes bandwidth usage by enabling several data channels to be carried simultaneously at various wavelengths, is one of the rapid breakthroughs in optical fiber (OPF) technology that are examined in this research. However, nonlinear event in-volved Self-Phase Modulation (S.P.M.), Four-Wave Mixing (FWM), and Stimulated Raman Scattering (S.R.S.) that are inherent in fiber optics frequently impair the performance of WDM systems. Signal distortion and energy loss may result from these causes. The study examines many digital modulation methods, such as Differential Phase Shift Keying (DPSK), Return-to-Zero (RZ), and Non-Return-to-Zero (NRZ), and evaluates how they affect system performance and efficiency at high bit-rates. The results point to a future path for optical communication system research and development, showing that DPSK provides improved sensitivity and lower bit error rates, while RZ modulation exhibits higher resilience to nonlinear effects.

The coaxial tilt-rotor (CTR) unmanned aerial vehicle (UAV) is a distinctive multirotor aircraft which incorporates two coaxial tilt-rotor (CTR) modules and a rear rotor, enabling it to execute diverse maneuvers and achieve high-speed forward flight. In this work, according to the specific configuration of the CTRUAV, a cascaded fixed-time (FT) control strategy and a nonlinear state-varying mixer are proposed to improve the CTRUAV's stability, transient performance, and robustness. The FT convergent property of the designed control strategy is validated and discussed by simulations. Finally, real-time experiments are implemented on a self-built CTRUAV experimental platform. The simulations and experimental results with different controllers demonstrate the effectiveness and superiority of the designed control method.

Abstract By using critical point theory in combination with periodic approximations, we obtain novel sufficient conditions for the existence of nontrivial homoclinic solutions for a class of periodic partial difference equations with sign-changing mixed nonlinearities. Notably, in certain specific cases, a necessary and sufficient condition is also established.

Hyperspectral unmixing (HU) aims to decompose mixed pixels into their constituent spectral signatures and estimate their corresponding fractional abundances. Recently, the nonlinear spectral mixing model (NLMM) has advanced significantly and offered strong physical interpretability. However, the effective integration of physics-driven NLMM with data-driven deep learning (DL) approaches still remains a critical challenge. To address this, we propose a diffusion-enhanced autoencoder (DEAE), a novel unsupervised framework that innovatively incorporates the diffusion model (DM) into nonlinear HU. DEAE introduces the residual second-order attention mechanism to capture global spectral information, adaptively weighting informative bands while compressing redundant bands. Subsequently, we integrate the extended multilinear mixing model (EMLM) into the DM-enhanced decoder, which extracts latent features from the linear autoencoder’s output and generates an enhanced reconstructed image while simultaneously estimating the transition probabilities of EMLM. Finally, a nonlinear decoder outputs the ultimate reconstructed image based on both the enhanced reconstructed image and transition probabilities. Experiments conducted on synthetic and three real-world datasets demonstrate the superior performance of DEAE compared to the state-of-the-art methods based on both LMM and NLMM.

A Nonlinear Ultrasonic Wave Mixing Method for Micro-damage Detection of 316L Austenitic Stainless Steel

We propose and demonstrate a modulation transfer protocol to increase the detection sensitivity of a Rydberg RF receiver to fields out of resonance from the transition between Rydberg levels. This protocol is based on a phase modulation of the control field used to create the Electromagnetically Induced Transparency signal. The nonlinear wave mixing of the multi-component coupling laser and the probe laser transfers the modulation to the probe laser, which is used for the RF-field detection. The measurements compare well with semi-classical simulations of atom–light interaction and show an improvement in the RF bandwidth of the sensor and an improved sensitivity of the response to weak fields.

We introduce a trident edge coupler design optimized for the simultaneous coupling of two widely separated wavelengths (2 µm and 1 µm) between a lensed fiber and a 600-nm-thick X-cut lithium-niobate-on-insulator (LNOI) waveguide. These wavelengths are commonly encountered in nonlinear wave mixing applications, representing either the fundamental and second harmonics in second harmonic generation (SHG) processes or the leading and trailing edges of an octave-spanning spectrum generated through broadband nonlinear processes such as frequency comb or supercontinuum generation. Achieving efficient coupling between fibers and strongly confined waveguides in integrated platforms, such as LNOI, can be challenging due to the significant difference in spot sizes between the two wavelengths. Our trident edge coupler offers coupling losses below 1.4 dB for the 2 µm and 1 µm spots simultaneously, showcasing an average transmission enhancement of around 10% compared to the baseline of a single linear taper. Furthermore, it enables a reduction of transmission at 1.5 µm, a typical pump wavelength, with an attenuation of transmission over 10 dB compared to those at the 2 µm and 1 µm wavelengths.

The paper considers a parallel electromagnetic oscillating circuit with a nonlinear inductance under conditions of excitation of ferroresonances. Physical mechanisms of dynamic self-regulation of the system of spin magnetic moments of ferromagnetic and ferrimagnetic dielectrics in the surrounding magnetic field are established. It is shown that upon entering the magnetic saturation regime, the effect of dynamic antiferroresonance is observed, due to the cyclic reversal of magnetization in the internal magnetic field. This effect has a collector character and corresponds to the maximum potential energy of the magnetic moment in the field and the antiparallel orientation of the moment with respect to the field. Such regimes are realized in thermodynamically non-equilibrium conditions and are correlated with unstable equilibrium positions of the corresponding mechanical analogues. The resulting forms of oscillations correlate with the dynamics of an inverted pendulum and have a significantly non-harmonic character. Autosynchronization of frequencies and nonlinear mixing of such forms with quasi-static modes imitating the time form of external excitation of oscillations were revealed. It is shown that the nonlinearity of ferromagnetic elements self-limits the height of resonance maxima. And on the other hand, it contributes to the cascade transport of energy by the spectrum of disturbances, which can have negative consequences when exciting low-frequency ferroresonances in power grids. The effect of dynamic antiferroresonance has the opposite direction to the known quasi-static behavior of the system of spin magnetic moments in an external field and must be taken into account when calculating and operating electrical systems with nonlinear inductances. Examples of collector self-oscillating modes similar in their physical mechanisms in nonlinear contact tribodynamics systems are given

Silicon nitride is widely used in integrated photonics for optical nonlinear wave mixing due to its low optical losses combined with relatively high nonlinear optical properties and a wide‐range transparency window. It is known that a higher concentration of Si in silicon‐rich nitride (SRN) magnifies both the nonlinear response and optical losses, including nonlinear losses. To address the trade‐off, four‐wave mixing (FWM) is implemented in over a hundred SRN waveguides prepared by plasma‐enhanced chemical vapor deposition in a wide range of SRN refractive indices varying between 2.5 and 3.2 (measured in the C‐band). It is determined that SRN with a refractive index of about 3 maximizes the FWM efficiency for continuous‐wave operation, indicating that the refractive index of SRN is indeed a crucial optimization parameter for nonlinear optics applications. The FWM efficiency is limited by large nonlinear optical losses observed in SRN waveguides with indices larger than 2.7, which are not related to two‐photon absorption. Finally, the third‐order susceptibility and the nonlinear refractive index are estimated for multiple SRN refractive indices, and, specifically, the nonlinearities as large as and are estimated in a waveguide with an SRN refractive index of 3.2.

Workforce thresholds and the non-linear association between registered nurse staffing and care quality in long-term residential care: A retrospective longitudinal study of English care homes with nursing

This paper is concerned with the existence of multiple normalized solutions to the elliptic problems { Δ 2 u = λu + h ( ϵx ) | u | q − 2 u + | u | p − 2 u in R N , ∫ R N u 2 d x = c , where c, 0 $ ]]> ϵ > 0 , N ≥ 5 , 2 < q < 2 + 8 N < p ≤ 4 ∗ := 2 N N − 4 , λ ∈ R is a Lagrangian multiplier and h : R N → [ 0 , ∞ ) is a continuous function. We find some 0 $ ]]> c 0 > 0 and present a class of reasonable assumptions on h to guarantee that the numbers of normalized solutions are at least the numbers of global maximus points of h when ε is small enough and 0 < c ≤ c 0 .