Calculated Dispersion Relations Research Articles

Fano-like resonance in large-area magnetic metamaterials fabricated by the nanoimprint technique

We experimentally and theoretically investigated the Fano-like resonance in large-area magnetic metasurfaces fabricated by nanoimprint lithography techniques based on elaborately designed Ag–SiN–Ag configuration. Asymmetric line shape is revealed in the reflection spectrum of magnetic metamaterials. The physical mechanism is elucidated through dispersion relation and electromagnetic field distribution analysis. Both the measured and calculated dispersion relation tell that there are magnetic resonance modes and surface lattices modes coexisting in magnetic metamaterials, their coupling leads to the asymmetric profile in the reflection spectrum. The calculated electromagnetic field distribution further consolidate the coupling phenomenon in the magnetic metamaterials. This work might significantly prompt the applications of metamaterials in sensing, lasing, and optical devices designing.

Unidirectional propagation of coupled edge states in sandwich topological photonic crystals

Topological photonic crystals (PCs) with exotic optical properties such as helical edge states have tremendous potential applications in the fields of photonic integrated circuits. Here, we propose a sandwich PC structure based on trivial-nontrivial-trivial topology with a robust unidirectional light propagation through coupling of two helical edge states in the nontrivial topological region. We calculate dispersion relations of the sandwich structures and observe a robust unidirectional light propagation excited by an external point source with orbital angular momentum. To evaluate the stability of light flow, a Z-shaped corner is established and positions or radii of several cylinders are changed randomly. Results show that the unidirectional propagation remains stable in the imperfect structures. The configuration may find potential applications for the construction of nanophotonic circuits.

ALPS: the Arbitrary Linear Plasma Solver

The Arbitrary Linear Plasma Solver (ALPS) is a parallelised numerical code that solves the dispersion relation in a hot (even relativistic) magnetised plasma with an arbitrary number of particle species with arbitrary gyrotropic equilibrium distribution functions for any direction of wave propagation with respect to the background field. ALPS reads the background momentum distributions as tables of values on a$(p_{\bot },p_{\Vert })$grid, where$p_{\bot }$and$p_{\Vert }$are the momentum coordinates in the directions perpendicular and parallel to the background magnetic field, respectively. We present the mathematical and numerical approach used by ALPS and introduce our algorithms for the handling of poles and the analytic continuation for the Landau contour integral. We then show test calculations of dispersion relations for a selection of stable and unstable configurations in Maxwellian, bi-Maxwellian,$\unicode[STIX]{x1D705}$-distributed and Jüttner-distributed plasmas. These tests demonstrate that ALPS derives reliable plasma dispersion relations. ALPS will make it possible to determine the properties of waves and instabilities in the non-equilibrium plasmas that are frequently found in space, laboratory experiments and numerical simulations.

Coherent guided acoustic phonons in GaN/AlN nanowire superlattices

We theoretically examine the coherent guided acoustic phonons generated and observed in a GaN/AlN nanowire superlattice by ultrafast pump–probe spectroscopy. We consider the symmetry of the present nanowire superlattice and carry out the variational calculation of dispersion relations. By comparing numerical results with the results approximated using Rytov’s equation, we examine the validity of the model used in the experimental explanation. The propagation processes of the guided coherent acoustic phonons previously observed are re-examined on the basis of our numerical results.

Ab initio calculation of thermal boundary resistance at the interface of metals with GeTe, In $$_3$$ 3 SbTe $$_2$$ 2 and In $$_2$$ 2 GeTe $$_3$$ 3 phase change compounds

First principles calculations of phonon dispersion relations have been performed to estimate the phononic contribution to the thermal boundary resistance at the interfaces between GeTe, In $$_3$$ SbTe $$_2$$ and In $$_2$$ GeTe $$_3$$ phase change compounds and metals (Al, Pt and TiN). The diffuse mismatch model has been used. The electron–phonon coupling constants provide an estimate of the electron–phonon contribution to the thermal boundary resistance. The electron–phonon and phononic contributions to the thermal boundary resistance turn out to be comparable and they have to be both included for a reliable estimate of the thermal conductance at the interface with phase change compounds.

Velocity shear Kelvin-Helmholtz instability with inhomogeneous DC electric field in the magnetosphere of Saturn

In this paper parallel flow velocity shear Kelvin-Helmholtz instability has been studied in two different extended regions of the inner magnetosphere of Saturn. The method of the characteristic solution and kinetic approach has been used in the mathematical calculation of dispersion relation and growth rate of K-H waves. Effect of magnetic field (B), inhomogeneity (P/a), velocity shear scale length (Ai), temperature anisotropy (T⊥/T||), electric field (E), ratio of electron to ion temperature (Te/Ti), density gradient (εnρi) and angle of propagation (θ) on the dimensionless growth rate of K-H waves in the inner magnetosphere of Saturn has been observed with respect to k⊥ρi. Calculations of this theoretical analysis have been done taking the data from the Cassini in the inner magnetosphere of Saturn in the two extended regions of Rs ∼4.60–4.01 and Rs ∼4.82–5.0. In our study velocity shear, temperature anisotropy and magnitude of the electric field are observed to be the major sources of free energy for the K-H instability in both the regions considered. The inhomogeneity of electric field, electron-ion temperature ratio, and density gradient have been observed playing stabilizing effect on K-H instability. This study also indicates the effect of the vicinity of icy moon Enceladus on the growth of K-H instability.

Surface plasmon polaritons at the interface of two nanowire metamaterials

The properties of surface-plasmon-polaritons (SPPs) at the interface of two nanowire metamaterials are investigated theoretically. Calculated dispersion relations and propagation lengths are presented. It is demonstrated that the SPPs can be tuned by controlling the metamaterial design. Tunability of these structures can be enhanced further by increasing the pore diameter, which leads the shift of the surface modes to higher frequencies. We specifically consider two different cases with the composite nanowire metamaterial stack composed of the same type of metamaterial in each layer as well as the case of a nanowire metamaterial stack with different materials in each metamaterial layer.

Calculation of phonon dispersion relation using new correlation functional

To extend the use of Local Density Approximation (LDA), a new analytical correlation functional is introduced. Correlation energy is an essential ingredient within density functional theory and used to determine ground state energy and other properties including phonon dispersion relation. Except for high and low density limit, the general expression of correlation energy is unknown. The approximation approach is therefore required. The accuracy of the modelling system depends on the quality of correlation energy approximation. Typical correlation functionals used in LDA such as Vosko-Wilk-Nusair (VWN) and Perdew-Wang (PW) were obtained from parameterizing the near-exact quantum Monte Carlo data of Ceperley and Alder. These functionals are presented in complex form and inconvenient to implement. Alternatively, the latest published formula of Chachiyo correlation functional provides a comparable result for those much more complicated functionals. In addition, it provides more predictive power based on the first principle approach, not fitting functionals. Nevertheless, the performance of Chachiyo formula for calculating phonon dispersion relation (a key to the thermal properties of materials) has not been tested yet. Here, the implementation of new correlation functional to calculate phonon dispersion relation is initiated. The accuracy and its validity will be explored.

Tunable surface waves at the interface separating different graphene-dielectric composite hyperbolic metamaterials.

Despite the fact that metal is the most common conducting constituent element in the fabrication of metamaterials, one of the advantages of graphene over metal is that its conductivity can be controlled by the Fermi energy. Here, we theoretically investigate multilayer structures comprising alternating graphene and dielectric layers as a class of hyperbolic metamaterials for THz frequencies based on a general simple model of the graphene and the dielectric layers. By employing a method of matching the tangential components of the electrical and magnetic fields, we derive the relevant dispersion relations and demonstrate that tuning can be achieved by modifying the Fermi energy. Moreover, tunability of the graphene-dielectric heterostructures can be enhanced further by changing either the thickness of the dielectric layers or the number of graphene sheets employed. Calculated dispersion relations, propagation lengths of plasmon modes in the system are presented. This allows us to characterize and categorize the modes into two groups: Ferrel-Berreman modes and surface plasmon polaritons.

Analytic Interatomic Forces in the Random Phase Approximation.

We discuss that in the random phase approximation (RPA) the first derivative of the energy with respect to the Green's function is the self-energy in the GW approximation. This relationship allows us to derive compact equations for the RPA interatomic forces. We also show that position dependent overlap operators are elegantly incorporated in the present framework. The RPA force equations have been implemented in the projector augmented wave formalism, and we present illustrative applications, including abinitio molecular dynamics simulations, the calculation of phonon dispersion relations for diamond and graphite, as well as structural relaxations for water on boron nitride. The present derivation establishes a concise framework for forces within perturbative approaches and is also applicable to more involved approximations for the correlation energy.

Free and forced vibrations of SC-cut quartz crystal rectangular plates with the first-order Mindlin plate equations

Mindlin plate theory was used to provide accurate solutions to thickness-shear vibrations of plates, which have a much higher frequency than usual flexural vibrations and are the functioning modes of quartz crystal resonators. The vibration frequency solutions obtained with the Mindlin plate theory are proven being accurate along with mode shapes. In this paper, straight-crested wave solutions of free and forced vibrations of doubly rotated SC-cut of quartz crystal plates of rectangular shapes with four free edges are obtained with validated Mindlin plate equations. A procedure has been established for the calculation of dispersion relations, frequency spectra, mode shapes, and capacitance ratios of forced vibrations needed in resonator design.

Investigation of mechanism: spoof SPPs on periodically textured metal surface with pyramidal grooves.

In microwave and terahertz frequency band, a textured metal surface can support spoof surface plasmon polaritons (SSPPs). In this paper, we explore a SSPPs waveguide composed of a metal block with pyramidal grooves. Under the deep subwavelength condition, theoretical formulas for calculation of dispersion relations are derived based on the modal expansion method (MEM). Using the obtained formulas, a general analysis is given about the properties of the SSPPs in the waveguides with upright and downward pyramidal grooves. It is demonstrated that the SSPPs waveguides with upright pyramidal grooves give better field-confinement. Numerical simulations are used to check the theoretical analysis and show good agreement with the analytical results. In addition, the group velocity of the SSPPs propagating along the waveguide is explored and two structures are designed to show how to trap the SSPPs on the metal surface. The calculation methodology provided in this paper can also be used to deal with the SSPPs waveguides with irregular grooves.

Appearance of novel modes ofD¯mesons with negative velocity in the dual chiral density wave

We calculate dispersion relations for $\bar{D}(0^-)$, $\bar{D}^*(1^-)$, $\bar{D}_0^*(0^+)$ and $\bar{D}_1(1^+)$ mesons in the Dual Chiral Density Wave (DCDW) where the chiral symmetry is spontaneously broken by inhomogeneous chiral condensate. Employing the Bloch's theorem, we show that all the modes have opposite group velocity to the momentum in the low-momentum region and the energy is minimized at non-zero momentum. Furthermore, the magnitude of momentum which realizes the minimum energy is equal to the wave number of the density wave.

Calculation of Dispersion Relation and Single Mode Operation in Surface Plasmon Resonance Based Fiber Optic Refractive Index Sensors

The dispersion relations of two lowest-order surface plasmon (SP) modes are derived for a structure consisting of a thin silver layer around a reduced cladding fiber. Mode splitting is formed by reducing metal thickness. Fulfillment of phase matching condition is investigated by inspection of the SPs’ and fiber modes’ dispersion diagrams. Propagation lengths, field patterns, and resonance wavelengths are determined with high accuracy. The sensitivity of 7.13 × 10−6 RIU is obtained for ambient refractive index range of 1.333–1.375. Short-range SP modes cannot be excited in this structure even in IR region. Dependence of SP cutoff conditions on the core radii, metal thickness, ambient refractive index, and operating wavelength are explored. It is proved that the proposed method is going to be useful for proper structural design of single plasmonic mode operation in SP resonance based fiber optic refractive index sensors.

PDRK: A General Kinetic Dispersion Relation Solver for Magnetized Plasma**supported by the National Magnetic Confinement Fusion Science Program of China (Nos. 2015GB110003, 2011GB105001, 2013GB111000), National Natural Science Foundation of China (No. 91130031), the Recruitment Program of Global Youth Experts

A general, fast, and effective approach is developed for numerical calculation of kinetic plasma linear dispersion relations. The plasma dispersion function is approximated by J-pole expansion. Subsequently, the dispersion relation is transformed to a standard matrix eigenvalue problem of an equivalent linear system. Numerical solutions for the least damped or fastest growing modes using an 8-pole expansion are generally accurate; more strongly damped modes are less accurate, but are less likely to be of physical interest. In contrast to conventional approaches, such as Newton's iterative method, this approach can give either all the solutions in the system or a few solutions around the initial guess. It is also free from convergence problems. The approach is demonstrated for electrostatic dispersion equations with one-dimensional and two-dimensional wavevectors, and for electromagnetic kinetic magnetized plasma dispersion relation for bi-Maxwellian distribution with relative parallel velocity flows between species.

Calculations of band diagrams and low frequency dispersion relations of 2D periodic dielectric scatterers using broadband Green's function with low wavenumber extraction (BBGFL).

The broadband Green's function with low wavenumber extraction (BBGFL) is applied to the calculations of band diagrams of two-dimensional (2D) periodic structures with dielectric scatterers. Periodic Green's functions of both the background and the scatterers are used to formulate the dual surface integral equations by approaching the surface of the scatterer from outside and inside the scatterer. The BBGFL are applied to both periodic Green's functions. By subtracting a low wavenumber component of the periodic Green's functions, the broadband part of the Green's functions converge with a small number of Bloch waves. The method of Moment (MoM) is applied to convert the surface integral equations to a matrix eigenvalue problem. Using the BBGFL, a linear eigenvalue problem is obtained with all the eigenmodes computed simultaneously giving the multiband results at a point in the Brillouin zone Numerical results are illustrated for the honeycomb structure. The results of the band diagrams are in good agreement with the planewave method and the Korringa Kohn Rostoker (KKR) method. By using the lowest band around the Γ point, the low frequency dispersion relations are calculated which also give the effective propagation constants and the effective permittivity in the low frequency limit.

Strong interaction effects at a Fermi surface in a model for voltage-biased bilayer graphene

Monte Carlo simulation of a 2+1 dimensional model of voltage-biased bilayer graphene, consisting of relativistic fermions with chemical potential mu coupled to charged excitations with opposite sign on each layer, has exposed non-canonical scaling of bulk observables near a quantum critical point found at strong coupling. We present a calculation of the quasiparticle dispersion relation E(k) as a function of exciton source j in the same system, employing partially twisted boundary conditions to boost the number of available momentum modes. The Fermi momentum k_F and superfluid gap Delta are extracted in the limit j tends to zero for three different values of mu, and support a strongly interacting scenario at the Fermi surface with Delta of order O(mu). We propose an explanation for the observation mu < k_F in terms of a dynamical critical exponent z < 1.

Comprehensive three-dimensional analysis of surface plasmon polariton modes at uniaxial liquid crystal-metal interface.

This paper describes the derivation of surface plasmon polariton modes associated with the generalized three-dimensional rotation of liquid crystal molecules on a metal film. The calculated dispersion relation was verified by coupling laser light into surface plasmon polariton waves in a one-dimensional grating device. The grating-assisted plasmon coupling condition was consistent with the formulated k(spp) value. This provides a general rule for the design of liquid-crystal tunable plasmonic devices.

Magnonic Band Structure in a Skyrmion Magnonic Crystal

We present a numerical investigation of the magnonic band structure of spin waves (SWs) in a novel magnonic crystal consisting of a waveguide with a linear array of periodically spaced skyrmions created along its center by micromagnetic simulations. The interfacial Dzyaloshinskii–Moriya interaction (DMI) induced the presence of skyrmions causes a periodical magnetization modulation of the waveguide, which can be dynamically controlled by changing either the strength of the external magnetic field or the period of the skyrmion lattice. The diameters of the skyrmions are highly dependent on the strength of the applied magnetic field, and they can exist for a wide magnetic field range depending on the density of the DMI. The calculated dispersion relation of SWs in the proposed skyrmion magnonic crystal, frequency versus wave vector, exhibits a periodical property, which is the characteristic feature of the band structure of conventional magnonic crystals. Similarly, the calculated magnonic spectra exhibits allowed frequency band and forbidden frequency bandgaps. Our findings could stimulate further exploration on multiple functionalities provided by magnonic crystals based on periodic skyrmion lattices.

Forced vibrations of SC-cut quartz crystal rectangular plates with partial electrodes by the Lee plate equations

Lee plate equations for high frequency vibrations of piezoelectric plates have been established and perfected over decades with the sole objective of obtaining accurate predictions of frequency and mode shapes to aid the analysis and design of quartz crystal resonators. The latest improvement includes extra terms related to derivatives of the flexural displacement to provide much accurate solutions for vibrations of the thickness-shear mode, which is the functioning mode of resonators and has much higher frequency than the flexural mode. The improved Lee plate equations have been used in the analysis of high frequency vibrations of quartz crystal plates as an essential step for analysis of AT- and SC-cut quartz crystal resonators after validations with fully electrode quartz crystal piezoelectric plates. In this study, closed-form solutions of free and forced vibrations of SC-cut quartz plates with partial electrodes are obtained. A procedure has been established for the calculation of dispersion relations, frequency spectra, selected vibration modes, and capacitance ratios of forced vibrations. The vibration solutions obtained with the first-order Lee plate equations are proven to be close to solutions from the Mindlin plate equations. It is now clear that both the Mindlin and Lee plate equations can be used in the analysis and design of quartz crystal resonators.