Eigenmode Theory Research Articles

Mixed bound states in the continuum: Disclosing BIC’s content via bulk normal modes

We present a nonperturbative theory of bound states in the continuum (BICs) based on the analytical theory of infinite-grating eigenmodes in the case of a planar grating waveguide, that is, 1D photonic crystal slab. We describe a mixed BIC mainly formed by a coherent mixture of two photonic-crystal normal modes in a vicinity of their avoided crossing where both of them have a nonzero coupling with a radiation-loss channel. We reveal the universal properties of the mixed BIC associated with the spatial parity symmetry breaking and self-similar spectral behavior of the bulk normal modes near Γ-point. We show that the mechanism of the mixed-BIC formation constitutes a special kind of the generic Friedrich–Wintgen mechanism. A cutoff from the radiation-loss channel and extremely high-Q narrow resonance are achieved due to the destructive interference of the two crossing normal modes. On the contrary, a conventional symmetry-protected BIC is formed mostly by a single photonic-crystal normal mode which has vanishing coupling Fourier coefficient with every available radiation-loss channel. Implementation of the mixed BICs in various photonic-crystals structures could lead to interesting applications.

An MLFMA-Based Eigenmode Theory for Electromagnetic Scattering Analysis From Electrically Large and Complex Conducting Objects

The eigenmode theory, which uses the modal currents solved from surface differential equations (SDEs) as the basis functions of the method of moment (MoM), has been applied to the analysis of electromagnetic scattering and radiation problems of electrically small and simple perfect electrically conducting (PEC) objects. In this article, a multilevel fast multipole algorithm (MLFMA)-based eigenmode theory is presented for analyzing electromagnetic scattering from electrically large and complex PEC objects. The method applies the MLFMA to accelerate the matrix-vector multiplications involved in filling the dense impedance matrix and therefore is much more efficient than the conventional eigenmode theory, especially for electrically large objects. Meanwhile, the way to determine a priori the number of the required modal currents for arbitrarily shaped objects is presented, which makes the MLFMA-based eigenmode theory applicable to the scattering analysis from complex objects. Numerical results verify the accuracy and efficiency of the proposed method.

First-order perturbation theory of eigenmodes for systems with interfaces

We present an exact first-order perturbation theory for eigenmodes in systems with interfaces causing material discontinuities. We show that when interfaces deform, higher-order terms of the perturbation series can contribute to the eigenmode frequencies in first order in the deformation depth. In such cases, the first-order approximation is different from the usual diagonal approximation and its single-mode result. Extracting additional first-order corrections from all higher-order terms enables us to recover the diagonal formalism in a modified form. A general formula for the single-mode first-order correction to electromagnetic eigenmodes in systems with interfaces is derived, capable of treating dispersive, magnetic, and chiral materials of arbitrary shape.

Spin excitation spectrum of biskyrmion in a confined nanodot

A biskyrmion, which consist of two stable Bloch skyrmions with opposite magnetic helicities has been observed in several centrosymmetric ferromagnets such as layered perovskite manganites and MnNiGa. Here, the spin excitation modes of biskyrmion in a confined nanodot were investigated by using micromagnetic simulations. An oscillation mode at the lower frequency and two mixed modes of breathing and rotation at higher frequencies are observed. In addition, the frequencies for mixed modes exhibit remarkable dependence on the change of magnetization profile. However, the in-plane orientation of biskyrmion does not shift the excitation frequencies corresponding to all eigenmodes. Our result indicates novel excitation modes which enrich the theory of eigenmodes for spin textures and offers a direct mean of detecting and characterizing biskyrmion in experiment.

Optically-Controlled Terahertz Multifunctional Polarization Conversion Metasurface with Reflection and Transmission Modes.

In the terahertz band, how integrating multiple functions into a device with a tiny unit structure is a challenge. In this paper, an optically-controlled multifunctional linear polarization conversion metasurface working in the terahertz band is proposed. The reflection and transmission polarization conversion functions can be realized by irradiating the metasurface with pump light with different wavelengths. The metasurface is designed with a multilayer structure, and a photosensitive semiconductor alone is used to control multiple functions, which makes the manipulation of multifunctional devices easy. When the photosensitive semiconductor germanium (Ge) and silicon (Si) are in different states, the metasurface can realize broadband reflection and transmission polarization conversion functions, the corresponding relative bandwidth are 102.4% and 98.9%, respectively, and the work efficiency can be regulated by pump light with different intensity and wavelength. In addition, the working principle of the metasurface is analyzed by eigenmode theory and surface current distributions. The stability of the metasurface to structural parameters and incident angles are discussed.

Eigenmode-BLT-Based Method for Calculating the Coupling to Microstrip Antenna Inside a Cavity

The electromagnetic (EM) coupling effects of microstrip antennas have become increasingly prominent in complicated electric systems. In this article, a hybrid method is proposed based on the combination of cavity eigenmode theory and BLT equation. First, the internal electric field generated by the transmission lines inside the resonant cavity is obtained via cavity eigenmode theory. Then, the coupling mechanism between the electric field and microstrip antenna is established through radiation coupling interference. On this basis, the BLT equation and numerical integration method are applied to determine the induced voltage at the target microstrip antenna. Eventually, the proposed approach is validated by a full-wave simulation method and the impact of the microstrip antenna parameters on the coupling interference is discussed. This article provides an analytical method for calculating the coupling of a microstrip antenna. Compared with numerical simulation, this method has certain potential advantages in solving closed electrically large objects. Furthermore, duplicate modeling can be avoided in the same type of scenario.

Derivation and Computation of Surface Differential Equations for the Induced Current on Perfectly Electrically Conducting Objects in Electromagnetics

Surface differential equations (SDEs) are derived for the induced current on the outer surface of a perfectly electrically conducting (PEC) object for the first time. The derived equations are wave equations that describe the propagation of surface current waves along a PEC surface. A numerical method based on SDEs is proposed, which is named the eigenmode theory in this article. In this method, SDEs are discretized into a generalized eigenvalue equation, which can be used to obtain a series of modal currents and expand the surface current induced by any excitation. The modal currents are only dependent on the shape and size of the PEC object and are independent of any specific excitation, including frequency, feeding location, and so on. This property results in an eigenmode theory with great potential in many challenging antenna designs. Numerical examples for both scattering and radiation analyses demonstrate the effectiveness and accuracy of eigenmode theory and, thus, give evidence for the correctness of SDEs.

A simple two-layer broadband metamaterial absorber for solar cells

A broadband absorber composed of silicon rods and nickel ground is proposed in the visible band. The absorption above 98% can be obtained in the frequency range of [Formula: see text] THz with strong polarization independence and angle independence. The impedance matching theory and field distributions of eigenmodes are used to analyze the physical mechanism of the broadband absorption. The absorber has a simple structure with only two layers, which is composed of silicon and nickel. Nickel is a non-precious metal, which is cheaper than the precious metal materials commonly used in metamaterial absorber. The proposed cost-effective absorber with simple structure has great potential in the application of solar cells.

Generalised theory of polarisation modes for resonators containing birefringence and anisotropic gain.

Polarisation eigenmode theory is well established for laser cavities in which the principal axes for gain and polarisation elements are parallel. Here we generalise the theory to include the case for gain axes at arbitrary angle to the birefringence, which is the case for Raman lasers based on cubic-class gain crystals that contain stress-induced birefringence. The theory describes regimes dominated by gain, linear or circular birefringence, and the intermediate regime in which elliptically polarised output modes are obtained. Previously reported behaviour for diamond Raman lasers are found to be in accord with the findings. Design criteria are obtained to enable prediction of polarisation behaviour as functions of birefringence and resonator design.

Kinetic Alfvén Waves Excited in Two‐Dimensional Magnetic Reconnection

AbstractKinetic Alfvén waves (KAWs) are believed to be capable of efficiently transporting energy and play an important role in facilitating magnetic reconnection. KAW eigenmode theory suggests that Hall fields can be considered as the components of KAW, providing a mechanism for the generation and dissipation of KAW in magnetic reconnection. Using particle‐in‐cell simulations, we examined Hall fields in the magnetic reconnection region and found that (1) Hall electric filed is balanced by the ion pressure gradient and (2) the ratio of Hall electric field to Hall magnetic field is on the order of Alfvén speed. These results are consistent with KAW physics. Simulation results also indicate that KAWs are excited in the reconnection site and then transmitted along the separatrices. The wave Poynting flux propagates parallel to the magnetic field lines, carrying substantial energy. It is further found that a thinner current sheet provides a favorable condition for the excitation of KAW and results in a higher ratio of the Hall fields.

Higher-order moment theories for dilute granular gases of smooth hard spheres

Grad’s method of moments is employed to develop higher-order Grad moment equations – up to the first 26 moments – for dilute granular gases within the framework of the (inelastic) Boltzmann equation. The homogeneous cooling state of a freely cooling granular gas is investigated with the Grad 26-moment equations in a semi-linearized setting and it is shown that the granular temperature in the homogeneous cooling state still decays according to Haff’s law while the other higher-order moments decay on a faster time scale. The nonlinear terms of the fully contracted fourth moment are also considered and, by exploiting the stability analysis of fixed points, it is shown that these nonlinear terms have a negligible effect on Haff’s law. Furthermore, an even larger Grad moment system, which includes the fully contracted sixth moment, is also scrutinized and the stability analysis of fixed points is again exploited to conclude that even the inclusion of the scalar sixth-order moment into the Grad moment system has a negligible effect on Haff’s law. The constitutive relations for the stress and heat flux (i.e. the Navier–Stokes and Fourier relations) are derived through the Grad 26-moment equations and compared with those obtained via the Chapman–Enskog expansion and via computer simulations. The linear stability of the homogeneous cooling state is analysed through the Grad 26-moment system and various subsystems by decomposing them into longitudinal and transverse systems. It is found that one eigenmode in both longitudinal and transverse systems in the case of inelastic gases is unstable. By comparing the eigenmodes from various theories, it is established that the 13-moment eigenmode theory predicts that the unstable heat mode of the longitudinal system remains unstable for all wavenumbers below a certain coefficient of restitution, while any other higher-order moment theory shows that this mode becomes stable above some critical wavenumber for all values of the coefficient of restitution. In particular, the Grad 26-moment theory leads to a smooth profile for the critical wavenumber, in contrast to the other considered theories. Furthermore, the critical system size obtained through the Grad 26-moment theory is in excellent agreement with that obtained through existing theories.

Parallel ion compressibility effects on kinetic ballooning mode for different magnetic shears

Various gyrokinetic simulations suggest that the kinetic ballooning mode (KBM) instability is sensitive to the numerical implementation of equilibrium magnetic configuration in tokamaks. In this work, the gyrokinetic code GTC is employed to investigate the KBM's sensitivity to equilibrium plasma profiles. An outward radial shift of the radial mode is found for the normal magnetic shear case, but there is no shift if the shear is negative. The simulation results are explained by a linear eigenmode theory. It is found that the observed phenomenon is an effect of the parallel ion compressibility.

Dark Mode Driven Extra-narrow and Multiband Absorber

Recently, metamaterial absorbers have received tremendous amount of interest because of their remarkable ability to manipulate the amplitude, phase, and polarization of light. However, most absorbers rely on the direct coupling of electric or magnetic field with external excitation, which lead to inevitable energy leakage to the surrounding environment and depress the quality factor of the structure. In this work, we investigate the multiband absorption property by exciting dark plasmonic modes in reflective symmetric and asymmetric metamaterials. Theoretically, the existence of dark plasmonic modes in asymmetric metamaterials is unambiguously illustrated by the improved eigen-mode theory. With the introduction of asymmetry, dark modes in metamaterials can be easily excited by normal incident plane wave. Moreover, we also directly excite the dark modes in symmetric absorber with oblique incidence. The dark modes splitting mechanism is also clarified with the excitation of designer surface plasmon. Dominated by magnetic dipole or higher-order multipole, these dark modes possess high quality factors (Q). Numerical results indicate that the metamaterial absorber maintains high absorbance within a wide-angle incidence (0~50°). The high Q asymmetric metamaterial absorber can be an excellent candidate for multiband plasmonic sensor.

Long-range surface plasmon polariton enhancement in double-electrode structure

Surface plasmon polariton (SPP) is a kind of highly confined surface-wave mode associated with collective electron charge oscillation. A remarkable feature of the SPP is its highly sensitive response to change in permittivity or refractive index of the material in the vicinity of the metal surface, and it can be used as a high sensitive sensor. Long-range surface plasmon polariton (LRSPP) is a low-loss surface wave supported by symmetric structure, such as symmetric insulator-metal-insulator (IMI) slab. In most of previous investigations, only the properties of the eigenmodes of LRSPPs are analyzed. In this paper, however, we investigate the phenomena associated with the excitations of LRSPPs which cannot be explained by the eigenmode theory. Double-electrode structures are studied in this paper. For simplicity, we assume that the structures are symmetric if no coupler is introduced. When the coupler is introduced, however, this system can have interesting new properties. The influence of the parameters of the structure on the LRSPP is discussed in detail, and the enhancement effect of the LRSPP excited by the attenuated total reflectance (ATR) method is found. The research on the parameters is based on the reflectivity and the field enhancement calculated by the characteristic matrix technique. Taking the coupler into consideration, there are six media in the double-electrode structure excited by ATR. It turns out that the LRSPP can have new properties other than those of eigenmodes supported by symmetric structures without couplers. This is due to the asymmetry brought by the coupler in the ATR method, thus it is possible to enhance the wanted mode while suppress the other mode. The asymmetry brought by the coupler in the ATR method leads to new and interesting phenomena. If the distance between the coupler and the closer metal film (denoted by s) and that between the two metal films (denoted by t) are properly chosen, the long-range mode will be enhanced while the other mode will be suppressed. It should be emphasized that s is a crucial parameter. When s is small, the long-range mode is suppressed and the other mode is enhanced; when s is large, the energy focuses more on the long-range mode. However, when s is too large, the exciting efficiency is very low. It is found that the appropriate parameters in the ATR-mothod-exciting double electrode structure are s=350 nm, t=(1)/4λ, where λ is the wavelength of the source light in vacuum and is taken to be 546.1 nm, and the thickness of each metal Ag film is taken to be 36 nm. These parameters are important for future experiments to observe this kind of phenomenon.It is also found that both the field enhancement factor and its sensitivity to the refractivity of the output-end medium are very high in LRSPP case, which is possible to be used as a biological or chemical sensor. The asymmetry brought by the coupler in the ATR method makes LRSPP have new and interesting features, one of which is the enhancement of the long-range mode. The present research has heuristic significance for studying the long-range surface plasmon in asymmetric excitation configuration.

The AK Transform

In this brief communication we present a new integral transform, so far unknown, which is applicable, for instance, to studying the kinetic theory of natural eigenmodes or transport excited in plasmas with bounded distribution functions such as in Q machines/plasma diodes or in the scrap-off layer of Tokamak fusion plasmas. The results are valid for functions of function spaces—Lebesgue spaces, which are defined using a natural generalization of the p-norm for finite-dimensional vector spaces, where is the real set, σs is the σ-algebra of Lebesgue measurable sets, and the μ Lebesgue measure. , so that . Note that, using a simpler notation, more natural/known to engineers, f could be considered any piecewise continuous function, that is: Here is a Euclidian space with the usual norm (inner product: ) given by: [1].

3D electrostatic gyrokinetic electron and fully kinetic ion simulation of lower-hybrid drift instability of Harris current sheet

The eigenmode stability properties of three-dimensional lower-hybrid-drift-instabilities (LHDI) in a Harris current sheet with a small but finite guide magnetic field have been systematically studied by employing the gyrokinetic electron and fully kinetic ion (GeFi) particle-in-cell (PIC) simulation model with a realistic ion-to-electron mass ratio mi/me. In contrast to the fully kinetic PIC simulation scheme, the fast electron cyclotron motion and plasma oscillations are systematically removed in the GeFi model, and hence one can employ the realistic mi/me. The GeFi simulations are benchmarked against and show excellent agreement with both the fully kinetic PIC simulation and the analytical eigenmode theory. Our studies indicate that, for small wavenumbers, ky, along the current direction, the most unstable eigenmodes are peaked at the location where k→·B→=0, consistent with previous analytical and simulation studies. Here, B→ is the equilibrium magnetic field and k→ is the wavevector perpendicular to the nonuniformity direction. As ky increases, however, the most unstable eigenmodes are found to be peaked at k→·B→≠0. In addition, the simulation results indicate that varying mi/me, the current sheet width, and the guide magnetic field can affect the stability of LHDI. Simulations with the varying mass ratio confirm the lower hybrid frequency and wave number scalings.

Helicon waves in uniform plasmas. IV. Bessel beams, Gendrin beams, and helicons

Electromagnetic waves in the low frequency whistler mode regime are investigated experimentally and by digital data superposition. The radiation from a novel circular antenna array is shown to produce highly collimated helicon beams in a uniform unbounded plasma. The differences to Bessel beams in free space are remarked upon. Low divergence beams arise from the parallel group velocity of whistlers with phase velocity either along the guide field or at the Gendrin angle. Waves with angular momentum are produced by phasing the array in the circular direction. The differences in the field topologies for positive and negative modes numbers are shown. It is also shown that in uniform plasmas, the radial amplitude profile of the waves depends on the antenna field topology. Thus, there are no helicon “eigenmodes” with radial Bessel function profiles in uniform plasmas. It is pointed out that phase measurements in helicon devices indicate radial wave propagation which is inconsistent with helicon eigenmode theory based on paraxial wave propagation. Trivelpiece-Gould modes also exist in uniform unbounded plasmas.

2‐bit polarisation agile antenna with high port decoupling

A practical method to achieve both decoupling and six polarisation states by employing the mode-based approach for a four-element antenna is presented. The eigenmode theory as well as a practical implementation scheme are presented. The resulting approach can operate with vertical, horizontal, slant +45°, slant −45°, right-hand circular polarisation, or left-hand circular polarisation. A prototype has been manufactured and measured results show good agreement with simulations.

Electromagnetic Fields of Eigenmodes in Spherical Resonators

In this article a physical theory of eigenmodes of electromagnetic resonators is presented. It is known, that Maxwell equations predict non-physical singular behavior of eigenmodes in spherical resonators. This shows that Maxwell theory is incomplete. For the improvement of the theory this problem is treated with the help of Maxwell-Einstein theory. Maxwell-Einstein equations take into account space-time curvature. Regular implementation of this approach permits to avoid the influence of singularity. Another result consists of that eigenmodes with large values of orbital angular momentum are not observable. An analogy with CMB in the Universe is made.

Interaction of localized surface plasmons with chiral molecules

We analyze theoretically the interaction between chiral molecules and localized surface plasmons in subwavelength metallic structures of arbitrary shape. The chiral molecule is modeled using Condon's classical description of the molecular dipole moment that depends on the magnetic field [E. U. Condon, Rev. Mod. Phys. 9, 432 (1937)]. This model is included in an eigenmode theory of coupled plasmonic systems. In the limit of dipole-dipole interactions, the theory predicts there is no change in the resonance frequency of the surface plasmon in the presence of a chiral molecule and there is no change in the amplitude of the resonance in the presence of a uniform distribution of chiral molecules. This implies that to observe the effects of the chirality of molecules it may be necessary to form localized surface plasmons with more complex charge distributions. We also examine the absorption of light of the combined system of the metal structure and chiral molecule. The theory predicts that the chirality-dependent absorption in the metal structure averages to zero for a uniform distribution of molecules, with the observed absorption occurring entirely within the molecule due to excitation by the incident light and the fields from the surface plasmon. Apart from the expected circular dichroism, the theory also predicts a chirality-dependent absorption arising from a metal nanostructure illuminated with linearly polarized light and an absorption arising from those chiral properties of the molecule usually associated with optical activity.