One-dimensional Maxwell Equations Research Articles

Testing Bicompact Schemes for the One-Dimensional Maxwell Equations in Stratified Media

Testing Bicompact Schemes for the One-Dimensional Maxwell Equations in Stratified Media

Topological properties of one-dimensional non-Hermite electromagnetic medium system

In this paper, we establish a one-dimensional periodic dielectric systems based on one-dimensional maxwell's equations, with abundant topological phase. Through the analysis of the system of chiral symmetry, the energy spectrum of the system and topological phase diagram under the influence of various parameters, particularly is a Hermitian topological phase diagram. By further numerical calculation of the energy spectrum and eigenfunction system, found a 0 or a PI energy advantage state borders, and around the edge with the number of boundary value is consistent, indicates that the system meet the volume boundary correspondence principle.

On the area of extremely short electromagnetic pulses in medium for problems of a finite integration region

Based on the one-dimensional Maxwell equations of electrodynamics of continuous medium, the balance ratios of electric and magnetic areas for problems solved in a finite region in space and time are obtained. Keywords: extremely short pulses, electrical pulse area.

Highly Accurate Methods for Solving One-Dimensional Maxwell Equations in Stratified Media

Highly Accurate Methods for Solving One-Dimensional Maxwell Equations in Stratified Media

Group velocity dispersion in terahertz frequency combs within a generalized Maxwell-Bloch framework

As many molecules have their rotovibrational resonance frequencies in the mid-infrared or terahertz regime, efficient generation of corresponding frequency combs may lead to large progress in gas spectroscopy and sensing. Quantum cascade lasers (QCLs) are among the most promising candidates for a compact and cheap radiation source in this frequency range. This contribution presents a full-wave numerical solution of the Maxwell-Liouville-von Neumann equations, thus avoiding the limited applicability of the rotating wave approximation to moderate field strengths and spectral bandwidths. We include losses and chromatic dispersion of the optically active material in the QCL. The semiclassical approach uses the finite-difference time-domain (FDTD) method to derive update equations for the electric field, starting from the one-dimensional Maxwell equations. There, the optical full-wave propagation is coupled to the electronic quantum system via a polarization term that arises from the evolution of the density matrix. Furthermore, dispersion effects are considered through a classical polarization term and losses are introduced by a finite material conductivity. This work mainly focuses on the integration of group velocity dispersion (GVD) due to the bulk material and, if applicable, the waveguide geometry into the update equations. It is known to be one of the main degradation mechanisms of terahertz frequency combs, but has not yet been added to the existing full-wave solver. The implementation is carried out as Lorentz model and is applied to an experimentally investigated QCL frequency comb setup from the literature. The reported results are in good agreement with the experimental data. Especially, they confirm the need for dispersion compensation for the generation of terahertz frequency combs in QCLs.

Mbsolve: An open-source solver tool for the Maxwell-Bloch equations

The Maxwell-Bloch equations are a valuable tool to model light-matter interaction, where the application examples range from the description of pulse propagation in two-level media to the elaborate simulation of optoelectronic devices, such as the quantum cascade laser (QCL). In this work, we present mbsolve, an open-source solver tool for the Maxwell-Bloch equations. Here, we consider the one-dimensional Maxwell's equations, which are coupled to the Lindblad equation. The resulting generalized Maxwell-Bloch equations are treated without invoking the rotating wave approximation (RWA). Since this full-wave treatment is computationally intensive, we provide a flexible framework to implement different numerical methods and/or parallelization techniques. On this basis, we offer two solver implementations that use OpenMP for parallelization. Program summaryProgram Title: mbsolveCPC Library link to program files:https://doi.org/10.17632/nvgnkfphj9.1Code Ocean capsule:https://codeocean.com/capsule/5425444/treeLicensing provisions: GPLv3Programming language: C++, Python bindingsNature of problem: The Maxwell-Bloch equations are frequently used to model light-matter interaction in general and the dynamics of optoelectronic devices, such as the quantum cascade laser, in particular. Especially when the rotating wave approximation is not invoked, the Maxwell-Bloch equations require numerical treatment. Here, efficient numerical methods and parallelization are necessary to solve the equations.Solution method: We present mbsolve, a flexible and open-source solver framework for the Maxwell-Bloch equations. The framework enables the specification of simulation setups, which can be subsequently used to evaluate and verify numerical methods and/or parallelization techniques. Additionally, mbsolve contains a finite-difference time-domain solver implementation based on OpenMP that is ready to be used, for example, in the simulation of quantum cascade laser dynamics.

A Finite-Difference Scheme for the One-Dimensional Maxwell Equations

This paper deals with a difference scheme of second-order approximation using Laquerre transform for the one-dimensional Maxwell equations. Supplementary parameters are introduced into this difference scheme. These parameters are obtained by minimizing the error of a difference approximation for a Helmholtz equation. The optimal parameters do not depend on the step size and the number of nodes in the difference scheme. It is shown that the use of the Laguerre decomposition method allows obtaining higher accuracy of approximation of the equations in comparison with similar difference schemes when using the Fourier decomposition method. The second-order finite difference scheme with the parameters is compared to a fourth-order difference scheme in two cases: The use of the optimal difference scheme when solving a problem of electromagnetic pulse propagation in an inhomogeneous medium yields a solution accuracy comparable to that obtained with the fourth-order difference scheme. When solving an inverse problem the second-order difference scheme allows obtaining higher solution accuracy as compared to the fourth-order difference scheme. In these problems the second-order difference scheme with the supplementary parameters has decreased the calculation time by 20–25% as compared to the fourth-order difference scheme.

The finite-difference scheme for one-dimensional maxwell's equations

The finite-difference scheme for one-dimensional maxwell's equations

Monte Carlo simulations of skin exposure to electromagnetic field from 10 GHz to 1 THz

In this study, we present an assessment of human-body exposure to an electromagnetic field at frequencies ranging from 10 GHz to 1 THz. The energy absorption and temperature elevation were assessed by solving boundary value problems of the one-dimensional Maxwell equations and a bioheat equation for a multilayer plane model. Dielectric properties were measured at frequencies of up to 1 THz at body temperature. A Monte Carlo simulation was conducted to assess variations of the transmittance into a skin surface and temperature elevation inside a body by considering the variation of the tissue thickness due to individual differences among human bodies. Furthermore, the impact of the dielectric properties of adipose tissue on temperature elevation, for which large discrepancies between our present measurement results and those in past works were observed, was also examined. We found that the dielectric properties of adipose tissue do not impact on temperature elevation at frequencies over 30 GHz. The potential risk of skin burn was discussed on the basis of the temperature elevation in millimeter-wave and terahertz-wave exposure. Furthermore, the consistency of the basic restrictions in the international guidelines set by ICNIRP was discussed.

A Fourier penalty method for solving the time-dependent Maxwell's equations in domains with curved boundaries

We present a high order, Fourier penalty method for the Maxwell's equations in the vicinity of perfect electric conductor boundary conditions. The approach relies on extending the smooth non-periodic domain of the equations to a periodic domain by removing the exact boundary conditions and introducing an analytic forcing term in the extended domain. The forcing, or penalty term is chosen to systematically enforce the boundary conditions to high order in the penalty parameter, which then allows for higher order numerical methods. We present an efficient numerical method for constructing the penalty term, and discretize the resulting equations using a Fourier spectral method. We demonstrate convergence orders of up to 3.5 for the one-dimensional Maxwell's equations, and show that the numerical method does not suffer from dispersion (or pollution) errors. We also illustrate the approach in two dimensions and demonstrate convergence orders of 2.5 for transverse magnetic modes and 1.5 for the transverse electric modes. We conclude the paper with numerous test cases in dimensions two and three including waves traveling in an irregular waveguide, and scattering off of a windmill-like geometry.

A lattice Boltzmann model for electromagnetic waves propagating in a one-dimensional dispersive medium

A first-order extended lattice Boltzmann (LB) model with special forcing terms for one-dimensional Maxwell equations exerting on a dispersive medium, described either by the Debye or Drude model, is proposed in this study. The time dependent dispersive effect is obtained by the inverse Fourier transform of the frequency-domain permittivity and is incorporated into the LB evolution equations via equivalent forcing effects. The Chapman–Enskog multi-scale analysis is employed to ensure that proposed scheme is mathematically consistent with the targeted Maxwell’s equations at the macroscopic limit. Numerical validations are executed through simulating four representative cases to obtain their LB solutions and compare those with the analytical solutions and existing numerical solutions by finite difference time domain (FDTD). All comparisons show that the differences in numerical values are very small. The present model can thus accurately predict the dispersive effects, and demonstrate first order convergence. In addition to its accuracy, the proposed LB model is also easy to implement. Consequently, this new LB scheme is an effective approach for numerical modeling of EM waves in dispersive media.

Polychromatic Solitary Waves in a Periodic and Nonlinear Maxwell System

We consider the one-dimensional Maxwell equations with low contrast periodic linear refractive index and weak Kerr nonlinearity. In this context, wave packet initial conditions with a single carrier frequency excite infinitely many resonances. On large but finite time-scales, the coupled evolution of backward and forward waves is governed by nonlocal equations of resonant nonlinear geometrical optics. For the special class of solutions which are periodic in the fast phase, these equations are equivalent to an infinite system of nonlinear coupled mode equations, the so-called extended nonlinear coupled mode equations, or xNLCME. Numerical studies support the existence of long-lived spatially localized coherent structures, featuring a slowly varying envelope and a train of carrier shocks. In this paper we explore, by analytical, asymptotic, and numerical methods, the existence and properties of spatially localized structures of the xNLCME system for the case where the refractive index profile consists of a periodic array of Dirac delta functions. We consider, in particular, the limit of small amplitude solutions with frequencies near a spectral band edge. In this case, stationary xNLCME is well approximated by an infinite system of coupled, stationary, nonlinear Schrödinger (NLS) equations, the extended nonlinear Schrödinger system, xNLS. We embed xNLS in a one-parameter family of equations, xNLS$^\epsilon$, which interpolates between infinitely many decoupled NLS equations ($\epsilon=0$) and xNLS ($\epsilon=1$). Using bifurcation methods we show existence of solutions for a range of $\epsilon\in(-\epsilon_0,\epsilon_0)$ and, by a numerical continuation method, establish the continuation of certain branches all the way to $\epsilon=1$. Finally, we perform time-dependent simulations of a truncated xNLCME and find the small-amplitude near–band edge gap solitons to be robust to both numerical errors and the NLS approximation.

MULTI-fs – A computer code for laser–plasma interaction in the femtosecond regime

The code MULTI-fs is a numerical tool devoted to the study of the interaction of ultrashort sub-picosecond laser pulses with matter in the intensity range from 10 11 to 10 17 W cm −2. Hydrodynamics is solved in one-dimensional geometry together with laser energy deposition and transport by thermal conduction and radiation. In contrast to long nanosecond pulses, short pulses generate steep gradient plasmas with typical scale lengths in the order of the laser wavelength and smaller. Under these conditions, Maxwellʼs equations are solved explicitly to obtain the light field. Concerning laser absorption, two different models for the electron–ion collision frequency are implemented to cover the regime of warm dense matter between high-temperature plasma and solid matter and also interaction with short-wave-length (VUV) light. MULTI-fs code is based on the MULTI radiation-hydrodynamic code [R. Ramis, R. Schmalz, J. Meyer-ter-Vehn, Comp. Phys. Comm. 49 (1988) 475] and most of the original features for the treatment of radiation are maintained. Program summary Program title: MULTI-fs Catalogue identifier: AEKT_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEKT_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 49 598 No. of bytes in distributed program, including test data, etc.: 443 771 Distribution format: tar.gz Programming language: FORTRAN Computer: PC (32 bits and 64 bits architecture) Operating system: Linux/Unix RAM: 1.6 MiB Classification: 19.13, 21.2 Subprograms used: Cat Id: AECV_v1_0; Title: MULTI2D; Reference: CPC 180 (2009) 977 Nature of problem: One-dimensional interaction of intense ultrashort (sub-picosecond) and ultraintense (up to 10 17 W cm −2) laser beams with matter. Solution method: The hydrodynamic motion coupled to laser propagation and several transport mechanisms is solved in one-dimensional geometry using a fractional step scheme. Fluid motion together with heat diffusion is solved by using an implicit Lagrangian method. Transport by thermal conduction and radiation as well as electron–ion energy transfer are treated in a two-temperature (electron and ion) model covering the wide range from solid state to high temperature plasma. Laser propagation is calculated from the one-dimensional Maxwell equations. Radiation transfer is solved by using the forward-reverse method for a discrete number of frequency groups. Matter properties are interpolated from tables (equations-of-state, ionization, opacities, and emissivities) generated by external codes. An alternative WKB laser deposition package is available to be used for long pulse lasers. Restrictions: The code has been designed for typical conditions prevailing in short pulse (fs–ps time scale) laser–matter interactions at moderate intensities (10 12–10 17 W cm −2). Although a wider range of situations can be treated, extrapolations to regions beyond this design range need special care. Additional comments: A graphical post processor is included in the package. Its use requires the previous installation of code MULTI2D (see “Subprograms used” above). Running time: 4.8 seconds for the example supplied.