Chiral Parameter Research Articles

Optical enantioseparation of chiral molecules using asymmetric plasmonic nanoapertures

Using electromagnetic modeling and analytical methods, we study the optimal conditions of an enantioselective optical process (EOP) through the interaction potential between enantiomers and localized chiral near-fields created by asymmetric plasmonic crescent moon (PCM) nanoapertures when it is illuminated with circularly polarized light. We introduce a chiral dissymmetry factor which measures the degree of chiral discrimination of the EOP and we found that it depends mainly on the differential field intensification, near-field optical chirality and the handedness of the enantiomers. Our results prove that a sub-10-nm non-magnetic enantiomer pair of chiral spherical molecules with chirality parameter up to $\pm 0.005$±0.005 can be passively separated under dual-symmetric conditions. The method and the proposed nanostructure may enable all-optical enantioseparation of single-chiral macromolecules, such as proteins and carbohydrates.

Geometrical optics approximation for forward light scattering by a large chiral sphere

The geometrical optics approximation (GOA) method is extended to the forward light scattering of a large-sized isotropic chiral medium (ICM) spherical particle illuminated by a polarized plane wave. Based on the boundary conditions, the reflection and refraction Fresnel coefficients at the surface of a chiral sphere are revisited. Expressions of the scattering fields are derived by a combination of the amplitudes of the externally reflected, the directly refracted, and the diffracted waves, where effects of polarization and the phase shift are taken into consideration. Numerical results of co-polarized and cross-polarized scattering intensity distributions of a large-sized ICM sphere are presented. Effects of the chiral parameter, permittivity, and size parameter of the sphere on the scattering patterns are investigated in detail.

Topological defects and critical phenomena in two-dimensional frustrated helimagnets

Using a simple model of a frustrated helimagnet, the critical behavior is numerically investigated for planar or isotropic spins, and for cases of one or two chiral order parameters. The helical structure in this model arises from the competition between exchange interactions of spins of the first two range orders in one direction (in both directions) of a square lattice. The main result is that the critical and temperature behavior is primarily determined by topological defects that are present in all cases. In the case of planar spins, vortices, fractional vortices and domain walls are present in the system. Their interaction leads to the appearance of the phase of a chiral spin liquid, or induces a single first-order transition, and in the vicinity of the Lifshitz point vortices lead to a reentrant phase transition to the phase with a collinear quasi-long-range order. When transitions in the chiral and continuous order parameters are separated in temperature, they are of the 2D Ising and Kosterlitz-Thouless types correspondingly. In the case of isotropic spins, so-called $\mathbb{Z}_2$ vortices are present. They do not lead to the appearance of a phase with long-range or quasi-long-range order in the case of one chiral order parameter. However, their interaction leads to a sharp change in the temperature dependence of the correlation length (crossover). In the case of two chiral parameters, there are long-range chiral order of the Ising type (chiral spin liquid) and domain walls. However, as a result of the interaction of vortices and walls, the crossover and chiral transition occur at the same temperature as a first-order transition.

Mechanical and thermal couplings in helical strands*

A generalized Timoshenko rod model is developed for helical strands and helically reinforced cylinders. The thermomechanical constitutive law has five effective elastic moduli, and two thermal coefficients, which can be obtained with the finite element method, or partly from analytic solutions. The model predicts nonclassical bending and thermoelastic behavior of helical strands. First, bending–shearing coupling is explicitly captured, which leads to non-planar bending under a transverse shear force, or a bending moment. Second, torsion and thermal expansion are coupled due to structural chirality. The dispersion relation of harmonic thermoelastic waves is governed by four non-dimensional parameters: two thermoelastic coupling constants, one chirality parameter and the Fourier number. The quasi-longitudinal and the quasi-torsional waves (“quasi” meaning the longitudinal mode is always coupled with a small torsional motion, and vice versa, due to chirality) are dispersive and damped, and dependent on temperature. The adiabatic-isothermal transition of the wave propagation is determined by the Fourier number.

Ising in a transverse field with added transverse Dzyaloshinskii-Moriya interaction

Abstract In this paper, a one-dimensional spin-1/2 Ising model in a transverse magnetic field (ITF) with added the transverse Dzyaloshinskii-Moriya (DM) interaction is considered. The Hamiltonian is exactly diagonalized using the fermionization approach. The energy spectrum, the magnetization and the chiral order parameter are calculated in the thermodynamic limit of the system. In the absence of the transverse magnetic field, a second order quantum phase transition into the chiral ordered phase is happened. In presence of the transverse magnetic field, the quantum critical point is changed. Based on obtained results, three phases named chiral, Neel and ferromagnetic are distinguished and the ground state phase diagram has been plotted. In addition to the response functions, the entanglement and the quantum discord between nearest and next to nearest pair of spins are also investigated. Regarding the quantum correlations, the existence of different ground state phases has been confirmed.

Mathematical Modeling of Multi-Element Antenna Arrays with Chiral Metamaterials Substrates Using Singular Integral Equations

In this paper, a physical model of the multi-element antenna arrays (MEAA) has been considered and a self-consistent numerical method for solving the problem of current distribution on the MEAA surface with chiral metamaterials substrate has been proposed. The algorithm of the input admittance matrix elements for chiral layer based on the conductive left and right-handed helices has been developed and elements of the matrix surface impedances for investigated structures have been found. A set of singular integral equations with a Cauchy kernel for calculating the current density on the surface of the MEAA has been derived. A numerical solution of the set is a well-posed in the sense of Hadamard. Calculations of current distribution on the MEAA surface, impedance characteristics of a three-element antenna array and the dependence of the isolation levels between emitters on the chirality parameter have been performed and analysed. It has been shown that the use of chiral substrates can substantially increase the isolation between emitters.

Characteristics of light–plasmon coupling on chiral–graphene interface

This theoretical study has been carried out on the characteristics of light–plasmon coupling on the chiral–graphene interface. The graphene’s conductivity is modeled in the framework of Kubo’s formulism. The impedance boundary condition approach is used to compute the dispersion relationship for the chiral–graphene interface and dispersion curve analysis is used to study the light–plasmon coupling on the chiral–graphene interface. This study concludes that the chiral–graphene interface supports the hybrid surface plasmon modes, i.e., the upper and lower modes that can be used to sense the chirality and chemical sense biochemical molecules. Furthermore, this study presents the influence of chirality (ξ), chemical potential (μg), and layers of graphene (N) on the dispersion relation, propagation length (Lp), and effective mode index (Neff), and it concludes that both the chiral and graphene parameters can be used to tune the plasmonics resonance frequencies. This study presents the cutoff chiral value (ξc) as a function of the frequency (ω) under different values of chemical potential (μg) and index of refraction (nc), and the numerical results revealed that light–plasmon coupled modes are exploitable for on-chip chiral sensing and enantiomeric detection applications.

Mechanics of curved-ligament hexachiral metastructures under planar deformations

This paper presents a study of the mechanical response of hexachiral honeycombs with transversally curved ligaments under planar uniaxial tensile, compressive and shear loads. The impact of the chiral cell design parameters on the resulting macroscopic behaviour is assessed utilising finite elements calculations. It is shown that the presence of ligament curvature permits to attain mechanical responses which are not achievable through conventional chiral honeycomb designs. In addition, the resulting responses exhibit, for all considered load cases, significant tunability through the investigated geometrical design parameters. Two chiral lattices with identical geometries, only differing in their ligament curvature, were manufactured and experimentally tested to validate the finite elements predictions. A connection and assembly strategy is presented and utilised, offering a fast and robust approach to build larger finite lattice structures through 3D printed single basic cells. The hexachiral lattices were tested in tension, compression and in-plane shear, showing good agreement with the numerical predictions.

Matrix solution 4x4 by the Wentzel-Kramers-Brillouin method for electromagnetic waves reflected on the boundary of inhomogeneous chiral layer

The propagation of a plane electromagnetic wave in a plane inhomogeneous chiral medium with oblique incidence is considered. The chirality parameter varies with the distance from the boundary. The problem reduces to solving a system of the ordinary differential equations (ODE) with variable coefficients 4x4. The solution was obtained by the Wentzel-Kramers-Brillouin method in the matrix form. We found a fundamental solution matrix and a Cauchy matrix for a chiral inhomogeneous medium with continuously varying properties along one of the coordinates. The dependence of the absolute values of the matrix coefficients of reflection and cross-polarization components on the reflection from the profile of the chirality parameter and the angle of incidence is shown.

Hybrid Surface Plasmon Polariton Wave Generation and Modulation by Chiral-Graphene-Metal (CGM) Structure

Theoretical investigations are carried out to study hybrid SPP wave propagation along the Chiral-Graphene-Metal (CGM) interface. The Kubo formulism is used for the physical modeling of single-layer graphene and the impedance boundary conditions approach is applied at the CGM interface to compute the dispersion relationship for hybrid SPP waves. It is demonstrated that the chirality (ξ) and chemical potential (μc) parameters can be used to modulate the resonance surface plasmon frequencies of the upper and lower propagating modes. Furthermore, the propagation bandgap between the upper and the lower modes can be tuned by changing the chirality parameter. The effect of the chemical potential (μc)and the relaxation time (τ) on the normalized propagation constant, propagation length, and the effective refractive index is studied. The present work may have potential applications in optical and chiral sensing in the terahertz frequency range.

Impedance Characteristics of a Two-Element Antenna Array with a Chiral Substrate

In this paper, we calculated the impedance characteristics of a two-element antenna array with a chiral metamaterial substrate. A system of singular integral equations with Cauchy-type singularity with respect to the unknown longitudinal distributions of the surface current density is obtained. The input impedance dependences on the normalized arm length for various substrate types, as well as various values of the chirality parameter of the substrate, are presented.

Electromagnetic field behavior of 3D Maxwell's equations for chiral media

This article focuses on numerically studying the eigenstructure behavior of generalized eigenvalue problems (GEPs) arising in three dimensional (3D) source-free Maxwell's equations with magnetoelectric coupling effects which model 3D reciprocal chiral media. It is challenging to solve such a large-scale GEP efficiently. We combine the null-space free method with the inexact shift-invert residual Arnoldi method and MINRES linear solver to solve the GEP with a matrix dimension as large as 5,308,416. The eigenstructure is heavily determined by the chirality parameter γ. We show that all the eigenvalues are real and finite for a small chirality γ. For a critical value γ=γ⁎, the GEP has 2×2 Jordan blocks at infinity eigenvalues. Numerical results demonstrate that when γ increases from γ⁎, the 2×2 Jordan block will first split into a complex conjugate eigenpair, then rapidly collide with the real axis and bifurcate into positive (resonance) and negative eigenvalues with modulus smaller than the other existing positive eigenvalues. The resonance band also exhibits an anticrossing interaction. Moreover, the electric and magnetic fields of the resonance modes are localized inside the structure, with only a slight amount of field leaking into the background (dielectric) material.

Sensing and Manipulation of Bianisotropic Biomolecules Using a Surface Plasmon Resonance Based Optical Fiber Sensor

We report a mechanism to sense and manipulate bianisotropic chiral biomolecules by a surface plasmon resonance based side-polished optical fiber sensor. To simulate such planar layered structure containing anisotropic and magnetoelectric coupling biomolecules, the propagation matrix method is expanded. This method allows us to access the radiation pressure exerted on the bianisotropic molecular layer via the derivation of the Maxwell stress tensor. The complicated behavior of incident plane waves on the sensing and trapping of biomolecules with different medium parameters is clarified. We find that the optical fiber sensor is capable of simultaneous detection of chirality parameter, anisotropy, and refractive index of biomolecules. The structure can also be used to separate chiral molecules from achiral ones by using an emerging sharp surface plasmon resonance. The paper may provide new insights for SPR based sensors and imaging systems, optical tweezers, and nanomechnical devices.

A bi-layered chiral metamaterial with high-performance broadband asymmetric transmission of linearly polarized wave

In this paper, a novel bi-layered chiral metamaterial (CMM) is presented to realize high–efficiency broadband asymmetric transmission (AT) of linearly polarized electromagnetic wave (EM) in the microwave region from 10.1 GHz to 15.1 GHz. For this purpose, a pair of modified resonators is employed on two sides of a thin dielectric substrate. The simulated and measured results confirm that linearly polarized wave in the form of x-polarized or y-polarized could be nearly converted into the orthogonal polarization after transmission through the introduced prototype which is affirmed by the polarization rotation azimuth angle θ. The polarization conversion ratio (PCR) is more than 92% at the mentioned frequency range. Full parametric simulation of modified resonators, azimuth rotation angle, and chirality parameter variable with frequency are discussed in detail. In addition, the surface current distributions of the structure have been demonstrated to investigate the physical mechanism of the cross-polarization and corresponding polarization conversion.

Internal and near-surface electromagnetic fields for a chiral cylinder with arbitrary monochromatic illumination

A semi-analytical solution is proposed to the electromagnetic scattering by an infinite chiral circular cylinder with arbitrary monochromatic illumination. The scattered and internal fields are expanded in terms of appropriate cylindrical vector wave functions, and their expansion coefficients are determined by virtue of the boundary conditions and the projection method. As a demonstration of the theoretical procedure, the normalized internal and near-surface field intensity distributions are evaluated for a fundamental Gaussian beam, and the scattering properties are discussed briefly for different chirality parameters.

Probing bianisotropic biomolecules via a surface plasmon resonance sensor.

The transfer matrix method is developed to probe bianisotropic biomolecules via a Kretschmann configuration surface plasmon resonance (SPR) sensor. This method employs wave vectors and 4 × 4 transfer matrices derived by using anisotropic and magnetoelectric coupling constitutive relations. The transfer matrices relate four eigenstates and trace four transverse field components through the multilayer to account for cross-polarization coupling due to the chirality of the biomolecule layer. The validity of the method is confirmed by means of numerical results. It is shown that cross-polarized reflection waves are enhanced around the SPR angle, as the water solution and bianisotropic biomolecules to be detected are placed in contact with the graphene layer of the sensor. The effects of optical activity and bianisotropy on the SPR sensor are investigated. This work enriches the transfer matrix theory for SPR sensors to detect the chirality parameter of bianisotropic chiral material, and may lead to a better design of SPR sensors against the chirality parameter variation.

Microstrip Patch Antennas Covered with Chiral Metamaterial Structures

In this working we present gain characteristic of microstrip patch antennas covered with chiral metamaterial. In order to determine gain of antennas covered with chiral metamaterial structure, S11 parameters and radiation pattern of antennas with chiral metamaterial and without chiral metamaterial are plotted and compared each other. The simulation results show that antennas covered with chiral metamaterial structure increase either gain or radiation pattern or both at operation frequency.

Electromagnetic form factors of spin- 1/2 doubly charmed baryons

We study the electromagnetic form factors of the doubly charmed baryons, using covariant chiral perturbation theory within the extended on-mass-shell (EOMS) scheme. Vector-meson contributions are also taken into account. We present results for the baryon magnetic moments, charge and magnetic radii. While some of the chiral Lagrangian parameters could be set to values determined in previous works, the available lattice results for $\Xi_{cc}^+$ and $\Omega_{cc}^+$ only allow for robust constraints on the low-energy constant (LEC) combination, $c_{89}(=-\frac{1}{3}c_8+4c_9)$. The couplings of the doubly charmed baryons to the vector mesons have been estimated assuming the Okubo--Zweig--Iizuka (OZI) rule. We also give the expressions for the form factors of the double beauty baryons considering the masses predicted in the framework of quark models. A comparison of our results with those obtained in heavy baryon chiral perturbation theory (HBChPT) at the same chiral order is made.

Chiral Material With Tunable Double Plates

A double slab with chiral structures based on three-segment cranks is analyzed for linearly polarized and normal incident waves. Both slabs are equal and are constituted by a two-dimensional lattice of four same-handedness metallic cranks. The slabs are parallel, with the unit cells perfectly aligned, and each layer is built on a standard FR4 board. Using a free-wave experimental setup and numerical simulations, the transmission and reflection coefficients were determined under normal incidence of linearly polarized waves. The retrieved values for the rotation angle, chirality parameter, refractive index, and ellipticity show a clear chiral behavior for a spacing lower than the slab width. It has also found that as the distance between the two layers increases, the resonant frequency also increases, and this dependence is close to exponential. Based on these observations, a system composed of two chiral slabs can be used as a tunable rotator or a polarization filter.

Nonlinear effects in chiral nihility metamaterial

In this paper, the characteristics of chiral nihility nonlinearities have been investigated theoretically. In the case of this medium, permittivity and permeability are equal to zero, regardless of the existence of nonlinear effects, which is due to the presence of cross-susceptibilities in chiral medium. We have made a study of hyperbolic secant (sech) pulse to define the influence of nonlinear chiral parameter on the propagation of an electromagnetic wave in chiral nihility media. Numerical results are given and discussed to confirm the characteristics investigated theoretically.