Electromagnetic Wave Equation Research Articles

Formation of hybrid higher-order cylindrical vector beams using binary multi-sector phase plates

Nowadays, the well-known cylindrical vector beams (CVBs) – the axially symmetric beam solution to the full-vector electromagnetic wave equation – are widely used for advanced laser material processing, optical manipulation and communication and have a great interest for data storage. Higher-order CVBs with polarisation order greater than one and superpositions of CVBs of various orders (hybrid CVBs) are especially of interest because of their great potential in contemporary optics. We performed a theoretical analysis of the transformation of first-order CVBs (radially and azimuthally polarised beams) into hybrid higher-order ones using phase elements with complex transmission functions in the form of the cosine or sine functions of the azimuthal angle. Binary multi-sector phase plates approximating such transmission functions were fabricated and experimentally investigated. The influence of the number of sectors and a height difference between neighbouring sectors, as well as the energy contribution of the different components in the generated hybrid higher-order CVBs were discussed in the context of polarisation transformation and vector optical field transformation in the focal region. The possibility of polarisation transformation, even in the case of weak focusing, is also demonstrated. The simple structure of the profile of such plates, their high diffraction efficiency and high damage threshold, as well as the easy-to-implement polarisation transformation principle provide advanced opportunities for high-efficient, quickly-switchable dynamic control of the generation of structured laser beams.

Exact ray theory for the calculation of the optical generation rate in optically thin solar cells

There is a profound duality between rays and waves. In fact, 70 years ago, in the context of quantum mechanics, Feynman showed that rays, properly equipped with phases and correctly summed, provide exact solutions of the quantum mechanical wave equation. In this paper, constructing explicit, exact ray solutions of the one-dimensional Helmholtz equation as a model for optically thin solar cells, we show that the ray-wave duality is also exact in the context of the electromagnetic wave equations. We introduce a complex index of refraction in order to include absorption. This have so far not been treated in the quantum ray-splitting literature. We show that inclusion of exact phases is mandatory and that a ray theory without phases may result in amplitude errors of up to 60%. We also show that in the case of multi-layered solar cells the correct summation order of rays is important. Providing support for the notion that rays provide the “skeleton” of electromagnetic waves, we perform a Fourier transform of the (experimentally measurable) solar cell reflection amplitude, which reveals the rays as peaks in the optical path length spectrum. An application of our exact ray theory to a silicon solar cell is also provided. Treating the one-dimensional case exactly, our paper lays the foundation for constructing exact ray theories for application to solar cell absorption cross section in two and three dimensions.

Polarization Rotation and Mode Splitting in Photonic Crystal Line-Defect Waveguides

In a line-defect waveguide of a planer photonic crystal (PhC), we found a new rotational state of polarised light, which exhibits `polarisation rotation' on the PhC plane, when a phase mismatch $m$ was added to the air-hole alignment of the waveguide, where mode splitting was simultaneously observed in the dispersion curve. To account for the polarisation rotation together with the mode splitting, we propose a two-state model that is constructed from Schr{\o}dinger equation obtained from the equation for electromagnetic waves. The proposed two-state model gives an explanation on the relation between the polarisation-rotational angle $\theta$ and the mismatch $m$ and on its rotational direction (i.e., clockwise or anticlockwise direction) that depends on the mode. Using the two-state model, we also discuss the angular momenta of the polarised light in the PhC waveguide, which are directly related to the Stokes parameters that characterise the polarisation rotations.

Acoustics of noise, vibration, and harshness

In this paper, we will go to a more fundamental level of treating acoustics. We introduced the gauge invariance into the acoustic wave equation of motion in 2007. This is an important milestone in the history of gauge invariance. The earliest gauge invariance is shown by Maxwell’s electromagnetic wave equations. The root of acoustics originated from fluid mechanics. We show that the usual form of acoustic wave equation for fluids is in fact the linearized form of the Navier Stokes equations. Hence there is in fact, no need to use acoustic analogy to derive the formula for the jet noise which was done by James Lighthill. In this paper we also treat finite amplitude sound wave and finite amplitude vibration using the deductive approach. This is a generalization of the linear theory to the nonlinear theory using relativistic and curvilinear spacetime treatment. This produces the linear case as a special case of the nonlinear case. The usual method is the reverse which starts from the linear theory and extend to the nonlinear theory. This will miss out some useful information. The treatment of vibration will need to incorporate the theory of elasticity. This paper is also the first introduction of singularities into vibration. Singularities is mathematically more sophisticated than resonance.

Nonlinear interaction of an intense radio wave with ionospheric D/E layer plasma

This paper considers the nonlinear interaction of an intense electromagnetic wave with the D/E layer plasma in the ionosphere. A simultaneous solution of the electromagnetic wave equation and the equations describing the kinetics of D/E layer plasma is obtained; the phenomenon of ohmic heating of electrons by the electric field of the wave causes enhanced collision frequency and ionization of neutral species. Electron temperature dependent recombination of electrons with ions, electron attachment to O2 molecules, and detachment of electrons from O2− ions has also been taken into account. The dependence of the plasma parameters on the square of the electric vector of the wave E02 has been evaluated for three ionospheric heights (viz., 90, 100, and 110 km) corresponding to the mid-latitude mid-day ionosphere and discussed; these results are used to investigate the horizontal propagation of an intense radio wave at these heights.

Defining cylindrical space optical resonators through supported mode properties: inverse numerical process.

Faraday's and Ampere's laws are converted to matrix operator form and rearranged such that the unknown relative permittivity and relative permeability tensors can be determined. The material and geometry of cylindrically symmetric optical resonator structures are determined through the electric and magnetic field component profiles and complex angular frequency of a proposed localized state. This differs from the usual utilization of the electromagnetic wave equations, solving for states given the material properties and geometry. Thus the technique presented here is an inverse numerical process. The theoretical expressions are provided based on a Fourier-Bessel numerical approach which is highly suitable for cylindrical geometry resonators. Without loss of the generality of the technique, examples of resonant structure determination are presented for non-magnetic and diagonal relative permittivity tensor. Axial field propagation is included to demonstrate the design capabilities related to optical fiber and photonic crystal fiber structures.

Standing Wave Field Distribution in Graded-Index Antireflection Coatings

Standing wave field distributions in three classic types of graded-index antireflection coatings are studied. These graded-index antireflection coatings are designed at wavelengths from 200 nm to 1200 nm, which is the working wavelength range of high energy laser system for inertial-fusion research. The standing wave field distributions in these coatings are obtained by the numerical calculation of electromagnetic wave equation. We find that standing wave field distributions in these three graded-index anti-reflection coatings are quite different. For the coating with linear index distribution, intensity of standing wave field decreases periodically from surface to substrate with narrow oscillation range and the period is proportional to the incident wavelength. For the coating with exponential index distribution, intensity of standing wave field decreases periodically from surface to substrate with large oscillation range and the period is also proportional to the incident wavelength. Finally, for the coating with polynomial index, intensity of standing wave field is quickly falling down from surface to substrate without an obvious oscillation. We find that the intensity of standing wave field in the interface between coating and substrate for linear index, exponential index and polynomial index are about 0.7, 0.9 and 0.7, respectively. Our results indicate that the distributions of standing wave field in linear index coating and polynomial index coating are better than that in exponential index coating for the application in high energy laser system. Moreover, we find that the transmittance of linear index coating and polynomial index coating are also better than exponential index coating at the designed wavelength range. Present simulation results are useful for the design and application of graded-index antireflection coating in high energy laser system.

Electromagnetic Wave Function and Equation, Lorentz Force in Rindler Spacetime

In the general relativity theory, we find the electro-magnetic wave function and equation in Rindler space-time. Specially, this article is that electromagnetic wave equation is corrected by the gauge fixing equation in Rindler space-time. We define the force in Rindler space-time We find Lorentz force (electromagnetic force) by electro-magnetic field transformations in Rindler space-time. In the inertial frame, Lorentz force is defined as 4-dimensional force. Hence, we had to obtain 4-dimensional force in Rindler space-time. We define energy-momentum in Rindler space-time.

Electromagnetic Wave Equation on Differential Form Representation

One of the indispensable part of the theoretical physics interest is geometry differential. This one interest of physical area has been developed such as in electromagnetism. Maxwell's equations have been generalized in two covariant forms in differential form representation. A beautiful calculus vector in this representation, such as exterior derivative and Hodge star operator, lead this study. Electromagnetic wave equation has been expressed in differential form representation using Laplace-de Rham operator. Explicitly, wave equation shows the same form in Minkowski space-time like vector representation. This study is able to introduce us to learn application of differential form in physics.

On beam models and their paraxial approximation

We derive focused laser pulse solutions to the electromagnetic wave equation in vacuum. After reproducing beam and pulse expressions for the well-known paraxial Gaussian and axicon cases, we apply the method to analyse a laser beam with Lorentzian transverse momentum distribution. Whilst a paraxial approach has some success close to the focal axis and within a Rayleigh range of the focal spot, we find that it incorrectly predicts the transverse fall-off typical of a Lorentzian. Our vector-potential approach is particularly relevant to calculation of quantum electrodynamical processes in weak laser pulse backgrounds.

Antireflection coating of barriers to enhance electron tunnelling: exploring the matter wave analogy of superluminal optical phase velocity

The tunnelling of electrons through barriers is important in field emission sources and in interconnects within electronic devices. Here we use the analogy between the electromagnetic wave equation and the Schrodinger equation to find potential barriers that, when added before an existing barrier, increase the transmission probability. A single pre-barrier of negative potential behaves as a dielectric “antireflection coating”, as previously reported. However, we obtain an unexpected and much greater enhancement of transmission when the pre-barrier has a positive potential of height smaller than the energy of the incident electron, an unfamiliar optical case, corresponding to media with superluminal phase velocities as in dilute free electron media and anomalous dispersion at X-ray frequencies. We use a finite difference time domain algorithm to evaluate the transmission through a triangular field emission barrier with a pre-barrier that meets the new condition. We show that the transmission is enhanced for an incident wavepacket, producing a larger field emission current than for an uncoated barrier. Examples are given of available materials to enhance transmission in practical applications. The results are significant for showing how to increase electron transmission in field emission and at interconnects between dissimilar materials in all types of electronic devices.

Optimal stability for a first order coefficient in a non-self-adjoint wave equation from Dirichlet-to-Neumann map

This paper is focused on the study of an inverse problem for a non-self-adjoint hyperbolic equation. More precisely, we attempt to stably recover a first order coefficient appearing in a wave equation from the knowledge of Neumann boundary data. We show in dimension n greater than two, a stability estimate of Hölder type for the inverse problem under consideration. The proof involves the reduction to an auxiliary inverse problem for an electro-magnetic wave equation and the use of an appropriate Carleman estimate.

The analytical solution of 2D electromagnetic wave equation for eddy currents in the cylindrical solid rotor structures

The paper presents the closed-form solution of two dimensional (2D) electromagnetic wave equation for eddy current problems in cylindrical structures. The magnetic field calculation is a complex issue for electrical machines especially. The paper provides an analytical solution for solid cylindrical structures with linear magnetization. This approach is extended to the electrical machines with the solid rotors. Multilayered cylindrical geometry is used for the solution. Two dimensional parabolic partial differential equation is solved for each layer. According to the analytical solution, eddy current and eddy current losses are calculated in the solid region and compared to the results of the finite element model.

Linear electromagnetic wave equations in materials

After a short review of microscopic electrodynamics in materials, we investigate the relation of the microscopic dielectric tensor to the current response tensor and to the full electromagnetic Green function. Subsequently, we give a systematic overview of microscopic electromagnetic wave equations in materials, which can be formulated in terms of the microscopic dielectric tensor.

Nonlinear fluid simulation study of stimulated Raman and Brillouin scatterings in shock ignition

We developed a new nonlinear fluid laser-plasma-instability code (FLAME) using a multi-fluid plasma model combined with full electromagnetic wave equations. The completed one-dimensional version of FLAME was used to study laser-plasma instabilities in shock ignition. The simulations results showed that absolute stimulated Raman scattering (SRS) modes growing near the quarter-critical surface were saturated by Langmuir-wave Decay Instabilities (LDI) and pump depletion. The ion-acoustic waves from LDI acted as seeds of Stimulated Brillouin Scattering, which displayed a bursting pattern and caused strong pump depletion. Re-scattering of SRS at the 1/16th-critical surface was also observed in a high temperature case. These results largely agreed with the corresponding Particle-in-Cell simulations.

A memory-efficient staining algorithm in 3D seismic modelling and imaging

The staining algorithm has been proven to generate high signal-to-noise ratio (S/N) images in poorly illuminated areas in two-dimensional cases. In the staining algorithm, the stained wavefield relevant to the target area and the regular source wavefield forward propagate synchronously. Cross-correlating these two wavefields with the backward propagated receiver wavefield separately, we obtain two images: the local image of the target area and the conventional reverse time migration (RTM) image. This imaging process costs massive computer memory for wavefield storage, especially in large scale three-dimensional cases. To make the staining algorithm applicable to three-dimensional RTM, we develop a method to implement the staining algorithm in three-dimensional acoustic modelling in a standard staggered grid finite difference (FD) scheme. The implementation is adaptive to the order of spatial accuracy of the FD operator. The method can be applied to elastic, electromagnetic, and other wave equations. Taking the memory requirement into account, we adopt a random boundary condition (RBC) to backward extrapolate the receiver wavefield and reconstruct it by reverse propagation using the final wavefield snapshot only. Meanwhile, we forward simulate the stained wavefield and source wavefield simultaneously using the nearly perfectly matched layer (NPML) boundary condition. Experiments on a complex geologic model indicate that the RBC-NPML collaborative strategy not only minimizes the memory consumption but also guarantees high quality imaging results. We apply the staining algorithm to three-dimensional RTM via the proposed strategy. Numerical results show that our staining algorithm can produce high S/N images in the target areas with other structures effectively muted.

Modification of electromagnetic fields and plasma resistance by thermal effects in helicon plasmas

The effects of the thermal motion of charged particles on physical characteristics of collisional helicon plasmas are investigated. First, the dielectric permittivity tensor of a helicon plasma is obtained by considering the thermal and collisional effects in the kinetic theory. Then, the electromagnetic wave and plasma resistance equations are presented and solved in a helicon plasma source with a Nagoya type III antenna. It is shown that by increasing the temperature of plasma electrons, the effective collision frequency is increased, and consequently, the peaks of resistance profiles are lowered and broadened.

Getting started with controlled-source electromagnetic 1D modeling

Forward modeling is an important part of understanding controlled-source electromagnetic (CSEM) responses. The diffusive term in the electromagnetic wave equation is dominant over the displacement term at these frequencies. It is the diffusive behavior that makes it difficult to imagine the actual propagation of the signal. An important tool in gaining experience therefore is forward modeling, and lots of it. The advantage of one-dimensional (1D) forward modeling, besides its speed, is to study isolated effects (see for instance Key, 2009): What is the influence of resistivity anisotropy, or of fine-scale resistivity variations? What is the influence of the airwave? With 1D modeling you can quickly study these effects in isolation before you go on to more complex models in higher dimensions. For an introduction to CSEM for hydrocarbon exploration see, for instance, Constable (2010).

Microscopic theory of the refractive index

We examine the refractive index from the viewpoint of modern first-principles materials physics. We first argue that the standard formula, n2=ɛrμr, is generally in conflict with fundamental principles on the microscopic level. Instead, it turns out that an allegedly approximate relation, n2=ɛr, which is already being used for most practical purposes, can be justified theoretically at optical wavelengths. More generally, starting from the fundamental, Lorentz-covariant electromagnetic wave equation in materials as used in plasma physics, we rederive a well-known, three-dimensional form of the wave equation in materials and thereby clarify the connection between the covariant fundamental response tensor and the various Cartesian tensors used to describe optical properties. Finally, we prove a general theorem by which the fundamental, covariant wave equation can be reformulated concisely in terms of the microscopic dielectric tensor.

Solution of electromagnetic wave equation in graded interface for exponential permeability and permittivity profile

The electromagnetic wave equation in graded interface for exponential permeability and exponential permittivity profile was solved using asymptotic iteration method (AIM). In exponential function, we obtained the graded graphs of permittivity and permeability. By using exponential permeability and permittivity profile in Maxwell equation, we reduced Maxwell equation into the second orde differential equation. The second orde differential equation was reduced to AIM-type differential equation using separation variable and suitable parameter. By AIM, the wave vector and field equations were obtained. The field equations were expressed in hypergeometric function.