Drude Dispersion Model Research Articles

Plasmonic equi-triangular slot loaded bowtie nano-antenna for quantum optical wireless communication

In this manuscript, the plasmonic equi-triangular slot loaded bowtie aluminium dipole nano-antenna is investigated on a glass substrate for quantum optical wireless communication The optical characteristics of aluminium, such as permittivity and refractive index, are analyzed using the Drude dispersive model, which exhibits the required criteria for plasmonic resonance. A nanocircuit model for bowtie nano-antennas using lumped circuit elements is proposed and validated through CST simulation. The four equi-triangular slot loaded bowtie nanostructures are designed to tune the resonating frequency from 111 THz to 292 THz. Further, detailed investigation of the equi-triangular slot loaded bowtie nano-antenna is performed through the design parameter Tc (thickness) to obtain the optimum characteristics appropriate for quantum optical wireless communication. The proposed single bowtie nano-antenna exhibits a directivity of 7.606 dBi and a field enhancement factor of 289.5 at the resonating frequency of 292 THz.

Simulation of the interaction of light with 3‐D metallic nanostructures using a proper orthogonal decomposition‐Galerkin reduced‐order discontinuous Galerkin time‐domain method

AbstractIn this artice, we report on a reduced‐order model (ROM) based on the proper orthogonal decomposition (POD) technique for the system of 3‐D time‐domain Maxwell's equations coupled to a Drude dispersion model, which is employed to describe the interaction of light with nanometer scale metallic structures. By using the singular value decomposition (SVD) method, the POD basis vectors are extracted offline from the snapshots produced by a high order discontinuous Galerkin time‐domain (DGTD) solver. With a Galerkin projection and a second order leap‐frog (LF2) time discretization, a discrete ROM is constructed. The stability condition of the ROM is then analyzed. In particular, when the boundary is a perfect electric conductor condition, the global energy of the ROM is bounded, which is consistent with the characteristics of global energy in the DGTD method. It is shown that the ROM based on Galerkin projection can maintain the stability characteristics of the original high dimensional model. Numerical experiments are presented to verify the accuracy, demonstrate the capabilities of the POD‐based ROM and assess its efficiency for 3‐D nanophotonic problems.

Graphene plasmonic nano-antenna for terahertz communication

In this manuscript, plasmonic nano patch antenna on the graphene material is designed and analyzed. The conductivity of the graphene material is modeled using Kubo conductivity formula and it is tuned using chemical potential of graphene. Further, analysis of Drude dispersive model for the graphene matrial exhibits negative real permittivity which is the required criterion for the plasmonic resonance. The designed graphene nano patch antenna provides a gain of 3.52 dB at 30 THz frequency which is suitable for terahertz communication. It is demonstrated that the graphene nano patch antenna resonates at multiple frequencies by varying the chemical potential and three resonating frequencies 30, 115, 176 THz with good characteristics are observed at 1.3 eV chemical potential. The gain of the graphene nano patch antenna is enhanced approximately three times by changing the shape of the patch from square to L-shape.

An electromagnetic wave attenuation superposition structure for thin-layer plasma

This work proposes a new plasma super-phase gradient metasurfaces (PS-PGMs) structure, owing to the limitations of the thin-layer plasma for electromagnetic wave attenuation. Based on the cross-shaped surface unit configuration, we have designed the X-band absorbing structure through the dispersion control method. By setting up the Drude dispersion model in the computer simulation technology, the designed phase gradient metasurfaces structure is superposed over the plasma, and the PS-PGMs structure is constructed. The electromagnetic scattering characteristics of the new structure have been simulated, and the reflectance measurement has been carried out to verify the absorbing effect. The results demonstrate that the attenuation effect of the new structure is superior to that of the pure plasma structure, which invokes an improved attenuation effect from the thin layer plasma, thus enhancing the feasibility of applying the plasma stealth technology to the local stealth of the strong scattering part of a combat aircraft.

A reduced-order discontinuous Galerkin method based on a Krylov subspace technique in nanophotonics

This paper is concerned with the design of a reduced-order model (ROM) based on a Krylov subspace technique for solving the time-domain Maxwell’s equations coupled to a Drude dispersion model, which are discretized in space by a discontinuous Galerkin (DG) method. An auxiliary differential equation (ADE) method is used to represent the constitutive relation for the dispersive medium. A semi-discrete DG scheme is formulated on an unstructured simplicial mesh, and is combined with a centered scheme for the definition of the numerical fluxes of the electric and magnetic fields on element interfaces. The ROM is established by projecting (Galerkin projection) the global semi-discrete DG scheme onto a low-dimensional Krylov subspace generated by an Arnoldi process. A low-storage Runge-Kutta (LSRK) time scheme is employed in the semi-discrete DG system and ROM. The overall goal is to reduce the computational time while maintaining an acceptable level of accuracy. We present numerical results on 2-D problems to show the effectiveness of the proposed method.

Study on stealth characteristics of metamaterials based on simulated annealing algorithm

Auxiliary differential equation finite-difference time domain (ADE-FDTD) expressions of drude dispersive medium model are applied to simulate stealth characteristics of metamaterials coating. Then, simulated annealing algorithm is used to optimize electromagnetic parameters considered include metamaterials coating, collision frequency drude frequency and coating thickness. The results show that monostatic RCS of metal cylinder covering with metamaterial coating can reduce 6.3dB and bistatic RCS of metal cylinder covering with metamaterial coating can shrink 0.1dB less than before. Simulated annealing algorithm can play an important effect on stealth characteristics of metamaterials.

Optical Properties of Thin Films of Zinc Phthalocyanines Determined by Spectroscopic Ellipsometry

The optical properties of thin films based on unsubstituted and tetrafluoro-substituted zinc phthalocyanines synthesized by physical vapor deposition are studied within the wavelength range of 250–1000 nm. Spectroscopic ellipsometry shows that films based on zinc phthalocyanines have uniform thicknesses and optical parameters, strongly absorb visible light, and have characteristic absorption peaks corresponding to electronic transitions in the system of conjugated double bonds of phthalocyanine rings. Introduction of fluorine substituents into peripheral positions of the zinc phthalocyanine molecule leads to an increase in light absorption and a shift of the main absorption maximum to longer wavelengths (bathochromic shift). The absorption spectra are described using the Lorentz–Drude dispersion model. It is shown that the films based on a mixture of phthalocyanines can be well described using the Bruggeman effective medium model.

Stability-Improved ADE-FDTD Implementation of Drude Dispersive Models

Graphene, which is considered to be a Drude dispersive model in the 0–10 THz frequency range, has recently received much attention due to its outstanding electrical and optical properties. This increases the interest in the auxiliary differential equation (ADE) implementation of Drude dispersion in the finite-difference time-domain (FDTD) algorithm. In this letter, detailed stability analysis of the ADE-FDTD scheme, which retains the second-order nature of Drude models, is investigated. It is shown that the stability of this scheme is more restrictive than the classical Courant–Friedrichs–Lewy constraint. To overcome this drawback, stability-improved implementation is presented. Numerical examples are included to verify these findings.

Reflected and transmitted powers of p-polarized electromagnetic waves through a dielectric slab surrounded by double negative materials

In this paper, reflected, transmitted, and loss powers of p-polarized electromagnetic waves through a lossless dielectric slab embedded between two double negative media are studied. Lorentz and Drude medium models are both considered for the dispersion of the double negative materials in the surroundings. The dependences of reflected, transmitted, and loss powers on the incidence angle, incident wave frequency, and dielectric slab thickness are investigated. The results reveal many interesting features. The damping frequency has a slight effect on reflected, transmitted, and loss powers in most waveguide configurations considered. Moreover, the loss power is small and can be significantly reduced by considering Drude dispersion model and careful choosing of the proposed structure parameters.

Broadband optical properties of aluminium zinc oxide thin films prepared by spatial atomic layer deposition

In this work, a broadband ellipsometric investigation of aluminium zinc oxide (AZO) from the infrared to the ultraviolet spectral range is presented. Aluminium zinc oxide samples were fabricated using spatial atomic layer deposition (SALD) having a range of percent aluminium incorporation. The AZO was deposited using a coflow of diethyl zinc (DEZ) and dimethyl aluminium isopropoxide (DMAI), where the amount of aluminium incorporation was controlled by varying the DMAI partial pressure. The broadband permittivity is reported as a function of the aluminium content of these aluminium zinc oxide thin films. A model dielectric function, which includes the contribution of recently predicted broad shallow donor states, is presented and discussed. We find that an increase in the aluminium content of the aluminium zinc oxide thin films results in a monotonically decreasing scattering time while the carrier density increases with diminishing efficiency. To demonstrate the necessity of broadband ellipsometric measurements for the accurate determination of the dielectric function of aluminium zinc oxide, a comparison with the classical Drude model and a semi-empirical extended Drude dispersion model, which are frequently employed in the literature to describe the optical response of aluminium zinc oxide, is given.

A reduced-order DG formulation based on POD method for the time-domain Maxwell’s equations in dispersive media

In this work, a proper orthogonal decomposition (POD) method is applied to time-domain Maxwell’s equations coupled to a Drude dispersion model, which are discretized in space by a discontinuous Galerkin (DG) method. An auxiliary differential equation (ADE) method is used to represent the constitutive relation for the dispersive medium. A POD–DGTD formulation with lower dimension and sufficiently high accuracy is established, together with the description of the POD reduced-order basis, its construction from a snapshot set, and its application to the solution of the time-domain Maxwell’s equations. The overall goal is to reduce the computational time while maintaining an acceptable level of accuracy, in order to obtain an efficient time-domain solver to be used as a starting-point for an optimization strategy. We provide results from numerical experiments for two-dimensional problems that illustrate the capabilities of the proposed POD–DGTD formulation and assess its efficiency.

Leap-Frog Continuous–Discontinuous Galerkin Time Domain Method for Nanoarchitectures With the Drude Model

A continuous–discontinuous Gakerkin time domain method (CDGTD) with vector basis functions is proposed to analyze the wideband response of plasmonic structures with the Drude dispersive model. Compared to the conventional time domain approaches, such as FDTD and PSTD, the unstructured mesh can provide a better geometrical approximation of curved surfaces and fine features. An EB scheme Riemann solver is employed to calculate the flux between adjacent subdomains. The relationship between the electric field and the polarization currents is modeled by a first order auxiliary differential equation (ADE). A leap-frog scheme is proposed to update Maxwell's equations, the ADEs of the Drude medium and the perfectly matched layer (PML) in an efficient manner. This new approach is validated by virtue of simulating the ultra-wideband behavior of a gold nanoloop antenna with and without a substrate as well as the reflectivity of a dual-band infrared absorber. Its advantage in computational cost is demonstrated via comparison to a commercial software package. In this light, the CDGTD method represents a more efficient forward modeling tool, which has been successfully employed here to perform a parametric study of a dual-band infrared absorber.

Maxwell–Hydrodynamic Model for Simulating Nonlinear Terahertz Generation From Plasmonic Metasurfaces

The interaction between the electromagnetic field and plasmonic nanostructures leads to both the strong linear response and inherent nonlinear behavior. In this paper, a time-domain hydrodynamic model for describing the motion of electrons in plasmonic nanostructures is presented, in which both surface and bulk contributions of nonlinearity are considered. A coupled Maxwell-hydrodynamic system capturing full-wave physics and free electron dynamics is numerically solved with the parallel finite-difference time-domain (FDTD) method. The validation of the proposed method is presented to simulate linear and nonlinear responses from a plasmonic metasurface. The linear response is compared with the Drude dispersion model and the nonlinear terahertz emission from a difference-frequency generation process is validated with theoretical analyses. The proposed scheme is fundamentally important to design nonlinear plasmonic nanodevices, especially for efficient and broadband THz emitters.

Establishment of THz dispersion model of metals based on Kramers-Kronig relation

The extraction of terahertz dispersion parameters is confined in a limited region due to the limitation of the existing THz techniques. A method of studying the dispersion model of metals from the measurements of reflection spectrum and analysis of Kramers-Kronig (KK) relation is proposed. The reflection spectrum is measured by Vertex 80V Fourier transform spectrometer. In order to eliminate the signal noise of measured reflection spectrum, the measured spectrum is smoothed by Drude estimation. Using the smoothed reflection spectra of copper (Cu) alloy and aluminum (Al) alloy in a range of 440 THz, the complex refractivities are inversed based on the KK relation of amplitude and phase of reflective coefficient. The constant extrapolations at lower frequencies and the exponential extrapolation at higher frequencies are adopted in the KK integration. The exponential extrapolation index is adjusted according to the calibrating complex refractivity measured from far-infrared ellipsometer. According to the inversed complex refractivity, the plasma frequency and damping frequency in Drude model are optimized using the genetic algorithm. The objective function is defined as the error between the fitted complex refractivity and KK inversion. Since the optimal plasma frequency and damping frequency are different for different fitting frequencies, the obtained Drude parameters are averaged in order to reduce the influences of errors from KK inversion, measured reflection spectrum and calibrations. The complex refractivity indexes in a range from 15 THz to 40 THz, calculated by the established Drude model, are in good agreement with the measured calibrations from ellipsometer, which demonstrates the accuracy of the established Drude dispersion model. The reflection spectra below 4 THz are greatly distorted due to the signal noise, and the calibrating refractivity is located in the far infrared region, thus the complex refractivity is inversed in a region of 440 THz by KK algorithm. The complex refractivity indexes in a range of 0.120 THz, obtained by the proposed scheme, are for the vacancy, which will provide great support for the dispersion analysis in the whole terahertz gap. The procedures are helpful for extrapolating the dispersion information to terahertz band from the far infrared region. The scheme takes the advantage of the spectrometer and ellipsometer, and it requires high experimental precisions of reflection spectrum and calibrating refractivity. In addition, the scheme is adaptive to both metals and nonmetals by applying proper dispersion model which depends on the property of the reflection spectrum. The established model determines the microscopic dispersion parameters of material, which provides great support for the investigation of terahertz dispersion analysis, scattering mechanisms and imaging processes.

Infrared laser protection of multi-wavelength with high optical switching efficiency VO2 film

Vanadium dioxide (VO2) film with nanoparticles is fabricated by reactive ion beam deposition (RIBD) technology and post-annealing method on a quartz glass substrate. RIBD can enhance the damage threshold of VO2 film and reduce its scattering at insulator-state. And post-annealing can eliminate the structure defects and residual stress. VO2 film exhibits first-order and reversible metal-to-insulator (MIT) phase transition at a temperature of 68 ℃. It also exhibits photo-induced MIT, in which process a metal-like phase of monoclinic VO2 appears. With many surprising features in heat-induced and photo-induced MIT processes, VO2 film turn to satisfy all the characteristics needed for a laser protection system. The thickness of VO2 film used in these experiments and simulations is about 100 nm. The double-frequency He-Ne laser at a wavelength of 3 m is used to perform the experiment of heat-induced MIT, with a temperature controlling system. The exact optimal annealing temperature is demonstrated to be 465 ℃, as the sample annealing at this temperature shows the sharpest transition properties and unmixed VO2 phase peaks in X-ray diffraction pattern. Drude and Drude-Lorentz dispersion models are taken to analyze the dielectric constant of VO2. Then, the complex refractive index is calculated for simulation. Simulations with the TFCale software show that the transmissions at high temperature and low temperature have high contrasts in the infrared range. MIT experiments at multi-wavelength, which cover heat-induced and photo-induced MIT phase transition, are performed to investigate the applicability of VO2 film in multi-wavelength laser protection for both continuous wave and pulsed lasers Thus the excellent performance of VO2 film for laser protection is roundly verified. The laser protection experiments on silicon photocell exhibit that the VO2 film enhances the anti-jamming capability of photocell system by about 2.6 times, demonstrating the applicability of VO2 film to laser protection system. The power density of MIT transition threshold of VO2 film with a thickness of 100 nm is 4.35 W/cm2 at room temperature, which is investigated with a continuous wave laser at a wavelength of 1.08 m with a continuous tunable system. In addition, atomic force microscope is used to observe the film surfaces, which are irradiated by lasers with different power densities for different times The experimental results demonstrate that the power density damage threshold of VO2 film becomes very high (404 W/cm2). The low MIT transition threshold and high damage threshold of VO2 film further demonstrate its applicability as a key role for a laser protection system. With the high switching efficiency ratio and high damage threshold, VO2 thin film can be used in optical switch, smart windows and photoelectric device.

Linear Optical Properties of Gold Colloid

Gold colloid was prepared by reducing HAuCl 4 ·4H 2 O with Na 3 C 6 H 5 O 7 ·2H 2 O. The morphology, size of gold nanoparticles and the optical property of colloid were characterized by transmission electron microscope and UV-Vis spectrophotometer, respectively. It shows that the gold nanoparticles are in the shape of spheres with diameters less than 8 nm, and the surface plasmon resonance absorption peak is located at about 438 nm. As the volume fraction of gold particles increases, the intensity of absorption peak strengthens. The optical property of gold colloid was analyzed by Maxwell-Garnett (MG) effective medium theory in the company of Drude dispersion model. The results show that the matrix dielectric constant is a main factor, which influences the optical property of gold colloid. DOI: http://dx.doi.org/10.5755/j01.ms.21.4.9558

Optimum Surface Plasmon Excitation and Propagation on Conductive Two-Dimensional Materials and Thin Films

The surface conductivity of two-dimensional (2-D) materials and thin conductive films is considered for surface plasmon (SP) excitation and propagation. It is shown that an ideal surface conductivity exists to maximize the SP field at a given position, based on a tradeoff relating to propagation loss and near-field excitation amplitude associated with the local density of photonic states. Dispersionless and Drude dispersion models are considered, as well as the effect of interband transitions. Simple formulas are presented to obtain a maximal SP field at a given distance from a canonical source. Examples are shown for graphene and thin metal films, and a discussion of the competition between propagation loss and SP excitation is provided.

Intrinsic evolutions of dielectric function and electronic transition in tungsten doping Ge2Sb2Te5 phase change films discovered by ellipsometry at elevated temperatures

Tungsten (W) doping effects on Ge2Sb2Te5 (GSTW) phase change films with different concentrations (3.2, 7.1, and 10.8%) have been investigated by variable-temperature spectroscopic ellipsometry. The dielectric functions from 210 K to 660 K have been evaluated with the aid of Tauc-Lorentz and Drude dispersion models. The analysis of Tauc gap energy (Eg) and partial spectral weight integral reveal the correlation between optical properties and local structural change. The order degree increment and chemical bond change from covalent to resonant should be responsible for band gap narrowing and electronic transition enhancement during the phase change process. It is found that the elevated crystalline temperature for GSTW can be related to improved disorder degree. Furthermore, the shrinkage of Eg for GSTW should be attributed to the enhanced metallicity compared with undoped GST.

Symplectic FDTD algorithm for the simulations of double dispersive materials

Combined with the Lossy Drude-Lorentz dispersive model, a symplectic finite-difference time-domain (SFDTD) algorithm is proposed to deal with the double dispersive model. Based on matrix splitting, symplectic integrator propagator and the auxiliary differential equation (ADE) technique, with the rigorous and artful formula derivation, the algorithm is constructed, and detailed formulations are provided. Excellent agreement is achieved between the SFDTD-calculated and exact theoretical results when transmittance coefficient in simulation of double dispersive film in one dimension is calculated. As to numerical results for a more realistic structure in three dimensions, the simulation of periodic arrays of silver split-ring resonators using the Drude dispersion model are also included. The transmittance, reflectance, and absorptance of the structure are presented to test the efficiency of the proposed method. Our method can be used as an efficiency simulation tool for checking the experimental data.

A parallel non-conforming multi-element DGTD method for the simulation of electromagnetic wave interaction with metallic nanoparticles

The present work is about the development of a parallel non-conforming multi-element discontinuous Galerkin time-domain (DGTD) method for the simulation of the scattering of electromagnetic waves by metallic nanoparticles. Such nanoparticles most often have curvilinear shapes, therefore we propose a numerical modeling strategy which combines the use of an unstructured tetrahedral mesh for the discretization of the scattering structures with a structured (uniform cartesian) mesh for treating efficiently the rest of the domain. The overall goal is to increase the flexibility in the meshing process while decreasing the needs in computational resources for the target applications. The latter are here modeled by the system of 3D time-domain Maxwell equations coupled to a Drude dispersion model for taking into account the material properties of nanoparticles at optical frequencies. We propose an auxiliary differential equation (ADE) based DGTD method for solving the resulting system and present numerical results demonstrating the benefits of using non-conforming multi-element meshes in this particular application context.