Nonlinear Coupling Coefficient Research Articles

Generation of a tripartite photonic state via a double-Λ configuration in a four-level system

Triphotons have a more abundant energy structure compared to biphotons. Furthermore, as the number of photons increases, excellent properties such as entangled multi-qubit states, high security, flexibility, and information capacity are observed. This leads to a growing demand for multi-body quantum information processing. Here, a method is proposed to generate a three-photon entangled state using a single six-wave mixing process in an atomic ensemble. The research examines the temporal correlation characteristics of the triphoton produced in photon coincidence counting measurements, with a focus on the linear and nonlinear susceptibilities of the six-wave mixing process. These properties primarily depend on the fifth-order nonlinear coupling coefficients responsible for the damping Rabi oscillations and the group delay determined by the longitudinal detuning function. To enhance the nonlinear interaction between the optical field and the atomic ensemble, placing the atomic ensemble in a high-quality cavity and utilizing laser cooling techniques to eliminate the internal Doppler broadening effect in the atomic gas hold promise.

Design of Horizontally Stacked AlN and Dielectric Cores Transverse Quasi‐Phase‐Matched Channel Waveguide for Squeezed Light Generation

AlN is a promising candidate for photonic integrated circuits. In this study, horizontally stacked transverse quasi‐phase‐matched (QPM) waveguides with an AlN center core and Si3N4, Ta2O5, and TiO2 side cores were designed to generate squeezed light at 920 nm. The squeezing level was calculated by considering the propagation loss at the wavelengths of the squeezed light and pump light. Using TiO2 for the side cores enhanced the electric field amplitude of the pump light in the AlN center core, and a high nonlinear coupling coefficient was obtained. Owing to the small propagation loss of the AlN waveguide on sapphire and high nonlinear coupling coefficient of the transverse QPM with TiO2 side cores, a squeezing level of over 8.1 dB was expected with a 1 cm long waveguide and pump power of 70 mW.

Inducing tunable conventional photon blockade and two-photon blockade in a second-order nonlinear system with two-level atoms

We have achieved a conventional photon blockade and two-photon blockade in a second-order nonlinear system with a two-level atom embedded in a high-frequency cavity. The physical mechanisms behind the implementation of both types of photon blockade are explained, and analytical conditions for achieving a conventional photon blockade are derived, which are consistent with the numerical solutions of the master equation in the steady-state limit. By appropriately setting the system parameters, we can achieve simultaneous conventional photon blockade in the high-frequency cavity and two-photon blockade in the low-frequency cavity. The effects of driving factors and environmental temperature on photon blockade are analyzed. The adjustability of the coupling coefficient between the high-frequency cavity and the atom, as well as the nonlinear coupling coefficient between different nanocavities, is discussed in the context of implementing conventional photon blockades. The tunability of these coupling coefficients may significantly reduce the experimental complexity of implementing the system.

Buried annealed proton-exchanged waveguide in periodically-poled MgO:LiTaO3 fabricated by surface-activated bonding for high-power wavelength conversion

Watt-class UV laser lights with symmetric spatial modes are suitable for high-resolution industrial applications. Channel waveguides with a guided mode of several ten microns diameter in MgO:LiTaO3 enhance integration capability while avoiding photorefractive damages during high-power wavelength conversion. We focused on buried waveguides fabricated by proton exchange, surface-activated bonding (SAB), and proton diffusion processes in periodically-poled (PP) MgO:LiTaO3. In this work, the mode profiles were simulated using the proton diffusion coefficients estimated by secondary ion mass spectrometry. Using the simulation results, the buried waveguides with a mode diameter larger than 30 μm were fabricated. By adopting designed PP structures, second harmonic generation (SHG) devices at a wavelength of 532 nm were fabricated. The nonlinear coupling coefficient was estimated to be 0.15 W−1/2 cm−1. Compared to the conventional annealed proton-exchanged waveguide SHG device without SAB, symmetric guided modes were obtained while maintaining the nonlinear coupling coefficient.

Quadripartite quantum steering generated by single-pass cascaded nonlinear processes

Quantum steering has become an important resource for quantum information due to its unique asymmetry. In this paper, quadripartite quantum steering generated by single-pass nondegenerate optical parametric amplification cascaded with a sum-frequency process is investigated. Firstly, an idler beam is produced by a different-frequency process between pump and signal. Secondly, a sum-frequency beam is generated by a cascaded sum-frequency process between idler beam and pump in the same optical superlattice. Quadripartite quantum steering among pump, signal, idler and sum-frequency beams is demonstrated based on the criterion for multipartite quantum steering. The influences of nonlinear coupling coefficients κ, dimensionless propagation length ξ, and the initial values of pump and signal on the variation characteristic of the quadripartite steering are also investigated. The results indicate that slightly larger nonlinear coupling coefficients of cascaded nonlinear processes and weaker signals can achieve better quadripartite quantum steering. This simple quadripartite quantum steering preparation scheme does not require a resonant cavity and is easier to implement experimentally, with potential applications in quantum communication and computing.

An efficient numerical method for the anisotropic phase field dendritic crystal growth model

In this paper, we propose and analyze an efficient numerical method for the anisotropic phase field dendritic crystal growth model, which is challenging because we are facing the nonlinear coupling and anisotropic coefficient in the model. The proposed method is a two-step scheme. In the first step, an intermediate solution is computed by using BDF schemes of order up to three for both the phase-field and heat equations. In the second step the intermediate solution is stabilized by multiplying an auxiliary variable. The key of the second step is to stabilize the overall scheme while maintaining the convergence order of the stabilized solution. In order to overcome the difficulty caused by the gradient-dependent anisotropic coefficient and the nonlinear terms, some stabilization terms are added to the BDF schemes in the first step. The second step makes use of a generalized auxiliary variable approach with relaxation. The Fourier spectral method is applied for the spatial discretization. Our analysis shows that the proposed scheme is unconditionally stable and has accuracy in time up to third order. We also provide a sophisticated implementation showing that the computational complexity of our schemes is equivalent to solving two linear equations and some algebraic equations. To the best of our knowledge, this is the cheapest unconditionally stable schemes reported in the literature. Some numerical examples are given to verify the efficiency of the proposed method.

Performance analysis of nonlinear piezoelectric energy harvesting system under bidirectional excitations

In this paper, a cantilever beam piezoelectric energy harvester model of nonlinear partial differential equation based on Hamilton's Principle is established. A piezoelectric device using a bimorph cantilever beam with a fixed is subjected to horizontal and vertical excitation. Based on the Euler-Bernoulli thin beam model assumptions and inextensible deformation, the analysis further includes the effects of geometric nonlinearity and damping nonlinearity. The reduced-order nonlinear partial differential equations of motion with electro-mechanical coupling distributed parameter are derived by using Galerkin method. By using the method of multiple scales and solving the equations of motion, the energy harvester in its fundamental first-order resonance response is analyzed and the amplitudes of fundamental transverse deflection, output voltage and output power are determined. The major influence aspects of excitation amplitude, linear damping coefficient, nonlinear damping coefficient, impedance, nonlinear electro-mechanical coupling coefficient on transverse deflection, voltage and power are analyzed. The result shows that the linear damping coefficient and resistance affect the initial threshold of parametric excitation. The combination of parametric excitation and direct excitation gives full play to the advantages of parametric excitation and improve the energy conversion efficiency of the energy harvesting system.

Benchmarking magnetised three-wave coupling for laser backscattering: analytic solutions and kinetic simulations

Understanding magnetised laser–plasma interactions is important for controlling magneto-inertial fusion experiments and developing magnetically assisted radiation and particle sources. For nanosecond pulses at non-relativistic intensities, interactions are dominated by coherent three-wave interactions, whose nonlinear coupling coefficients became known only recently when waves propagate at oblique angles with the magnetic field. In this paper, backscattering coupling coefficients predicted by warm-fluid theory are benchmarked using particle-in-cell simulations in one spatial dimension, and excellent agreements are found for a wide range of plasma temperatures, magnetic field strengths and laser propagation angles, when the interactions are mediated by electron-dominant hybrid waves. Systematic comparisons between theory and simulations are made possible by a rigorous protocol. On the theory side, the initial boundary value problem of linearised three-wave equations is solved, and the transient-time solutions allow the effects of growth and damping to be distinguished. On the simulation side, parameters are carefully chosen and calibration runs are performed to ensure that comparisons are well controlled. Fitting simulation data to analytical solutions yields numerical growth rates that match theory predictions within error bars. Although warm-fluid theory is found to be valid for a wide parameter range, genuine kinetic effects have also been observed.

Stress-Induced Transformations of Polarization Switching in CuInP2S6 Nanoparticles

Using the Landau-Ginzburg-Devonshire approach, we study stress-induced transformations of polarization switching in ferrielectric CuInP2S6 nanoparticles for three different shapes: a disk, a sphere, and a needle. Semiconducting properties of a nanoparticle are modeled by a surface charge layer, whose effective screening length can be rather small due to the field-effect. We reveal a very strong and unusual influence of hydrostatic pressure on the appearance of polarization switching in CuInP2S6 nanoparticles, hysteresis loops shape, magnitude of the remanent polarization, and coercive fields, and explain the effects by the anomalous temperature dependence and "inverted" signs of CuInP2S6 linear and nonlinear electrostriction coupling coefficients. In particular, by varying the sign of the applied pressure (from tension to compression) and its magnitude (from zero to several hundreds of MPa), quasi-static hysteresis-less paraelectric curves can transform into double, triple, pinched, or single hysteresis loops. Due to the sufficiently wide temperature and pressure ranges of double, triple, and pinched hysteresis loop stability (at least in comparison with many other ferroelectrics), CuInP2S6 nanodisks can be of particular interest for applications in energy storage (in the region of double loops), CuInP2S6 nanospheres maybe suitable for dynamic random access multibit memory, and CuInP2S6 nanoneedles are promising for non-volatile multibit memory cells (in the regions of triple and pinched loops). The stress control of the polarization switching scenario allows the creation of advanced piezo-sensors based on CuInP2S6 nanocomposites.

Quantum Langevin theory for two coupled phase-conjugated electromagnetic waves

While loss-gain-induced Langevin noises have been intensively studied in quantum optics, the effect of a complex-valued nonlinear coupling coefficient on the noises of two coupled phase-conjugated optical fields has never been questioned before. Here, we provide a general macroscopic phenomenological formula of quantum Langevin equations for two coupled phase-conjugated fields with linear loss (gain) and complex nonlinear coupling coefficient. The macroscopic phenomenological formula is obtained from the coupling matrix to preserve the field commutation relations and correlations, which does not require knowing the microscopic details of light-matter interaction and internal atomic structures. To validate this phenomenological formula, we take spontaneous four-wave mixing in a double-$\Lambda$ four-level atomic system as an example to numerically confirm that our macroscopic phenomenological result is consistent with that obtained from the microscopic Heisenberg-Langevin theory. Finally, we apply the quantum Langevin equations to study the effects of linear gain and loss, complex phase mismatching, as well as complex nonlinear coupling coefficient in entangled photon pair (biphoton) generation, particularly to their temporal quantum correlations.

Squeezed states generation by nonlinear plasmonic waveguides: a novel analysis including loss, phase mismatch and source depletion

In this article, a full numerical method to study the squeezing procedure through second harmonic generation process is proposed. The method includes complex nonlinear coupling coefficient, phase mismatch, and pump depletion. Attention has been also paid to the effects of accumulated noises in this work. The final form of the numerical formula seems to be much simpler than the analytical solutions previously reported. The function of this numerical method shows that it works accurately for different mechanisms of squeezed state generations and does not suffer from instabilities usually encountered even for non-uniform, coarse steps. The proposed method is used to examine the squeezing procedure in an engineered nonlinear plasmonic waveguide. The results show that using the nonlinear plasmonic waveguide, it is possible to generate the squeezed states for the pump and the second harmonic modes with high efficiency in a propagation length as short as 2 mm which is much shorter than the needed length for the traditional nonlinear lithium niobate- based optical waveguides being of the order of 100 mm. This new method of squeezed states generation may find applications in optical communication with a noise level well below the standard quantum limit, in quantum teleportation, and in super sensitive interferometry.

Operator split, Picard iteration and JFNK methods based on nonlinear CMFD for transient full core models in the coupling multiphysics environment

Operator Split (OS), Picard iteration and Jacobian-free Newton Krylov (JFNK) methods based on nonlinear coarse mesh finite difference (CMFD) with nodal expansion methods (NEM) are respectively introduced to solve the transient full core coupled models in the COupling Multiphysics Environment (COME). In the COME, in addition to the traditional OS and Picard coupled methods, we develop two different JFNK-based coupled methods with physics and algebraic-based hybrid preconditioners at each time step: OS_JFNK and JFNK coupled methods. Specifically, the efficient JFNK method is applied to solve CMFD discrete models of only neutronics in the OS framework for OS_JFNK coupled strategies or whole Neutronics-Thermal Hydraulic (N-TH) coupled models for JFNK coupled methods. Then nonlinear corrective coupling coefficients are updated by the two-node NEM every few Newton steps at each time step. Six cases of NEACRP 3D core transient benchmarks are analyzed and numerical solutions of OS, OS_JFNK, Picard and JFNK methods in the COME generally agree well with other published solutions. JFNK and Picard coupled methods can track the reference solutions better than OS and OS_JFNK coupled methods due to multiple iterations or simultaneous solutions between neutronics and TH models in the tight coupled form. Furthermore, OS_JFNK or JFNK methods can obtain higher computational efficiency than OS or Picard methods with or without the fission source extrapolation acceleration, respectively, which indicates the potential of the developed COME using different coupled methods for the transient full core multiphysics coupled problems.

Hydrodynamic coefficients of the DARPA SUBOFF AFF-8 in rotating arm maneuver - Part Ⅱ: Test results and discussion

The study of submarine maneuverability is an important part in the overall design of submarines. The goal of this investigation is to study the hydrodynamic coefficients of SUBOFF AFF-8 in rotating arm maneuver. This paper consists of two parts, which deal with the test technology and test results, respectively. Part Ⅱ of this paper presents the angular velocity-dependent derivatives and spatial coupling coefficients of SUBOFF AFF-8 and investigates the forces and moments in steady turn. The forces and moments of SUBOFF AFF-8 are investigated and the hydrodynamic coefficients of SUBOFF AFF-8 are fitted. The results show the coefficients with r in the lower corner represent the linearity of hydrodynamic forces. In order to get more accurate nonlinear coefficients and coupling coefficients, the drift angle should not be too small in the rotating arm test. When SUBOFF AFF-8 has both drift angle and attack angle, the nonlinear degree of rotation increases sharply, which will bring great difficulties to the measurement of forces and moments.

Resonant and near-resonant internal wave triads for non-uniform stratifications. Part 2. Vertically bounded domain with mild-slope bathymetry

Weakly nonlinear internal wave–wave interaction is a key mechanism that cascades energy from large to small scales, leading to ocean turbulence and mixing. Oceans typically have a non-uniform density stratification profile; moreover, submarine topography leads to a spatially varying bathymetry ( $h$ ). Under these conditions and assuming mild-slope bathymetry, we employ multiple-scale analysis to derive the wave amplitude equations for weakly nonlinear wave–wave interactions. The waves are assumed to have a slowly (rapidly) varying amplitude (phase) in space and time. For uniform stratifications, the horizontal wavenumber ( $k$ ) condition for waves (1, 2, 3), given by ${k}_{(1,a)}+{k}_{(2,b)}\!+\!{k}_{(3,c)}\!=\!0$ , is unaffected as $h$ is varied, where $(a,b,c)$ denote the mode number. Moreover, the nonlinear coupling coefficients (NLC) are proportional to $1/h^2$ , implying that triadic waves grow faster while travelling up a seamount. For non-uniform stratifications, triads that do not satisfy the condition $a=b=c$ may not satisfy the horizontal wavenumber condition as $h$ is varied, and unlike uniform stratification, the NLC may not decrease (increase) monotonically with increasing (decreasing) $h$ . NLC, and hence wave growth rates for weakly nonlinear wave–wave interactions, can also vary rapidly with $h$ . The most unstable daughter wave combination of a triad with a mode-1 parent wave can also change for relatively small changes in $h$ . We also investigate higher-order self-interactions in the presence of a monochromatic, small-amplitude topography; here, the topography behaves as a zero-frequency wave. We derive the amplitude evolution equations and show that higher-order self-interactions might be a viable mechanism of energy cascade.

Jacobian-free Newton Krylov two-node coarse mesh finite difference based on nodal expansion method

A Jacobian-Free Newton Krylov Two-Nodal Coarse Mesh Finite Difference algorithm based on Nodal Expansion Method (NEM_TNCMFD_JFNK) is successfully developed and proposed to solve the three-dimensional (3D) and multi-group reactor physics models. In the NEM_TNCMFD_JFNK method, the efficient JFNK method with the Modified Incomplete LU (MILU) preconditioner is integrated and applied into the discrete systems of the NEM-based two-node CMFD method by constructing the residual functions of only the nodal average fluxes and the eigenvalue. All the nonlinear corrective nodal coupling coefficients are updated on the basis of two-nodal NEM formulation including the discontinuity factor in every few newton steps. All the expansion coefficients and interface currents of the two-node NEM need not be chosen as the solution variables to evaluate the residual functions of the NEM_TNCMFD_JFNK method, therefore, the NEM_TNCMFD_JFNK method can greatly reduce the number of solution variables and the computational cost compared with the JFNK based on the conventional NEM. Finally the NEM_TNCMFD_JFNK code is developed and then analyzed by simulating the representative PWR MOX/UO2 core benchmark, the popular NEACRP 3D core benchmark and the complicated full-core pin-by-pin homogenous core model. Numerical solutions show that the proposed NEM_TNCMFD_JFNK method with the MILU preconditioner has the good numerical accuracy and can obtain higher computational efficiency than the NEM-based two-node CMFD algorithm with the power method in the outer iteration and the Krylov method using the MILU preconditioner in the inner iteration, which indicates the NEM_TNCMFD_JFNK method can serve as a potential and efficient numerical tool for reactor neutron diffusion analysis module in the JFNK-based multiphysics coupling application.

Landau damping of electron-acoustic waves due to multi-plasmon resonances

The linear and nonlinear theories of electron-acoustic waves (EAWs) are studied in a partially degenerate quantum plasma with two-temperature electrons and stationary ions. The initial equilibrium of electrons is assumed to be given by the Fermi–Dirac distribution at finite temperature. By employing the multi-scale asymptotic expansion technique to the one-dimensional Wigner–Moyal and Poisson equations, it is shown that the effects of multi-plasmon resonances lead to a modified complex Korteweg–de Vries (KdV) equation with a new nonlocal nonlinearity. In addition to giving rise to a nonlocal nonlinear term, the wave–particle resonance also modifies the local nonlinear coupling coefficient of the KdV equation. The latter is shown to conserve the number of particles; however, the wave energy decays with time. A careful analysis shows that the two-plasmon resonance is the dominant mechanism for nonlinear Landau damping of EAWs. An approximate soliton solution of the KdV equation is also obtained, and it is shown that the nonlinear Landau damping causes the wave amplitude to decay slowly with time compared to the classical theory.

Two dimensionless parameters and a mechanical analogue for the HKB model of motor coordination

The widely cited Haken–Kelso–Bunz (HKB) model of motor coordination is used in an enormous range of applications. In this paper, we show analytically that the weakly damped, weakly coupled HKB model of two oscillators depends on only two dimensionless parameters; the ratio of the linear damping coefficient and the linear coupling coefficient and the ratio of the combined nonlinear damping coefficients and the combined nonlinear coupling coefficients. We illustrate our results with a mechanical analogue. We use our analytic results to predict behaviours in arbitrary parameter regimes and show how this led us to explain and extend recent numerical continuation results of the full HKB model. The key finding is that the HKB model contains a significant amount of behaviour in biologically relevant parameter regimes not yet observed in experiments or numerical simulations. This observation has implications for the development of virtual partner interaction and the human dynamic clamp, and potentially for the HKB model itself.

Quantum Kerr nonlinear coupler: analytical versus phase-space method

The generation of squeezed states of light in a two-mode Kerr nonlinear directional coupler (NLDC) was investigated using two different methods in quantum mechanics. First, the analytical method, a Heisenberg-picture-based method where the operators are evolving in time but the state vectors are time-independent. In this method, an analytical solution to the coupled Heisenberg equations of motion for the propagating modes was proposed based on the Baker–Hausdorff (BH) formula. Second, the phase space method, a Schrödinger-picture-based method in which the operators are constant and the density matrix evolves in time. In this method, the quantum mechanical master equation of the density matrix was converted to a corresponding classical Fokker–Planck (FP) equation in positive-P representation. Then, the FP equation was converted to a set of stochastic differential equations using Ito rules. The strengths and weaknesses of each method are discussed. Good agreement between both methods was achieved, especially at early evolution stages and lower values of linear coupling coefficient. On one hand, the analytical method seems insensitive to higher values of nonlinear coupling coefficients. Nevertheless, it demonstrated better numerical stability. On the other hand, the solution of the stochastic equations resulting from the phase space method is numerically expensive as it requires averaging over thousands of trajectories. Besides, numerically unstable trajectories appear with positive-P representation at higher values of nonlinearity.

Nonlinear-mode-coupling-induced soliton crystal dynamics in optical microresonators

Dissipative Kerr solitons based on microresonators have wide applications from optical communications to optical ranging for the high-repetition rate and broad bandwidth. Restricted by the bending losses and dispersion control of the optical waveguide, it could be hard to further realize ultrahigh-repetetion rate reaching several terahertz by simply reducing the size of microresonators. Soliton crystals, which completely fill the microresonator with a series of equidistant temporal pulses, can be an effective approach to realize ultrahigh-repetition rate in the common cavity length. In this paper, we investigate the generation of soliton crystals in the presence of nonlinear mode coupling, which can induce a modulation on the background wave and modify the cavity dynamics. Under the condition of suitable wave vector mismatch and nonlinear-coupling-coefficient, high-deterministic perfect soliton crystals can be realized. Besides, the drifting behavior of the soliton crystals is demonstrated to be determined by the match between the wave vector mismatch and nonlinear coupling coefficient. Finally, we successfully observe the recrystallization of the perfect soliton crystals.

Experimental investigations of seeding mechanisms of TMI in rod fiber amplifier using spatially and temporally resolved imaging.

In this work we investigate transverse mode instability (TMI) in the presence of pump intensity noise and a controlled perturbation of the input coupling for a rod-type fiber amplifier using spatially and temporally resolved imaging (ST). We show that inherent pump intensity noise from the power supply can define significant peaks in the resulting TMI spectrum. ST measurements show that the TMI in the transition region consists of different orientations of LP11. This finding indicates that the simple picture of TMI being seeded by the combination of a static initial fraction of LP11 and pump or signal intensity noise is not valid for our measurements. Furthermore we present seeding of TMI by perturbing the input coupling dynamically. ST measurements of the resulting TMI as a function of perturbation frequency provides quantitative information regarding the frequency response of the non-linear coupling coefficient. Finally, ST measurements of the resulting TMI as a function of signal power shows that the TMI experiences an exponential gain long before visible beam fluctuations appear.