Local Field Amplitude Research Articles

Statistical evaluation of electric field distributions in 3D composites with a random spatial distribution of dielectric inclusions

Electromagnetic applications of composites often impose constraints on the internal electric fields, such as an upper limit on the field strength to prevent local heating or dielectric breakthrough. However, owing to heterogeneity, the local fields in a composite differ from those in a homogeneous material. Moreover, they are accessible neither by experiment nor by effective medium theories, at least for arbitrary microstructures. In this work, we use numerical simulations to evaluate the electric field distribution and the effective permittivity for 3D systems of monodisperse impenetrable spheres dispersed in a continuous matrix phase. We restrict ourselves to loss-free dielectric materials and to a random spatial distribution of particles. Samples are placed in a parallel plate waveguide and exposed to a transverse electromagnetic wave. The local field amplitudes are calculated via the finite element method and are normalized to those of a homogeneous sample exhibiting the same effective permittivity and geometry. We analyze the distribution of the local electric field strength in both constituents, namely, particles and matrix. Thus, we evaluate mean values and standard deviations as well as the field strengths characterizing the highest and lowest percentiles. Increasing particle concentration or permittivity enhances heterogeneity, and so the local electric field strength in some domains can become much higher than its average value. The methods we apply here can also be used in further investigations of more complex systems, including lossy materials and agglomerating particles.

Verifying Ray Tracing Amplitude Methods for Global Magnetospheric Modeling

AbstractRay tracing is a commonly used method for modeling the propagation of electromagnetic waves in Earth's magnetosphere. To apply ray tracing results to global models of wave‐particle interaction such as energetic electron scattering, it is useful to map the discrete rays to a volume filling mesh. However, some methods have inherent losses of energy from the wave source, or do not account for the full range of wave properties within a sample volume. We have developed and tested a 3D magnetospheric ray tracing code “MESHRAY” which resolves these issues. MESHRAY uses the conservation of Poynting flux through ray triplets with finite volume to determine the local field amplitudes. Electromagnetic wave energy density from all ray data points is mapped to a mesh and verified against the wave source power for energy conservation varying time step length, number of rays, and total time steps. We find that the method is self‐consistent and numerically robust. We further investigate whether the neglect of phase information and superposition has a significant impact on the accuracy of mapping wave intensity to a mesh. We find excellent agreement between the analytic solution for waves emitted by a line source in a plane‐stratified medium and an equivalent ray tracing solution. When phase information is excluded, ray tracing reproduces an average amplitude spread over regions of coherent constructive and destructive interference. This may be an important consideration for interpolating ray tracing results of longer wavelength waves such as magnetosonic, electromagnetic ion cyclotron, or ULF waves.

Reflection Characteristics of Airy Beams Impinging on Graphene-Substrate Surfaces

In this work, we analytically and numerically investigate the reflection characteristics of the airy beams impinging on graphene-substrate surfaces. The explicit analytical expressions for the electric and magnetic field components of the airy beams reflected from a graphene-substrate interface are derived. The local-field amplitude, Poynting vector, and spin and orbital angular momentum of the reflected airy beams with different graphene structure and beam parameters are presented and discussed. The results show that the reflection properties of the airy beams can be flexibly tuned by modulating the Fermi energy of the graphene and have a strong dependence on the incident angle and polarization state. These results may have potential applications in the modulation of airy beams and precise measurement of graphene structure parameters.

Geometric phase for “dark” subspaces in coherent population trapping

The concept of geometric phase acquired by a quantum state during its evolution is generalized to the subspace of states of evolving quantum system. Physical motivation of this generalization comes from the effect of coherent population trapping. Under certain conditions, there exists a two-dimensional “dark” subspace of atomic ground states that does not interact with the external radiation. The structure of this “dark” subspace depends on the local field amplitude. We show that certain mathematical difficulties in finding the geometric phase for “dark” subspaces can be circumvented with the help of the orthogonal “bright” subspace.

High power microwave plasma discharge

High-power microwave (HPM) has broad applications in scientific research, civil and military community. HPM has the character of peak power of tens of Giga-Watt and the pulse width from tens of to hundreds of nanosecond. The intense electromagnetic breakdowns in the HPM generation, transmission and radiation systems, seriously limit the HPM systematic power capacity, and become the bottle neck of the HPM technology-development and the international technical challenge. In this paper, the recent developments of intense electromagnetic breakdown at vacuum and air sides of output window and on metal surfaces are reviewed and discussed. To understand the breakdown mechanism at window, several multipactor dynamic models are developed, especially involving electron-neutral collision and ionization in the desorbed gas layer, analytically obtaining the influence of desorption gas on multipactor saturation, and space charge field and potential distribution above dielectric surface formed by multipactor and plasma. By diagnosing the time- and space-evolution optical emissions, the mechanisms of nano-second microwave-driven discharges near the dielectric/vacuum and dielectric/air interface were discussed. For breakdown at the dielectric/vacuum interface, multipactor and plasma developing in a thin layer of several millimeters above interface, revealing intense ionization concentrated in a desorbed high-pressure layer. For breakdown at the dielectric/air interface, nonlinear positive feedback of formation of a space-charge microwave sheath near the dielectric surface, accelerated by the normal components of the microwave field, significantly enhances the local-field amplitude and hence ionization near the dielectric surface. The mechanism and methods of using magnetic field satisfying specific amplitude and direction perpendicular to E rf x E dc to suppress microwave multipactor were theoretically studied and experimental demonstrated. The methods of the external resonant magnetic field have been demonstrated by proof-of principle S-band large power experiments to significantly improve the power capacity by 9 times. The Halbach-like magnets to generate the transverse homogeneous B-field in a large scale was designed to suppress multipactor, and the window breakdown threshold was significantly enhanced at multi-Giga-watt. The methods of periodic surface profiles on suppressing microwave multipactor were discussed. The three-dimensional periodic ripple profile with each unit of rotational symmetric surface is proposed and theoretically and experimentally demonstrated to suppress multipactor for arbitrary electromagnetic mode with any polarization. In theoretical aspect, basic physics courses are described qualitatively, the basic models of secondary electron multipator, gas desorption and plasma avalance are established, but lack of quantitive results and experimental diagnostic of plasma energy and density. The physical and chemical methods of periodici surface, resonant magnet, and surface fluorination are successfully used in suppressing breakdown and improving the power capacity, but there is distance away from practical application.

Enhancement of the Local Electromagnetic Field over Planar “Particles” Formed on the Surface of a Polar Crystal

Small “particles” of an open surface were formed on a SiC polar crystal with openings in the opaque metal mask covering the sample. The dimensions of the holes were about surface phonon polariton wavelength. Such a sample was irradiated with an electromagnetic wave ( λ = 10.68μm) at a frequency close to the lattice resonance of SiC. A significant enhancement in the field amplitude of surface phonon polariton waves was detected over such “particles” compared to the amplitude over an infinite open surface of SiC. Such a phenomenon, observed by us in the IR band, is similar to plasmon resonance on small metal particles in the visible band, but the lateral resolution of the ASNOM used (no worse than 30 nm at 10 μm) makes the obtained field distribution more detailed. The maps of the local field amplitude and phase obtained on SiC surface with ASNOM are in a good quantitative agreement with simulations using the Green’s function.

Frequency-domain modelling of gain in pump-probe experiment by an inhomogeneous medium

Introduction of a gain medium in lossy plasmonic metamaterials reduces and compensates losses or even amplifies an incident light often with nonlinear optical effect. Here, optical gain in a pump-probe experimental setup is effectively calculated in the frequency-domain by approximating a gain material as an inhomogeneous medium. Spatially varying local field amplitudes of the pump and probe beams are included in the model to reproduce the inhomogeneous gain effect, in which population inversion occurs most strongly near the surface and decays along the propagation direction. We demonstrate that transmission spectra calculated by this method agree well with finite-difference time-domain simulation results. This simplified approach of gain modelling offers an easy and reliable way to analyze wave propagation in a gain medium without nonlinear time-domain calculation.

Effects of asymmetric nanostructures on the extinction difference properties of actin biomolecules and filaments.

In this paper, symmetric and asymmetric tapering on the arms of the gammadion nanostructure is proposed to enhance both local field distribution and extinction difference (ED). The asymmetric tapered gammadion with tapering fraction (TF) of 0.67 is seen to have the largest ED and spatial local field distribution, producing a large wavelength shift of more than 50 percent as compared to the untapered gammadion nanostructures when immersed in a solution of actin molecules and filaments. The optical chirality, ζ shows that the larger local field amplitudes produced by the asymmetric designs increases the rate of chiral molecules excitation. This enhanced field is strongly rotating and highly sensitive to single molecules and larger filaments. Here, we show that the ED, optical chirality, sensitivity and rate of chiral molecules excitation can be improved by incorporating asymmetric designs into chiral gammadion nanostructures through tapering.

Ultrafast high-power microwave window breakdown: Nonlinear and postpulse effects

The time- and space-dependent optical emissions of nanosecond high-power microwave discharges near a dielectric-air interface have been observed by nanosecond-response four-framing intensified-charged-coupled device cameras. The experimental observations indicate that plasma developed more intensely at the dielectric-air interface than at the free-space region with a higher electric-field amplitude. A thin layer of intense light emission above the dielectric was observed after the microwave pulse. The mechanisms of the breakdown phenomena are analyzed by a three-dimensional electromagnetic-field modeling and a two-dimensional electromagnetic particle-in-cell simulation, revealing the formation of a space-charge microwave sheath near the dielectric surface, accelerated by the normal components of the microwave field, significantly enhancing the local-field amplitude and hence ionization near the dielectric surface. The nonlinear positive feedback of ionization, higher electron mobility, and ultraviolet-driven photoemission due to the elevated electron temperature are crucial for achieving the ultrafast discharge. Following the high-power microwave pulse, the sheath sustains a glow discharge until the sheath collapses.

Apertureless SNOM imaging of the surface phonon polariton waves: what do we measure?

The apertureless scanning near-field microscope (ASNOM) mapping of surface phonon polariton (SPP) waves being excited at the surface of the SiC polar crystal at a frequency corresponding to the lattice resonance was investigated. The wave with well-defined direction and source position, as well as a well-known propagation law, was used to calibrate the signal of an ASNOM. An experimental proof is presented showing that the signal collected by the ASNOM in such a case is proportional (as a complex number) to the local field amplitude above the surface, regardless of the tip response model.

Near-field spatial mapping of strongly interacting multiple plasmonic infrared antennas

Near-field dipolar plasmon interactions of multiple infrared antenna structures in the strong coupling limit are studied using scattering-type scanning near-field optical microscope (s-SNOM) and theoretical finite-difference time-domain (FDTD) calculations. We monitor in real-space the evolution of plasmon dipolar mode of a stationary antenna structure as multiple resonantly matched dipolar plasmon particles are closely approaching it. Interparticle separation, length and polarization dependent studies show that the cross geometry structure favors strong interparticle charge-charge, dipole-dipole and charge-dipole Coulomb interactions in the nanometer scale gap region, which results in strong field enhancement in cross-bowties and further allows these structures to be used as polarization filters. The nanoscale local field amplitude and phase maps show that due to strong interparticle Coulomb coupling, cross-bowtie structures redistribute and highly enhance the out-of-plane (perpendicular to the plane of the sample) plasmon near-field component at the gap region relative to ordinary bowties.

General formulation for direct evaluation of the local field amplitude and transition amplitude based on the Fredholm determinant

We develop a determinantal method in a quantum scattering system for direct evaluation of various quantities including the local field amplitude and transition amplitude ($S$-matrix element). This method is applicable to multichannel elastic and inelastic scattering systems without rearranging the particles. The underlying principle of our formulation is that requested information can be extracted from a wave operator without solving the wave equation. The wave operator is the master operator maintaining all of the information about a system; the determinant of the inverse wave operator is just the Fredholm determinant. In the 1960s, a similar determinantal method was developed for the $S$-matrix element or equivalently the far-field amplitude of the wave function. Until now, however, no determinantal method for near-field quantities existed, although de Broglie and electromagnetic near fields are observable using scanning probe microscopes. Additionally, we prove that our formula for $S$-matrix element covers the known formula (the Le Couteur-Newton formula).

Luminescence of Tb3+ doped TeO2–ZnO–Na2O–PbO glasses containing silver nanoparticles

Luminescence properties of Tb3+ doped TeO2–ZnO–Na2O–PbO glasses containing silver nanoparticles (NPs) were investigated. The absorption band due to the surface plasmon resonance in the NPs was observed. Its amplitude increases with the heat treatment of the samples that controls the nucleation of the NPs. Tb3+ emission bands centered at ≈485, ≈550, ≈585, and ≈623 nm were detected for excitation at 377 nm. The whole spectrum is intensified by the appropriate annealing time of the samples. Enhancement by ≈200% of the Tb3+ luminescence at 550 nm was observed for samples annealed at 270 °C during 62 h. This enhancement effect is due to the local field amplitude that increases with the amount of silver NPs and their aggregates.

Strong coupling between surface plasmon-polaritons and organic molecules in subwavelength hole arrays

The interaction of a $J$-aggregate and surface plasmon polariton modes of a subwavelength hole array have been studied in detail. By measuring the effects of hole array period, angular dispersion and concentration of the $J$-aggregate on the transmission of the array, the existence of a strong coupling regime is demonstrated with a Rabi splitting of 250 meV. This large splitting is explained not only by the high oscillator strength of the dye but also by the high local field amplitudes generated by surface plasmons of the metallic structure.

Resonant excitation of tip plasmons for tip-enhanced Raman SNOM

The conditions necessary for the optimisation of tip-enhanced scanning near-field optical microscopy have been determined. The Raman scattering efficiency can be enormously increased by enhancements in the local field amplitude, such as that which can occur in the vicinity of a metallic nanostructure. The field enhancement in the vicinity of a silver tip is investigated theoretically here using the finite difference time domain method. Field enhancements from electron oscillations on the tip are shown to display strong maxima at resonant illumination wavelengths and the nature of these enhancements at the substrate surface beneath the tip, both on and off resonance, has been calculated. The enhancement of the Raman signal on the surface decreases exponentially as the tip–substrate separation is increased and a peak Raman enhancement of 10 7 is theoretically achievable at a tip–surface separation of 2 nm. The resolution is also strongly related to the distance between the tip and the substrate surface narrowing to <7 nm, significantly smaller than the radius of curvature of the end of the tip.

Mapping the confined optical field in a microcavity via the emission from a conjugated polymer

The distribution of a confined optical field within a microcavity was determined using a thin layer of the fluorescent polymer PPV as a probe of the local-field amplitude. It is shown that the photoluminescence emission intensity from the cavity is a function of the axial position of the polymer, and confirms that a microcavity can be used to control spontaneous emission.

Aircraft measurement of electric field: Self‐calibration

The electric field of a thunderstorm is distorted by the metallic surfaces of airplanes and rockets. The amplitude of the local, distorted electric field can be measured at selected locations on the surface of the vehicle with electric field meters. Measuring the thunderstorm field entails finding the relations between the local fields at the meters and the ambient, undistorted electric field that would exist in the absence of the vehicle. Calibration can be performed in the following steps: (1)Find linear combinations F0, F1, …, of local field amplitudes that are independent of the charge on the vehicle. (2) While the ambient electric field is constant in the Earth coordinate system, rotate the vehicle (roll and turn or roll and pitch) and record the local field amplitudes and the roll, pitch, and heading angles. Find the direction of the electric vector and the ratios between all of the calibration coefficients that best fit the linear combinations of local field amplitudes. (3) Find the magnitude of one of the coefficients by comparison with a calibrated instrument; from this magnitude and all of the ratios, find all of the magnitudes. With this method of calibration, finding out how the linear combinations F0, F1, … depend on the ambient electric field does not require a symmetric placement of the electric field meters, nor does it require any knowledge of the locations of the field meters. However, inverting the expressions to find the ambient field components as functions of the F𝒾 does place constraints on the locations of the field meters. The results of the above calibration can be used only when the signal at each field meter is a linear function of four parameters: the charge on the airplane and the three components of a uniform electric field from distant charge. When there are five or more electric field meters, the presence of nearby charge can be detected because it is possible to find linear combinations of the signals from five field meters whose value is not zero only when there is nearby charge. This paper presents one method of finding the linear combinations.

Electrical Control in Photoferroelectric Materials for Optical Storage

After defining photoferroelectrics as photosensitive and nonlinear electrooptic materials, we report electrical control of holographic diffraction efficiency in PLZT ceramics and electrical fixation and erasure of holograms recorded in SBN single crystals. On the basis of experimental data, these effects are explained in terms of the local field amplitude, computed as the sum of the applied field and the photoinduced space charge field and high nonlinear electrooptic effects associated with ferroelectric phase transitions.