Lorentz Dispersion Research Articles

Unified GSTC-FDTD Algorithm for the Efficient Electromagnetic Analysis of 2D Dispersive Materials

The finite-difference time-domain (FDTD) method has been widely used for the electromagnetic wave analysis of complex media. Conventional FDTD analyses of very thin two-dimensional (2D) dispersive materials require overwhelming computing resources because they should use very refined FDTD spatial grids. In this work, we propose a computationally efficient and unified FDTD formulation for 2D dispersive materials based on a combination of the generalized sheet transition condition (GSTC) and the modified Lorentz dispersion model. The proposed FDTD formulation can lead to a significant improvement in computational efficiency compared to the conventional FDTD method, while maintaining high accuracy. Numerical examples validate the improved computational efficiency of the proposed FDTD formulation.

New optical dispersion models for the accurate description of the electrical permittivity in direct and indirect semiconductors

We propose new optical dispersion models to describe the imaginary part of the electrical permittivity of dielectric and semiconductor materials in the fundamental absorption region. We work out our procedure based on the well-known structure of the semi-empirical Tauc–Lorentz dispersion model and the band-fluctuations approach to derive a five-parameter formula that describes the Urbach, Tauc and high-absorption regions of direct and indirect semiconductors. Main features of the dispersion models are the self-consistent generation of the exponential Urbach tail below the bandgap and the incorporation of the Lorentz oscillator behavior due to electronic transitions above the fundamental region. We apply and test these models on optical data of direct (MAPbI3, gallium arsenide and indium phosphide), indirect (gallium phosphide and crystalline silicon), and amorphous hydrogenated silicon semiconductors, accurately describing the spectra of the imaginary part of the electrical permittivity. Lastly, we compare our results with other similarly inspired dispersion models to assess the optical bandgap, Urbach tail and oscillator central resonance energy.

Electromagnetic forces on a discrete concentrator under time-harmonic illumination

We study electromagnetic forces and torques experienced on both perfect and discretized transformation-based concentrators, under time-harmonic illumination. The effect of the concentration is investigated in both cases and compared to the case of a perfect cloak. The effect of a Lorentz dispersion model on the optical force and torque is also investigated, and the force experienced by a dielectric particle located at the center of the concentrator is studied.

An energy-stable finite element method for nonlinear Maxwell's equations

In this paper, we consider the three-dimensional (3D) nonlinear Maxwell's equations in the optical media characterized by linear Lorentz dispersion, nonlinear Kerr effect and delayed Raman scattering. Using Crank-Nicolson time discretization and special treatment of the nonlinearity, we propose a second order accurate (in time) finite element method for the nonlinear problem. Fully discrete energy stability analysis is established to show that the scheme is unconditionally stable. The nonlinear system is solved by Newton-Krylov method. In order to efficiently solve the linearized algebraic system in each Newton sub-iteration, we further develop an effective preconditioner by using suitable approximations to the nonlinearity and the auxiliary space preconditioning technique. Numerical experiments are provided to examine the accuracy, the energy stability, the parallel scalability and the robustness in preconditioning of our proposed scheme. We then apply the scheme to simulate the spatial soliton propagation in 3D nonlinear glass. We also demonstrate the performance of the scheme in handling complex geometry through simulating the wave scattering by a spherical hole in the nonlinear optical glass.

Improved analysis of THz metamaterials for glucose sensing based on modified Lorentz dispersion model

Resonant structures, such as metamaterials, which can focus electromagnetic fields on a localized spot, are essential to perform label-free detection with high sensitivity in the terahertz (THz) range. Moreover, the refractive index (RI) of a sensing analyte is the most important aspect in the optimization of the characteristics of a highly sensitive resonant structure. However, in previous studies, the sensitivity of metamaterials was calculated while considering the RI of an analyte as a constant value. Consequently, the result for a sensing material with a specific absorption spectrum was inaccurate. To solve this problem, this study developed a modified Lorentz model. Split-ring resonator-based metamaterials were fabricated to verify the model, and the glucose-sensing range from 0 to 500 mg/dL was measured using a commercial THz time-domain spectroscopy system. In addition, a finite-difference time-domain simulation was implemented based on the modified Lorentz model and fabrication design of the metamaterials. The calculation results were compared with the measurement results and were found to be consistent.

Comprehensive study of electromagnetic wave absorption properties of GdMnO3-MoSe2 hybrid composites

Recently, the public does not avoid the use of RF/microwave communication and non-communication devices, which means they will be constantly exposed to radiation from those devices, which will worsen their health in the long term, as well as there will be interference and coupling effects between devices. In this paper, a novel and high-performance absorber material is created and analyzed. The microscopic and macroscopic properties of Gadolinium Manganite (GdMnO3), Molybdenum Diselenide (MoSe2), and three mixtures of GdMnO3-MoSe2 (GdMo) with 20, 30, and 40% filler loading were investigated. The procedure for producing the five materials was explained and described in detail. The mixture of GdMo with 20, 30, and 40 wt% filler loading has the features of GdMnO3 and MoSe2. For macroscopic analysis, the measured relative complex permittivity and permeability of the five synthesized materials are modeled using the Lorentz dispersion model. Among the five study materials, GdMo with 40 wt% filler loading shows the highest electric and magnetic losses with loss tangent, tan δe ≈ 0.228 and tan δm ≈ 0.38 where the absorption performance is better compared to its pristine components, namely GdMnO3 and MoSe2. Based on the transmission theory of metal plate backing materials, the GdMo with 40 wt% filler loading and thicknesses ranging from 0.0014 m to 0.0021 m, which is terminated by a metal plate on the back side, exhibited the optimum microwave absorption performance with a minimum reflection loss value better than −20 dB at X-band operating frequency. Without a metal backing, a 0.008 m thickness of GdMo with 40 wt% can achieve reflection loss, RL of −10 dB from 9.2 GHz to 12.4 GHz, and RL of −20 dB from 11.1 GHz to 12.4 GHz.

Modified Hawking temperature and entropy of general stationary black holes by Lorentz invariance violation

Correction of Lorentz dispersion relation can be carried out through Lorentz invariance violation (LIV). In the curved space-time with the general stationary black holes, the fermions dynamic equations have been modified more accurately according to the modified Lorenz dispersion relation, and the equations have been solved to obtain a new expression of quantum tunneling rate, black hole Hawking temperature, black hole entropy, and other physical quantities of stationary black holes. These expressions not only are related to factors such as Lorentz invariance violation but also have more contents akin to black hole physics.

Spectroscopic ellipsometry characterization of photoinduced phenomena in Ge25Sb5Se70 films using the Cody–Lorentz parameterized model

Variable angle spectroscopic ellipsometry (VASE) was employed to examine the photoinduced effect on the optical properties of Ge25Sb5Se70 thin films, that were prepared by thermal evaporation method. The measurements were carried out at room temperature and in the UV–vis–NIR (near infrared) spectral region for photon wavelengths from 280 to 1000 nm. For data analysis, we employed linear combination consist from two Cody–Lorentz (CL) dispersion model in the entire measured photon range. The photo bleaching (increase in bandgap) was identified by this model. The behavior of the Cody–Lorentz model parameters with the time of light illumination is discussed in detail. To obtain a good fitting to the variation of fundamental CL amplitude with the time of exposer, we proposed a simple phenomenological model based on the alternation of bond formation and breaking. Good agreement between calculated and experimental data is obtained.

Light propagation and magnon-photon coupling in optically dispersive magnetic media

Achieving strong coupling between light and matter excitations in hybrid systems is a benchmark for the implementation of quantum technologies. We recently proposed (Bittencourt, Liberal, and Viola-Kusminskiy, arXiv:2110.02984) that strong single-particle coupling between magnons and light can be realized in a magnetized epsilon-near-zero (ENZ) medium, in which magneto-optical effects are enhanced. Here we present a detailed derivation of the magnon-photon coupling Hamiltonian in dispersive media both for degenerate and nondegenerate optical modes, and show the enhancement of the coupling near the ENZ frequency. Moreover, we show that the coupling of magnons to plane-wave nondegenerate Voigt modes vanishes at specific frequencies due to polarization selection rules tuned by dispersion. Finally, we present specific results using a Lorentz dispersion model. Our results pave the way for the design of dispersive optomagnonic systems, providing a general theoretical framework for describing and engineering ENZ-based optomagnonic systems.

A new touch temperature of the event horizon and Rindler horizon in the Kinnersley spacetime

The Kinnersley spacetime not only describes a non-spherical symmetric, non-stationary and accelerating black hole, but also can be used to explore the characteristics of collision of two black holes because it has two horizons: the Rindler horizon and the event horizon. Previous research shows Rindler horizon and the event horizon cannot touch due to violation of the third law of thermodynamics. By solving a fermion dynamical equation including the Lorentz dispersion relation, we obtain a modified radiation temperature at the event horizon of the black hole, as well as the colliding temperature at the touch point of Rindler horizon and the event horizon. We find the temperature at the touch point is not equal to zero if {dot{r}}_Hne 0. This result indicates that the event horizon and Rindler horizon can collide without violation of the third law of thermodynamics when Lorentz dispersion relation is considered.

Modeling Dispersive Media in Finite-Difference Time-Domain Method for Radiative Cooling Applications

Radiative cooling offers a new strategy to address building cooling problems in an environmentally friendly way, compared with traditional cooling methods that require high-power consumption. The goal of radiative cooling is to maximize absorption at the mid-infrared (MIR) spectrum (8– <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$13~\mu m$ </tex-math></inline-formula> ). Thus, it is important to characterize the dispersive relationship of the radiative cooling materials (TiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , Si <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> , SiC, SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) in the MIR regime. In this work, we use the multi-pole Lorentz dispersion equation to model frequency-dependent dielectric constants of radiative cooling materials, which requires particle swarm optimization to solve multidimension optimization problems. This modeling can be directly applicable to the auxiliary differential equation (ADE)-based finite-difference time-domain (FDTD) method for simulating emissivity of radiative cooling materials. Further, we limit the number of Lorentz poles to five, which minimizes the computational burden in ADE–FDTD. Then, we validate our FDTD results against an analytic prediction calculated by the transfer matrix method. Finally, we demonstrate a highly efficient radiative cooling structure based on a simple SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> grating. The proposed material modeling can accelerate the nano/microstructural design of the radiative cooling strategies.

Error-optimized finite-difference modeling of wave propagation problems with Lorentz material dispersion

In the context of finite-different time-domain (FDTD) methods, errors associated with numerical dispersion can be reduced by introducing high-order or error-optimized derivative approximations. Although there exist various accuracy-enhanced FDTD techniques for modeling wave propagation within non-dispersive media, the equally interesting case of dispersive materials is commonly neglected. In this paper, we present a suitable design procedure that derives FDTD algorithms based on the (2,4) stencil, which accomplish reduced errors levels in problems featuring Lorentz dispersion. In essence, novel finite-difference formulae for spatial derivatives are defined, based on two different treatments of a suitable error estimator, aiming at either single-frequency or wide-frequency optimization. Theoretical studies and numerical tests verify the expected performance improvement, and validate the desirable accuracy amendment of the (2,4) FDTD scheme in cases where dispersive materials need to be considered.

Far-IR to deep-UV adaptive supercontinuum generation using semiconductor nano-antennas via carrier injection rate modulation

Supercontinuum generating sources, which incorporate a non-linear medium that can generate a wideband intensity spectrum under high-power excitation, are ideal for many applications of photonics such as spectroscopy and imaging. Supercontinuum generation using ultra-miniaturized devices is of great interest for on-chip imaging, on-chip measurement, and for future integrated photonic devices. In this study, semiconductor nano-antennas are proposed for ultra-broadband supercontinuum generation via analytical and numerical investigation of the electric field wave equation and the Lorentz dispersion model, incorporating semiconductor electron dynamics under optical excitation. It is shown that by a rapid modulation of the carrier injection rate for a semiconductor nano-antenna, one can generate an ultra-wideband supercontinuum that extends from the far-infrared (Far-IR) range to the deep-ultraviolet (Deep-UV) range for an infrared excitation of arbitrary intensity level. The modulation of the injection rate is achieved by high-intensity pulsed-pump irradiation of the nano-antenna, which has a fast nonradiative electron recombination mechanism that is on the order of sub-picoseconds. It is shown that when the pulse period of the pump irradiation is of the same order with the electron recombination time, rapid modulation of the free electron density occurs and electric energy accumulates in the nano-antenna, allowing for the generation of a broad supercontinuum. The numerical results are compared with the semiempirical second harmonic generation efficiency results for validation and a mean accuracy of 99.7% is observed. The aim of the study is to demonstrate that semiconductor nano-antennas can be employed to achieve superior supercontinuum generation performance at the nanoscale and the process can be programmed in an adaptive manner for continuous spectral shaping via tuning the pulse period of the pump irradiation.

Temperature-dependent optical properties of AgGaS2 in the terahertz range

The temperature-dependent optical properties of the AgGaS2 crystal were characterized in the 0.2–2 THz range by terahertz time-domain spectroscopy (TDS). The refractive indices and the absorption coefficients along and orthogonal to the optical axis (c axis) were measured, and the temperature-dependent Sellmeier equations were fitted for various applications of linear and nonlinear optical devices. An E mode vibrating orthogonal to the c axis centering at 1.03 THz (34 cm−1) and a B2 mode along the c axis centering at 1.86 THz (62 cm−1), were observed for the first time. The phonon softening during the temperature rise was discussed and analyzed with the help of Raman spectroscopy. According to the measured absorption spectrum of AgGaS2, we also fitted the parameters of the low-frequency phonon modes at room temperature with the Lorentz dispersion model, which is helpful in predicting the lattice dynamics and optical behaviors of the crystal.

Time-Domain Finite-Element Method for Near-Field Applications With Magnetic Metamaterials

Magnetic metamaterials exhibit extraordinary electromagnetic properties and have shown great potential in low-frequency near-field electromagnetic applications. A near-field device or system is consisted of different natural media and low-frequency metamaterials, and it is essential to develop a numerical methodology to compute the transient response of such a device or system. However, most existing works are dedicated to high-frequency metamaterials and wave propagation problems, whereas the study of numerical methodology for low-frequency metamaterials in magnetoquasistatic (MQS) fields is still blank and challenging. In this regard, a time-domain finite-element method (TDFEM) is first derived for MQS field applications of low-frequency metamaterials. The metamaterials are modeled as continuous media and approximated by a nonstandard Lorentz dispersion equation. The formulas to handle dispersive media in near field are derived based on the auxiliary equation method. The proposed method is validated in a 2-D axisymmetric case study by comparing its results with those of frequency-domain computations.

Nonlinear Lorentz Model for Explicit Integration of Optical Nonlinearity in FDTD

Including optical nonlinearity in FDTD software in a stable, efficient, and rigorous way can be challenging. Traditional methods address this challenge by solving an implicit form of Maxwell’s equations iteratively. Reaching numerical convergence over the entire numerical space at each time step demands significant computational resources, which can be a limiting factor for the modeling of large-scale three-dimensional nonlinear optics problems (complex photonics devices, laser filamentation, ...). Recently, we proposed an explicit methodology based on a nonlinear generalization of the Lorentz dispersion model and developed example cases where it was used to account for both linear and nonlinear optical effects. An overview of this work is proposed here.

플라즈마의 특성 분석을 위한 수정된 로렌츠 분산 모형 기반 FDTD 알고리즘

In this paper, to analyze the dispersive characteristics of plasma, a dispersive model suitable for the finite-difference time-domain (FDTD) method is proposed. The dispersive characteristics of plasma with varying electrical properties according to frequency were accurately and efficiently expressed using the modified Lorentz dispersive model. The coefficient of the modified Lorentz dispersive model was extracted by applying complex curve fitting based on the weighted least squares method. The method of applying the modified Lorentz dispersion model to the FDTD is discussed. The plasma model based on the modified Lorentz dispersion model proposed in this paper was verified to match the data of the dielectric barrier discharge (DBD) plasma generator from dielectric slab equivalent modeling. The accuracy of the proposed FDTD algorithm based on the modified Lorentz dispersive model was verified by comparison with the results of the broadband radar cross-section (RCS) measurement experiment.

Modeling the temperature dependence of the optical properties of anisotropic SnS0.52Se0.48

We report the parameter values of the model dielectric function ( $$\varepsilon = \varepsilon_{1} + i\varepsilon_{2}$$ ) of SnS0.52Se0.48 in the spectral range from 0.74 to 6.42 eV and the temperature range from 27 to 350 K. An analytic representation, obtained using the Tauc–Lorentz (TL) dispersion model, allows interpolation of the parameters with respect to both energy and temperature. We used reported experimental spectra as the basis of our approach and verified that the TL model can parameterize the model dielectric function so as to reproduce the experimental data well and yield values of the dielectric function and the refractive index at arbitrary temperatures that are useful for device applications.

Modification to tunneling radiation of arbitrary spin fermions in stationary axisymmetric Sen black hole space–time

Considering the modified Lorentz dispersion relation, combined with the Dirac equation and Rarita–Schwinger equation of fermions in stationary axisymmetric Sen black hole space–time, the fermion tunneling radiation of the black hole is modified accurately, and meaningful physical quantities such as the modified fermion tunneling rate, event horizon temperature, and entropy of the black hole are obtained. The discussion of the conclusions shows that the effect of the Lorentz dispersion relation and Lorentz violation theory on particle dynamics must be considered in curved space–time during the study of quantum theory and Hawking tunneling radiation.

Accurate correction of arbitrary spin fermion quantum tunneling from non-stationary Kerr-de Sitter black hole based on corrected Lorentz dispersion relation * *Supported by National Natural Science Foundation of China (11573022), National Natural Science Foundation of China (11273020) and Natural Science Foundation of Shandong Province, China (ZR2019MA059)

According to a corrected dispersion relation proposed in the study on the string theory and quantum gravity theory, the Rarita-Schwinger equation was precisely modified, which resulted in the Rarita-Schwinger-Hamilton-Jacobi equation. Using this equation, the characteristics of arbitrary spin fermion quantum tunneling radiation from non-stationary Kerr-de Sitter black holes were determined. A number of accurately corrected physical quantities, such as surface gravity, chemical potential, tunneling probability, and Hawking temperature, which describe the properties of black holes, were derived. This research has enriched the research methods and enabled increased precision in black hole physics research.