Wavelength Limit Research Articles

First principles homogenization of periodic metamaterials and application to wire media

Here, we present an overview of a first principles homogenization theory of periodic metamaterials. It is shown that in a rather general context it is possible to formally introduce effective parameters that describe the time evolution of macroscopic (slowly-varying in space) initial states of the electromagnetic field using an effective medium formalism. The theory is applied to different types of characterized by a strong spatial dispersion in the long wavelength limit. It is highlighted that the spatial dispersion may tailor in unique ways the wave phenomena in wire metamaterials leading to exotic tunneling effects and broadband lossless anomalous dispersion.

Magnon Landau Levels and Spin Responses in Antiferromagnets.

We study gauge fields produced by gradients of the Dzyaloshinskii-Moriya interaction and propose a model of an AFM topological insulator of magnons. In the long wavelength limit, the Landau levels induced by the inhomogeneous Dzyaloshinskii-Moriya interaction exhibit relativistic physics described by the Klein-Gordon equation. The spin Nernst response due to the formation of magnonic Landau levels is compared to similar topological responses in skyrmion and vortex-antivortex crystal phases of AFM insulators. Our studies show that AFM insulators exhibit rich physics associated with topological magnon excitations.

Manifestly gauge-invariant cosmological perturbation theory from full loop quantum gravity

We apply the full theory of Loop Quantum Gravity (LQG) to cosmology and present a top-down derivation of gauge-invariant cosmological perturbation theory from quantum gravity. The derivation employs the reduced phase space formulation of LQG and the new discrete path integral formulation defined in arXiv:1910.03763. We demonstrate that in the semiclassical approximation and continuum limit, the result coincides with the existing formulation of gauge-invariant cosmological perturbation theory in e.g. arXiv:0711.0117. Time evolution of cosmological perturbations is computed numerically from the new cosmological perturbation theory of LQG, and various power spectrums are studied for scalar mode and tensor mode perturbations. Comparing these power spectrums with predictions from the classical theory demonstrate corrections in the ultra-long wavelength regime. These corrections are results from the lattice discretization in LQG. In addition, tensor mode perturbations at late time demonstrate the emergence of spin-2 gravitons as low energy excitations from LQG. The graviton has a modified dispersion relation and reduces to the standard graviton in the long wavelength limit.

Dynamical polarization and plasmons in noncentrosymmetric metals

We study the dynamical polarization function and plasmon modes for spin-orbit coupled noncentrosymmetric metals (NCMs). These systems have different Fermi surface topology for Fermi energies above and below the spin degenerate point which is also known as the band touching point (BTP). We calculate the exact dynamical polarization function numerically and also provide its analytical expression in the long wavelength limit. We obtain the plasmon dispersion within the framework of random phase approximation. In NCMs, there is a finite energy gap in between intra and interband particle hole continuum (PHC) for vanishing excitation wavevector. In the long wavelength limit, the width of interband PHC behaves differently for Fermi energies below and above the BTP as a clear signature of the Fermi surface topology change. We find a single undamped optical plasmon mode lying in between the intra and interband PHC for Fermi energies above and below the BTP. The plasmon mode below the BTP has smaller velocity than that of above the BTP. It is interesting to find that as we tune the Fermi energy around the BTP, the plasmon mode becomes damped within a range of e-e interaction strength. For Fermi energies above and below the BTP, we also obtain an approximate analytical result of plasma frequency and plasmon dispersion which match well with their numerical counterparts in the long wavelength limit. The plasmon dispersion is $\propto q^2$ with $q$ being the wave vector for plasmon excitation in the long wavelength limit. We find that varying the carrier density with fixed e-e interaction strength or vice versa does not change the number of undamped plasmon mode, although damped plasmon modes can be more in number for some values of these parameters. We demonstrate our results by calculating the loss function and optical conductivity which can be measured in experiments.

A simple theory of mixtures for the study of the temperature dependence of thermo-structural properties of Al-Ga liquid alloy

A simple theory of mixtures for symmetric alloys was used to study the thermodynamic and structural properties of the Al-Ga alloy in the liquid state at 1023 K. The computed thermodynamic properties are in a very good agreement with the observed values and show that the alloy is weakly interacting. The computed structural properties show that the Al-Ga alloy is segregating in nature which is in agreement with the observed values. The excess free energy of mixing, activity of monomers and concentration fluctuation in the long wavelength limit was extrapolated to higher temperatures by optimising the temperature dependent parameters. As the temperature increases, the behaviour of the alloy shifts towards the ideality.

Optical properties of bismuth tellurite glasses doped with holmium oxide

The study of polarizability, optical basicity, and electric susceptibility carried out on the new and very rare set of bismuth - tellurite glasses doped with Ho3+ ions were fabricated by the conventional melt quenching process. The non-crystalline nature was confirmed by X-ray diffractometer measurements. Physical properties such as rare earth ion concentration, interionic distance, polaron radius, and average tellurium - tellurium separation were investigated by appropriate formulae. By UV absorption spectra, optical properties of Ho3+ ions doped glasses were found in the wavelength limit from 400 to 700 nm. The optical properties like optical dielectric constant, electronic polarizability, metallization criterion, electronegativity, optical basicity, and electric susceptibility were measured with appropriate mathematical relations. The impact of Ho3+ ions on nonlinearity in optical parameters discloses bismuth tellurite glass as a new applicant for holmium doped fiber amplifier applications.

Trade-offs in absorption and scattering by nanophotonic structures.

Trade-offs between absorption and scattering cross sections of lossy obstacles confined to an arbitrarily shaped volume are formulated as a multi-objective optimization problem solvable by Lagrangian-dual methods. Solutions to this optimization problem yield a Pareto-optimal set, the shape of which reveals the feasibility of achieving simultaneously extremal absorption and scattering. Two forms of the trade-off problems are considered involving both pre-assigned loss and reactive material parameters. Numerical comparisons between the derived multi-objective bounds and several classes of realized structures are made. Additionally, low-frequency (electrically small, long wavelength) limits are examined for certain special cases.

Reconstructed Gaussian basis to characterize flexural wave collimation in plates with periodic arrays of annular acoustic black holes

While embedding acoustic black holes (ABHs) in plates has proved to be a lightweight and useful solution for noise and vibration reduction, their potential for wave manipulation is only in its beginnings. Recent studies seem to indicate that amazing properties can be attained with them. A plate with ABH indentations can be viewed as a single-phase metamaterial that can alter wave propagation direction thanks to the ABH power-law thickness profile. Some typical unconventional dispersion properties of multi-phase metamaterials, like collimation or negative refraction, can be recovered in a simple way. This work focuses on the collimation of flexural waves in plates by means of ABH arrangements. The first goal of the paper is to propose a predictive semi-analytical method to describe such phenomenon in an efficient manner. The method is also expected to allow one to perform quick parametric analyses for different ABH configurations. To that purpose, the Gaussian expansion method (GEM) is extended to deal with ABH phononic crystals on infinite plates. The Lagrangian for a single cell is built and a new basis of Gaussian functions is constructed satisfying the periodic boundary conditions of the problem. The Rayleigh-Ritz method is then adopted to compute the displacement field of annular and circular ABH arrays. The accuracy of the reconstructed GEM approach is validated by comparing dispersion curves and modal shapes with those obtained from finite element simulations. Equi-frequency contours are then used to determine the frequency bands prone to collimation. The focus is placed on annular ABH configurations which allow one to achieve collimation at lower frequencies than the circular ones. The second main contribution of this work therefore consists of a thorough analysis to characterize the influence of geometric parameters on the performance of ABH arrays. Moreover, new designs of annular ABH arrangements on plates are proposed for wave conduction, including curvature, and energy focusing in the long wavelength limit.

Fractional Nonlocal Elasticity and Solutions for Straight Screw and Edge Dislocations

Nonlocal elasticity assumes integral stress constitutive equation, takes into account interatomic long-range forces, reduces to the classical theory of elasticity in the long wave-length limit and to the atomic lattice theory in the short wave-length limit. In this paper, we propose the nonlocal elasticity theory with the kernel (the weight function in the integral stress constitutive equation) which is the Green function of the Cauchy problem for the fractional diffusion equation and is expressed in terms of the Mainardi function and Wright function being the generalizations of the exponential function. The solutions for the straight screw and edge dislocations in an infinite solid are obtained in the framework of the proposed theory.

Surface Waves in a Collisional Quark-Gluon Plasma

Surface waves propagating in the semi-bounded collisional hot QCD medium (quark-gluon plasma) are considered. To investigate the effect of collisions as damping and non-ideality factor, the longitudinal and transverse dielectric functions of the quark-gluon plasma are used within the Bhatnagar-Gross-Krook (BGK) approach. The results were obtained both analytically and numerically in the long wavelength limit. First of all, collisions lead to smaller values of surface wave frequency and their stronger damping. Secondly, the results show that non-ideality leads to the appearance of a new branch of surface waves compared to the collisionless case. The relevance of the surface excitations (waves) for the QGP realized in experiments is discussed.

Spectro-Spatial Wave Features in Nonlinear Metamaterials: Theoretical and Computational Studies

Abstract Considerable attention has been given to nonlinear metamaterials because they offer some interesting phenomena such as solitons, frequency shifts, and tunable bandgaps. However, only little is known about the spectro-spatial properties of a wave propagating in nonlinear periodic chains, particularly, a cell with multiple nonlinear resonators. This problem is investigated here. Our study examines both hardening and softening nonlinearities in the chains and in the local resonators. Explicit expressions for the nonlinear dispersion relations are derived by the method of multiple scales. We validate our analytical results using numerical simulations. The numerical simulation is based on spectro-spatial analysis using signal processing techniques such as spatial-spectrogram and wave filtering. The spectro-spatial analysis provides detailed information about the interactions of dispersive and nonlinear phenomena of waveform in both short- and long-wavelength domains. Furthermore, we validate and demonstrate the theoretically obtained bandgaps, wave distortion, and birth of solitary waves through a computational study using finite element software, ansys. The findings, in both theoretical and computational analyses, suggest that nonlinear resonators can have more effect on the waveform than the nonlinear chains. This observation is valid in both short and long wavelength limits.

Thermoacoustic instability in a two-dimensional dusty plasma: A study in the weakly and strongly coupled regime

Thermoacoustic instability in a two-dimensional unmagnetized dusty plasma has been investigated with the implementation of the general hydrodynamic model both in strongly and weakly coupled regimes. It has been found that the thermoacoustic modes are unstable in the long wavelength limit both in strongly and weakly coupled regimes although the modes literally die out in the weakly coupled regime due to viscous damping. The amplification of the thermoacoustic mode is triggered by the positive feedback response of the system via density and temperature fluctuations. The higher the thermal diffusivity, the higher the chances of mode stabilization.

ENHANCING CELL INJECTION SYSTEMS BY REAL TIME CONFIRMATION OF CYTOPLASMIC PENETRATION

Visual assessment of true cell penetration with a microinjection pipette is not always feasible due to cloudy solutions, adjacent cells, and light microscopy wavelength limitations. This is especially true for microinjection in bovine oocytes and zygotes due to their cytoplasmic opacity. We hypothesized that an increase in electrical resistance upon bovine zygote plasmatic membrane piercing can serve as a real-time tool to confirm cell penetration and embryo viability.

Dispersive limit for the pressureless two-fluid Euler–Poisson system

The long wavelength limit for the pressureless two-fluid Euler–Poisson system in three-dimensional whole space case is discussed in the present paper. It is shown that the smooth solutions for the two-fluid Euler–Poisson system converge strongly to those of the Zakharov–Kuznetsov equation in an O(ε−3∕2) time interval by the Gardner–Morikawa transform and the elaborate energy method.

A multi-system tightly-combined model with consideration of differential inter-systems code biases

Knowledge of differential inter-systems phase/code biases are critical to integrate observations from several different Global Navigation Satellite Systems. Many studies on tightly-combined model have mostly focused on the overlapping frequencies and short baselines, and fewer have focused on non-overlapping frequencies and medium-long baselines. Considering differential inter-systems code biases and inter-frequency code biases, we propose a tightly combined real-time kinematic model by a reparameterization process for non-overlapping frequencies among GPS/GLONASS/BDS systems. Compared with the traditional double-difference ambiguity parameter, we use single-difference ambiguity as the parameter to be estimated, which is not affected by reference satellite switching and wavelength limitation. The paper first analyzes the stability of differential inter-systems code biases and inter-frequency code biases with several zero and ultra-short baselines. Then, the paper tests the positioning performance under occlusion environment. The experiment shows that the tightly-combined model is more robust than the loosely-combined model and the average time to first fix is shortened by approximately 22.4%. At last, the paper compares the positioning performance of tightly-combined model, loosely-combined model, and tightly-combined model after calibration under the medium and long baselines. The experiment shows that the tightly-combined model after calibration is better than the tightly-combined model and loosely-combined model in the ambiguity resolution rate, initialization speed and positioning accuracy, respectively. Compared with intra-system loosely-combined model, the positioning accuracy of tightly-combined model after calibration is improved by 42.1%, 25.5%, and 32.3% in the three-dimensional directions, respectively.

A cancellation problem in hybrid particle-in-cell schemes due to finite particle size

The quasi-neutral hybrid particle-in-cell algorithm with kinetic ions and fluid electrons is a popular model to study multi-scale problems in laboratory, space, and astrophysical plasmas. Here, it is shown that the different spatial discretizations of ions as finite-spatial-size particles and electrons as a grid-based fluid can lead to significant numerical wave dispersion errors in the long wavelength limit (kdi≪1, where k is the wavenumber and di is the ion skin-depth). The problem occurs when high-order particle-grid interpolations, or grid-based smoothing, spreads the electric field experienced by the ions across multiple spatial cells and leads to inexact cancellation of electric field terms in the total (ion + electron) momentum equation. Practical requirements on the mesh spacing Δx/di are suggested to bound these errors from above. The accuracy impact of not respecting these resolution constraints is shown for a non-linear shock problem.

Efficient Statistical Model for Predicting Electromagnetic Wave Distribution in Coupled Enclosures

The Random Coupling Model (RCM) has been successfully applied to predicting the statistics of currents and voltages at ports in complex electromagnetic (EM) enclosures operating in the short wavelength limit. Recent studies have extended the RCM to systems of multi-mode aperture-coupled enclosures. However, as the size (as measured in wavelengths) of a coupling aperture grows, the coupling matrix used in the RCM increases as well, and the computation becomes more complex and time-consuming. A simple Power Balance Model (PWB) can provide fast predictions for the \textit{averaged} power density of waves inside electrically-large systems for a wide range of cavity and coupling scenarios. However, the important interference induced fluctuations of the wavefield retained in the RCM is absent in PWB. Here we aim to combine the best aspects of each model to create a hybrid treatment and study the EM fields in coupled enclosure systems. The proposed hybrid approach provides both mean and fluctuation information of the EM fields without the full computational complexity of coupled-cavity RCM. We compare the hybrid model predictions with experiments on linear cascades of over-moded cavities. We find good agreement over a set of different loss parameters and for different coupling strengths between cavities. The range of validity and applicability of the hybrid method are tested and discussed.

Why paramagnetic chiral correlations in the long-wavelength limit do not contribute to muon spin relaxation

A crystal structure that cannot be superposed on its mirror image by any combination of rotations and translations is classified as chiral. Such crystal structures have gained importance in recent years since they are prone to host unconventional magnetic orders and to exhibit topological magnetic textures. These properties result from the Dzyaloshinskii-Moriya antisymmetric exchange interaction which is authorized when space inversion is broken. While recent reports have shown the muon spin rotation and relaxation technique to provide unique information about structural and dynamical properties which are specific to chiral magnets in their ordered phase, the question here is whether this technique is sensitive to paramagnetic chiral correlations that are observed in neutron scattering experiments above the critical temperature. In the relevant long wavelength limit, it is shown that they do not contribute to the relaxation rate, which in turn only probes non-chiral correlations.

Scattering coefficients for a sphere in a visco-acoustic medium for arbitrary partial wave order

Analytical solutions are reported for the scattering coefficients of a solid elastic sphere suspended in a viscous fluid for arbitrary partial wave order. Expressions are derived for incident compressional and shear wave modes, taking into account the viscosity of the surrounding fluid and resultant wave mode conversion. The long compressional wavelength limit is employed to simplify the derivation, whereas no restriction is placed on the shear wavelength in the fluid compared to the particle dimension. The analytical approximations are compared with numerical results obtained from matrix inversion of the boundary equations and agree within the validity domain of the solutions.

Parallel propagating electromagnetic waves in magnetized quantum electron plasmas with finite temperature.

We studied parallel propagating electromagnetic waves in a magnetized quantum electron plasma of finite temperature, as an extension of our previous study on a zero temperature plasma. We obtained simple analytic dispersion relations in the long wavelength limit that included the thermal effect as correction terms to the zero temperature results. As in the zero temperature case, the lower branch of the R wave showed significant damping and became ill-defined at short wavelengths. Quantum effects seemed to give qualitative changes, such as the appearance of anomalous dispersion regions, to the classical dispersion relations when v_{F}/v_{th}≤0.2 for a set of exemplary parameters of v_{F}=0.1c and ω_{ce}/ω_{pe}=0.05 was used. We also noted that introduction of the Planck constant in the quantum Vlasov equation changed the shape of the anomalous dispersion region qualitatively, by forming a normal dispersion region in the middle of the original single broad anomalous dispersion region.