Maxwell Wave Equation Research Articles

A simple graphics processing unit-accelerated propagation routine for laser pulses in the strong-field regime.

We present a simple and easy-to-implement Graphics Processing Unit (GPU)-accelerated routine to numerically simulate the propagation of ultrashort and intense laser pulses as they interact with a medium. The routine is based on the solution of Maxwell's wave equation in the frequency domain with an extended Crank-Nicolson algorithm implemented in the Nvidia CUDA C++ programming language. The main advantages of our method are its significant speed-up factor and its ease of implementation, requiring only basic knowledge of CUDA and C++. In this article, we review the strong-field wave equations to be solved and their discretization and demonstrate how to implement a numerical solver for them on an Nvidia GPU. We show the results of the simulation of a near-infrared laser pulse propagating through a partially ionized atomic gas and discuss the performance of our GPU-accelerated scheme. Compared to a naïve central processing unit implementation of the same routine, our GPU-accelerated version is up to 198 times faster in standard regimes.

Direct generation of a narrowband EUV vortex with ring Pearcey-Gaussian-vortex-beam-driven harmonics.

The generation of tunable extreme-ultraviolet (EUV) vortex beams is highly sought after for optoelectronic applications in the EUV region. In this study, we investigate the generation of vortex high-order harmonics using a ring Pearcey-Gaussian vortex beam as the driving source. We analyze the beam's spatial structure through phase-matching conditions and simulate high-order harmonic generation by solving the Maxwell wave equations. The beam's self-focusing characteristics and low-diffraction properties after focusing significantly enhance harmonics near the 53rd order, indicating the generation of a narrowband EUV vortex. Our findings underscore the advantages of using a ring Pearcey-Gaussian vortex beam for narrowband EUV vortex generation, paving the way for creating tunable vortex high-order harmonics or attosecond pulses with innovative vortex beams.

Migration-Enhanced Epitaxial Growth of InAs/GaAs Short-Period Superlattices for THz Generation

The low-temperature-grown InGaAs (LT-InGaAs) photoconductive antenna has received great attention for the development of highly compact and integrated cheap THz sources. However, the performance of the LT-InGaAs photoconductive antenna is limited by its low resistivity and mobility. The generated radiated power is much weaker compared to the low-temperature-grown GaAs-based photoconductive antennas. This is mainly caused by the low abundance of excess As in LT-InGaAs with the conventional growth mode, which inevitably gives rise to the formation of As precipitate and alloy scattering after annealing. In this paper, the migration-enhanced molecular beam epitaxy technique is developed to grow high-quality (InAs)m/(GaAs)n short-period superlattices with a sharp interface instead of InGaAs on InP substrate. The improved electron mobility and resistivity at room temperature (RT) are found to be 843 cm2/(V·s) and 1648 ohm/sq, respectively, for the (InAs)m/(GaAs)n short-period superlattice. The band-edge photo-excited carrier lifetime is determined to be ~1.2 ps at RT. The calculated photocurrent intensity, obtained by solving the Maxwell wave equation and the coupled drift–diffusion/Poisson equation using the finite element method, is in good agreement with previously reported results. This work may provide a new approach for the material growth towards high-performance THz photoconductive antennas with high radiation power.

Local enhancement in transient absorption spectroscopy by gating the resonance in the time domain

The concept of resonant perfect absorption, enabled by the combined action of pulse propagation and an auxiliary gate pulse, was recently proposed and demonstrated in a group of two-level systems [Y. He , ]. Here we exploit this method in a more realistic scenario by solving the coupled time-dependent Schrödinger equation and the Maxwell wave equation in helium. Through emptying the population of the 1s2p excited state after its excitation, we explore the evolution of the spectral profile with time delay and propagation distance and link the observations to the controlled interference between the original field and the gated new field. We find that resonant absorption for higher-lying states can also be strongly enhanced, in spite of the congestion of multiple resonances and the presence of complex laser-induced couplings. Our results show that interferometric control of absorption using intense laser fields can be applied selectively in both the temporal and spatial domains. Published by the American Physical Society 2024

Numerical Investigation of Optical Properties in Carbon Tetrachloride-Filled Photonic Crystal Fibers

In this work, we design circular lattice photonic crystal fibers using Lumerical Mode Solution software, its hollow core filled with carbon tetrachloride. Optical properties including effective refractive index, chromatic dispersion, nonlinearity, and fiber loss were investigated numerically in detail based on solving Maxwell's wave equations. The small effective mode areas of only a few µm2, and confinement loss as low as 14.799 dB/m at specific pump wavelengths were obtained. It was found that near-zero ultra-flattened chromatic dispersion with fluctuations of ±0.44 ps/nm.km spans from 1300 to 1830 nm. Three photonic crystal fibers with optimal structure and features were suggested for broadband supercontinuum generation orientation.

Design and modeling of the nonlinear properties of octagonal lattice Ge20Sb5Se75 photonic crystal fibers

Most silica photonic crystal fibers have limited spectral broadening in the infrared region, making them less than ideal in terms of technological applications. In this work, we propose a new Ge20Sb5Se75 chalcogenide octagonal photonic crystal fiber that provides diverse dispersions with all-normal and anomalous regimes and multiple zero-dispersion wavelengths. The nonlinear properties are investigated over a wide wavelength range up to 14 µm by numerically solving Maxwell's wave equations using Lumerical Mode Solutions software. The full-vector finite-difference eigenmode method minimizes the losses so that low confinement losses in the short-wavelength region of 1 − 6 µm are found and nonlinear coefficients as high as thousands of W−1.km−1 are achieved. Three fibers with an all-normal dispersion profile and anomalous dispersion with one or three zero dispersion wavelengths are proposed for supercontinuum generation. The fibers provide small dispersion values of −0.88, 0.08, and 1.646 ps/(nm.km) at suitable pump wavelengths. Furthermore, the very small confinement loss of approximately 10−5 to 10−11 dB/m is the outstanding advantage of these optical fibers. A broadband spectrum with low input power is expected as a result of the proposed fiber-based supercontinuum generation.

A study on the optical properties of a novel flower-core photonic crystal fiber infiltrated with CCl4

A novel design of photonic crystal fiber with a flower-core is proposed for the first time to optimize dispersion suitable for broadband supercontinuum generation. The numerical simulation of the propagation of light modes in optical fibers is computed by solving Maxwell's wave equations with the full-vector finite-difference eigenmode method. As a result, near-zero ultra-flat all-normal and anomalous dispersion was achieved with fluctuations of ±0.978 ps/nm.km in the 294 nm wavelength region and ±1.168 ps/nm.km in the 432 nm wavelength region, respectively. Furthermore, the dispersion value at the pump wavelength is about 10 times lower than in previous papers. The combination of CCl4 infiltration into the hollow core and the air hole's size heterogeneity in the cladding also enhances the nonlinear properties of the fibers. The effective mode areas less than 2 µm2 at the pump wavelength can help the supercontinuum spectrum to broaden further towards the red wavelength region. Three fibers with structural parameters Ʌ = 0.8 µm, d1/Ʌ = 0.45, Ʌ = 0.9 µm, d1/Ʌ = 0.5, and Ʌ = 0.9 µm, d1/Ʌ = 0.45 are proposed for supercontinuum generation with low peak power due to the nonlinear coefficients as high as hundreds W−1.km−1. These fibers are a new class of optical fibers, highly efficient laser sources that replace traditional glass-core optical fibers.

Analysis and research on the resonance of mobile phone shielding cabinet

In order to cut off the connection between the mobile terminal and mobile communication base stations or Wi-Fi, it is necessary to improve the electromagnetic shielding efficiency of the mobile phone shielding cabinet. This paper analyzes the resonant characteristics of mobile phone shielding cabinets. The test method of electromagnetic shielding has been introduced. Through Maxwell wave equation and boundary conditions, the cavity resonant frequency of every small drawer on the mobile phone shielding cabinet has been derived, and the rectangular cavity research model was established. Using the high-frequency finite element method (FEM) simulation to calculate the cut-off frequency of the first 10-order high-order mode in the cavity, the resonant standing wave field distribution of every small drawer on the mobile phone shielding cabinet has been analyzed. This paper can offer a theory instruction for the product design of mobile phone shielding.

Special Relativity in Six Dimensions

In the four-dimensional spacetime theory of special relativity, the space coordinate is time contracted along the motion, while perpendicular coordinates are invariant and time varies with position. This leads to a velocity transformation valid at speed of light and used in showing invariance electric and magnetic fields which are invariant along x-axis but change occur along y, and z-axes, contrary to the classical electrodynamics. In this work we introduce a new six-dimensional spacetime theory which allows time (position) change of position (time) in three coordinate axes and still satisfy the Lorentz invariance conditions of metric and Maxwell’s wave equations between two frames. We derive a new velocity transformation rule which is valid at any relative speed of massive frames moving with respect to each other. We derived expressions for relativistic mass, energy, Doppler shift, time dilation, length contraction, photon rest mass, and used the conservation of relativistic power to prove that the electric and magnetic fields and consequently, Maxwell wave equations are Lorentz invariant between two massive frames with and without nonzero photon mass in vacuum and materials medium. Calculated photon mass is in excellent agreement with the measured and observed upper bounds of 1.24x10-54 kg and1.75x 10-53 kg, respectively.

Multiple Airy beam generation by a digital micro mirror device.

The Airy beam is the solution of Maxwell's wave equation and since this equation is linear, a superposition of Airy beams still remains the solution of the wave equation. In this paper, we propose a method for generating multiple Airy beams that includes a desirable number of up to 6 individual Airy beams with desirable acceleration properties. By introducing a decenter into the designed diffractive optical element (DOE) of an Airy beam the problem of generating dual airy beams patterns by an amplitude-based spatial light modulator is solved. By superimposing the designed DOEs of individual Airy beams and scaling them to the proper gray level range, the DOE of the multiple Airy beams is generated. Displaying this DOE on a digital micromirror device, multiple Airy beams are experimentally produced. The experimental studies of these beams show good agreement with the performed simulations.

Two-dimensional electromagnetically induced phase grating via composite vortex light

We investigate the performance of a symmetrical two-dimensional electromagnetically induced grating produced in a four-level $N$-type atomic scheme, which interacts with a weak probe field and two simultaneous coupling fields: a two-dimensional standing wave and a composite optical vortex beam. Based on the Maxwell wave equation, we study numerically the behavior of the amplitude, the phase modulations, as well as the probe field diffraction intensities of different order under various conditions for the coupling field detunings and the orbital angular momentum of the Laguerre-Gaussian field. The different orders of diffraction are altered when the azimuthal angle of the composite vortex light changes, thus producing a two-dimensional symmetric grating which transfers the probe energy to higher orders of diffraction. A detailed analysis of the probe field energy transfer to these different orders proves the possibility for direct control over the performance of the grating.

Macroscopic phase-matching mechanism for orbital angular momentum spectra of high-order harmonics by mixing two Laguerre-Gaussian vortex modes

The high-order harmonic generation (HHG) by the interaction of an intense vortex infrared laser and a gas medium has been employed to produce the extreme ultraviolet (XUV) light beam carrying a high value orbital angular momentum (OAM). Here we extend this approach to generate the XUV light with superimposed OAM modes by mixing two different Laguerre-Gaussian (LG) modes as the driving beam. By solving the three-dimensional Maxwell's wave equations of the high-harmonic field and calculating the coherence lengths of HHG, we reveal the complex nature of phase-matching conditions in the gas medium, especially their dependence on the azimuthal angle. We demonstrate that the OAM spectra of the HHG can be tailored by varying the harmonic order, the position of gas medium, and the energy ratio of two LG beams. We also uncover that only including short-trajectory contribution in the single-atom response could broaden the OAM spectrum of the macroscopic HHG because of the featured phase-matching characteristics caused by the atomic intrinsic phase. We anticipate this work to stimulate some interests in generating an XUV vortex beam with the tunable OAM spectrum through the gaseous HHG process as well as in separating different OAM modes of an XUV vortex beam by advanced techniques.

Azimuthal modulation of electromagnetically induced grating using structured light

We propose a theoretical scheme for creating a two-dimensional Electromagnetically Induced Grating in a three-level Lambda -type atomic system interacting with a weak probe field and two simultaneous position-dependent coupling fields—a two dimensional standing wave and an optical vortex beam. Upon derivation of the Maxwell wave equation, describing the dynamic response of the probe light in the atomic medium, we perform numerical calculations of the amplitude, phase modulations and Fraunhofer diffraction pattern of the probe field under different system parameters. We show that due to the azimuthal modulation of the Laguerre–Gaussian field, a two-dimensional asymmetric grating is observed, giving an increase of the zeroth and high orders of diffraction, thus transferring the probe energy to the high orders of direction. The asymmetry is especially seen in the case of combining a resonant probe with an off-resonant standing wave coupling and optical vortex fields. Unlike in previously reported asymmetric diffraction gratings for PT symmetric structures, the parity time symmetric structure is not necessary for the asymmetric diffraction grating presented here. The asymmetry is due to the constructive and destructive interference between the amplitude and phase modulations of the grating system, resulting in complete blocking of the diffracted photons at negative or positive angles, due to the coupling of the vortex beam. A detailed analysis of the probe field energy transfer to different orders of diffraction in the case of off-resonant standing wave coupling field proves the possibility of direct control over the performance of the grating.

A NOVEL HETEROGENEOUS MODEL OF LAYERED STRUCTURES FOR NUMERICAL MODELING AND SIMULATION AT MICROWAVE FREQUENCIES VIA FDTD

Numerous destructive and nondestructive techniques using different energy sources have been offered for material characterization. Among the non-destructive testing techniques that suggest monitoring the content of different materials and concrete structures, the techniques using microwaves offer important advantages because they are not radioactive, provide good penetration, provide excellent contrast with rebar and are not affected by ambient temperature. In this paper, a non-destructive testing (NDT) technique is represented to simulate a novel heterogeneous rectangular geometric structures containing different materials such as concrete, pavement, mortar, rebar and soil based on their dielectric properties. Maxwell wave equations are used to simulate how wave propagates in structures with different dielectric properties. For numerical simulation a Finite Difference Time Domain (FDTD) is used and Absorbing Boundary Conditions (ABCs) is proposed to prevent re-entering of propagating waves into the computation domain.

The Research for Approaches to Increase Power of the Compact THz Emitters Based on Low-Temperature Gallium Arsenide Heterostructures

The design and technological conditions for the manufacture of photoconductive antennas based on low-temperature gallium arsenide (LT-GaAs) have been developed. The optimized photoconductive THz antenna is made based on LT-GaAs with the flag geometry of the contacts and with the interdigitated structure including metal closing through the dielectric of each second period. LT-GaAs samples were obtained by molecular beam epitaxy at temperatures of 210 °C, 230 °C, 240 °C on GaAs substrates (100). Dark and photocurrent were measured depending on the bias voltage of the LT-GaAs heterostructure at the EP6 probe station. Full wave finite element method solver has been used to investigate the proposed plasmon PCA electrical and optical behavior by combining the Maxwell's wave equation with the drift-diffusion/Poisson equations.

N2+ lasing: Gain and absorption in the presence of rotational coherence

We simulate the pump-probe experiments of lasing in molecular nitrogen ions with particular interest on the effects of rotational wave-packet dynamics. Our computations demonstrate that the coherent preparation of rotational wave packets in N$_2^+$ by an intense short non-resonant pulse results in a modulation of the subsequent emission from $B^2\Sigma_u^+ \rightarrow X^2\Sigma_g^+$ transitions induced by a resonant seed pulse. We model the dynamics of such pumping and emission using density matrix theory to describe the N$_2^+$ dynamics and the Maxwell wave equation to model the seed pulse propagation. We show that the gain and absorption of a delayed seed pulse is dependent on the pump-seed delay, that is, the rotational coherences excited by the pump pulse can modulate the gain and absorption of the delayed seed pulse. Further, we demonstrate that the coherent rotational dynamics of the nitrogen ions can cause lasing without electronic inversion.

High dimensional finite elements for two-scale Maxwell wave equations

We develop an essentially optimal numerical method for solving two-scale Maxwell wave equations in a domain D⊂Rd. The problems depend on two scales: one macroscopic scale and one microscopic scale. Solving the macroscopic two-scale homogenized problem, we obtain the desired macroscopic and microscopic information. This problem depends on two variables in Rd, one for each scale that the original two-scale equation depends on, and is thus posed in a high dimensional tensorized domain. The straightforward full tensor product finite element (FE) method is exceedingly expensive. We develop the sparse tensor product FEs that solve this two-scale homogenized problem with essentially optimal number of degrees of freedom, i.e. the number of degrees of freedom differs by only a logarithmic multiplying factor from that required for solving a macroscopic problem in a domain in Rd only, for obtaining a required level of accuracy. Numerical correctors are constructed from the FE solution. We derive a rate of convergence for the numerical corrector in terms of the microscopic scale and the FE mesh width. Numerical examples confirm our analysis.

Harmonic Analysis in Gaseous Helium by Coherent Schrödinger-Maxwell Method

This paper concentrates on harmonic analysis in gaseous helium, including microscopic generation, selective filtration and macroscopic propagation. A coherent method is proposed, with time-dependent Schrodinger equation for harmonic generation and Maxwell's wave equation for harmonic propagation. By introducing the polarization source based on the microscopic single-atom response, the macroscopic nonlinear propagation can be efficiently solved by a set of linear equations at each harmonic frequency. Using the proposed method, we numerically investigate the propagation effects of selective harmonics in gaseous helium. Our results reveal that specific harmonics allow the synthesis of an isolated attosecond pulse, which presents a high beam quality and an excellent spatial profile with Gaussian-like distribution. Moreover, the generated pulse provides a promising potential on high power defense, quantum radar and communication.

Comprehensive design analysis of ZnO anti-reflection nanostructures for Si solar cells

Six different shapes of zinc oxide (ZnO) nanostructured antireflective coatings on Si substrate, namely hemispheres, pyramids, motheye-like, cubes, rods and hexagonal prisms, were modeled numerically using finite element simulation, by solving Maxwell wave equation for periodic nanostructure arrays. COMSOL Multiphysics commercial package was used to perform the simulation by adopting the wave optics module. Geometrical parameters including structure size and period were studied in order to obtain better insight on how light and matter interaction is affected by structure geometry. However, among the studied structure geometries, hemispherical ones have the worst optical performance with a maximum reflectance of 45% for a 20 nm hemisphere radius. Pyramidal, motheye and cubic shapes yielded an intermediate optical performance while rod and hexagonal shapes revealed a minimum reflectance (less than 5%) values over a wide range of wavelengths and also showing interesting interference patterns.

Second order approximations for kinetic and potential energies in Maxwell's wave equations

In this paper we propose a numerical scheme for wave type equations with damping and space variable coefficients. Relevant equations of this kind arise for instance in the context of Maxwell's equations, namely, the electric potential equation and the electric field equation. The main motivation to study such class of equations is the crucial role played by the electric potential or the electric field in enhanced drug delivery applications. Our numerical method is based on piecewise linear finite element approximation and it can be regarded as a finite difference method based on non-uniform partitions of the spatial domain. We show that the proposed method leads to second order convergence, in time and space, for the kinetic and potential energies with respect to a discrete L2-norm.