Transfer Matrix Method Research Articles

Effect of graphene on absorption spectrum of Si/SiO2 multilayer

In recent decades, photonic crystals have emerged as a key technology in several fields, including light management, photovoltaics, detection, and lasing. This success can be attributed to the ability to regulate electromagnetic waves, which can be achieved by, through a variety of techniques, disruption the periodicity of crystals. In this study, the introduction of graphene as a material defect in a one-dimensional photonic crystal consisting of six Si/SiO2 patterns is subjected to investigation. The calculations are performed using the transfer matrix method, with the experimental data serving as the input, following a protocol that involves exploring the variation of the absorption spectra as a function of the parameters of the material system and the incident electromagnetic wave. The findings illustrate that the absorption peak exhibits a pronounced dependency on the positioning of the material defect, the graphene layer thickness, and the incident angle. This paves the way for a more detailed inquiry into its potential utility in the domain of detection.

A method for dynamic parameter identification of an industrial robot based on frequency response function

AbstractHaving accurate values of the dynamic parameters is necessary to characterize the dynamic behaviors of mechanical systems and for the prediction of their responses. To accurately describe the dynamic characteristics of industrial robots (IRs), a new method for dynamic parameter identification is proposed in this study with the goal of developing a real IR dynamics model that combines the multibody system transfer matrix method (MSTMM) and the nondominated sorting genetic algorithm‐II (NSGA‐II). First, the multibody dynamics model of an IR is developed using the MSTMM, by which its frequency response function (FRF) is calculated numerically. Then, the experimental modal analysis is conducted to measure the IR's actual FRF. Finally, the objective function of the minimum errors between the calculated and measured eigenfrequencies and FRFs are constructed to identify the dynamic parameters of the IR by the NSGA‐II algorithm. The simulated and experimental results illustrate the effectiveness of the methodology presented in this paper, which provides an alternative to the identification of IR dynamic parameters.

Bandgap estimation and broadening of piezoelectric metamaterial beams undergoing longitudinal vibration

Abstract In the realm of acoustic metamaterials, two crucial challenges have attracted significant interests: (1) How to predict the bandgap range fast and accurately? (2) How to achieve a broader bandgap at a relatively low cost? This paper addresses these challenges by analyzing a type of piezoelectric metamaterial beams comprising unit cells with sub-cells undergoing longitudinal vibration. The longitudinal bandgap estimation relationship based on the effective medium theory is proposed for the first time to estimate the bandgap range of piezoelectric metamaterial beams with unit cells containing sub-cells, and verified with the transfer matrix method. Moreover, novel methods are introduced to construct graded piezoelectric metamaterial beams by combining different sub-cells within a single cell. The proposed graded piezoelectric metamaterial beams occupy significantly less space than conventional graded counterparts and exhibit wider longitudinal bandgaps compared to uniform piezoelectric metamaterial beams.

Transfer Matrix Method with Gouy Phase Shift correction applied to a High Numerical Aperture fiber-to-fiber optical coupling analysis

In this paper, we present the transmittance and reflectance study of the optical coupling between two High Numerical Aperture (HNA) fibers using a new model based on the Transfer Matrix Method (TMM). The TMM is corrected by the effects of the Gouy phase shift and the mode overlap is used in the material between the fibers to calculate the coupling loss. The coupling is also simulated using the Eigenmode Expansion (EME) method, and these numerical results are compared with experimental ones. The Gaussian beam nonparaxial field equations are used to evaluate the phase of the light in the coupling region and to obtain the effective refractive index of the wave between the fiber facets. Our TMM approach produced results close to experimental ones. Our model is, at least, two orders of magnitude faster than a commercial solver, and easy to coding; highlighting this approach’s importance as a transmittance/reflectance simulation tool.

An (AlN/GaN)N D (AlN/GaN)N Photonic Crystal-based Gas Sensor

Over the past few years, more studies have been conducted on the use of photonic crystals (PCs) in the detection field. Particularly fascinating for use as gas sensors are these materials’ outstanding spectrum sensitivity and small design. Using one-dimensional PCs as the theoretical foundation, this work aims to develop and analyze a nanoscale system that can identify the concentration of gases in ambient air and differentiate it from contaminated air. The intended structure is composed of layers of gallium nitride (GaN) and aluminum nitride (AlN) that alternate. In between these layers is a defective layer cavity that is filled with polluted air, which has a refractive index that is quite similar to pure air. The transfer matrix method (TMM) was used to perform numerical results for the proposed sensor. This sensor achieves average sensitivity of 1791 nm/RIU, average quality factor and figure of merit (FoM) of 1833 and 2287, respectively. We therefore think that the suggested detector’s design offers a strong candidate for accurate and efficient detection.

CaF2/TiO2 nanophotonic biosensor based on a one-dimensional photonic crystal for Chikungunya virus detection

An optical sensor based on a defective photonic crystal is proposed to identify the Chikungunya virus in blood components, including plasma, platelets, red blood cells (RBCs), and uric acid. Under healthy conditions, each blood component has a unique refractive index; this value is altered if the person is infected with the Chikungunya virus. The infected blood sample results in a deviation in the refractive index of the sample as compared to a normal sample due to the presence of the infection in the human blood. With the help of our suggested structure, this alteration can be detected, and the normal cell can be distinguished from the infected one. To simulate the results, the transfer matrix method (TMM) is applied. The sensitivity of the suggested structures loaded separately with the sample containing plasma, platelets, red blood cells, and uric acid is found to be 1411, 1352, 1335, and 795 nm/RIU, respectively. These results are enough to support our claim that the present design can be used as an ultra-sensitive nanophotonic biosensor for the detection of the Chikungunya virus.

Unlocking high-efficiency solar energy: optimizing P3HT/Si hybrid solar cells through numerical simulation

This study numerically investigates the optimization of P3HT/Si hybrid solar cells for maximum efficiency via numerical simulation using SCAPS ID. The analysis identifies P3HT layer thickness and Si donor density as critical parameters, with optimal values of 20 nm and 1017 cm−3, respectively. Exceeding these values leads to decreased efficiency due to reduced hole mobility, increased recombination, and enhanced absorption loss. Furthermore, minimizing defect density in Si is crucial for achieving high efficiency. The optical properties of the P3HT/Si hybrid thin film were investigated using the transfer matrix method (TMM), yielding exceptional transmittance (94.5%), low reflectance (4.5%), and minimal absorption (1.0%) at a wavelength of 0.5876 μm. This highlights the material’s potential for efficient and transparent photovoltaic devices. By optimizing these parameters, a maximum efficiency of ∼24% was achieved, demonstrating the potential for high-performance hybrid solar cells. This work underscores the significance of numerical analysis in designing efficient hybrid solar cells, paving the way for the development of low-cost, high-performance devices via spin coating, a groundbreaking advancement in solar energy harvesting.

Self-referencing refractive index sensor based on graphene-assisted TAMM plasmon cavity resonance.

In this Letter, we report TAMM plasmonic polaritons (TPPs) generated by few-layer MoS2 with a distributed Bragg reflector (DBR) structure in the terahertz frequency region by utilizing the transfer matrix method (TMM) and finite element method (FEM). By inserting a mono-graphene embedded cavity layer, we realize the graphene-induced mode strong coupling (GCM), which is a strategy of a refractive index sensor by optimizing the cavity layer spacing. By adjusting the chemical potential of graphene, GCM is modulated. μc = 0.1 eV and μc = 0.9 eV are selected as the on-off-state parameters, respectively. The difference in reflectance spectra presents a differential signal and a self-reference operation. The sensitivity of the designed refractive index sensor is 7.8 THz/RIU and a figure of merit (FOM) of 882 RUI-1 can be obtained. The proposed structure in our Letter demonstrates its potential application in high-performance self-reference refractive index sensors.

Improvement of Sound-Absorbing Wool Material by Laminating Permeable Nonwoven Fabric Sheet and Nonpermeable Membrane

Thin sound-absorbing materials are particularly desired in space-constrained applications, such as in the automotive industry. In this study, we theoretically analyzed the structure of relatively thin glass wool or polyester wool laminated with a nonpermeable polyethylene membrane and a permeable nonwoven fabric sheet. We also measured and compared the sound-absorption coefficients of these samples between experimental and theoretical values. The sound-absorption coefficient was derived using the transfer matrix method. The Rayleigh model was applied to describe the acoustic behavior of glass wool and nonwoven sheet, while the Miki model was used for polyester wool. Mathematical formulas were employed to model an air layer without damping and a vibrating membrane. These acoustic components were integrated into a transfer matrix framework to calculate the sound-absorption coefficient. The sound-absorption coefficients of glass wool and polyester wool were progressively enhanced by sequentially adding suitable nonwoven fabric and PE membranes. A sample approximately 10 mm thick, featuring permeable and nonpermeable membranes as outer layers of porous sound-absorbing material, achieved a sound-absorption coefficient equivalent to that of a sample occupying 20 mm thickness (10 mm of porous sound-absorbing material with a 10 mm back air layer).

Efficient and broadband sound absorption properties of slotted aluminum foam

To enhance the sound absorption performance of aluminum foam, a slotted structure was developed. Firstly, the theoretical model of sound absorption for the slotted aluminum foam was established by the transfer matrix method. Secondly, the finite element model was established using COMSOL software to predict the sound absorption coefficient. The reliability of the theoretical and finite element models was validated through impedance tube experiments. The sound absorption mechanism is investigated by analyzing the internal sound field. Finally, the sound absorption properties of aluminum foam with other slot patterns are investigated. Additionally, the factors that influence sound absorption properties are investigated. The results indicate that the slots alter the sound pressure distribution within the material, inducing a pressure diffusion effect. When sound waves enter the interior of the material through the narrow slots, they are absorbed and dissipated by the matrix material on the sides of the slots. The sound absorption coefficient can be improved by increasing the thickness, slot scale, and slot depth of the slotted aluminum foam. Specifically, when the slot depth is 15 mm, and the slot width is 5 mm, the average sound absorption coefficient of incompletely slotted aluminum foam in the frequency range of 1000 ∼ 6300 Hz is 0.86, which can realize broadband sound absorption. With the increase of slot depth, the sound absorption peak becomes more pronounced.

A design method of large-scale partial similar model test for cementing casing string system

When the cementing casing string system (CCSS) is subjected to a large-scale equal-scale model test, the huge aspect ratio of the system makes the wall thickness of the model casing string too thin to be manufactured. Therefore, this paper proposes a design method for model test with unequal scale of axial size and radial size of the CCSS. Firstly, the dynamic model of the CCSS is established and solved by the transfer matrix method (TMM), and the modal test is carried out and the results show that the numerical calculation error of the first five natural frequencies of the system is less than 4 %. Then, based on the dynamic model, the similarity laws of the complete similarity model and the partial similarity model of the CCSS are derived by equation analysis method, and the design process of the similarity model test is given. The advantages of the research are elaborated in details through examples. To verify the correctness of the similarity model’s similarity laws of the CCSS, similarity models with different parameters are designed, and the prediction errors of prototype response are analyzed based on numerical calculations. The results show that the maximum prediction error of the first eight natural frequencies of the prototype system is less than 3 %, and the response prediction results of the system are also accurate. Finally, considering uncertain factors of the partial similarity test, the similarity model test with the axial size of double scale is designed, and the results show that the maximum prediction error of the first three natural frequencies is 7.06 %, which meets the engineering requirements. This study can provide useful theoretical guidance for the large-scale model test design of the CCSS.

Axisymmetric Indentation of Circular Rigid Plate on Layered Elastic Halfspace with Transverse Isotropy

This paper investigates the contact problem of a layered elastic halfspace with transverse isotropy under the axisymmetric indentation of a circular rigid plate. Fourier integral transforms and a backward transfer matrix method are used to obtain the analytical solution of the contact problem. The interaction between the rigid plate and the layered halfspace can be expressed with the standard Fredholm integral equations of the second kind. The induced elastic field in the layered halfspace can be expressed as the semi-infinite integrals of four known kernel functions. The convergence and singularity of the semi-infinite integrals near or at the surface of the layered halfspace are resolved using an isolating technique. The efficient numerical algorithms are used and developed for accurately calculating the Fredholm integral equations and the semi-infinite integrals. Numerical results show the correctness of the proposed method and the effect of layering non-homogeneity on the elastic fields in layered transversely isotropic halfspace induced by the axisymmetric indentation of a circular rigid plate.

Ising-Like Model Hasn't Yet Said Its Last Word: Exact and Mean-Field Investigations of 2, 3 and 4-Body Interactions in 1D Ising Chain of Binuclear Spin-Crossover Solids.

We investigate the static properties of a new class of 1D Ising-like Hamiltonian for binuclear spin-crossover materials accounting for two-, three-, and four-body short-range interactions between binuclear units of spins and . The following 2-, 3-, and 4-body , , and terms are considered, in addition to intra-binuclear interactions, such as effective ligand-field energy and exchange-like coupling. An exact treatment is carried out within the frame of the transfer matrix method, leading to a 4×4 matrix from which, we obtained the thermal evolution of the thermodynamic quantities. Several situations of model parameter values were tested, among which that of competing intra- and inter-molecular interactions, leading to the occurrence of (i) one-step spin transition, (ii) two-, three-, and four-step transitions, obtained with a reasonable number of parameters. To reproduce first-order phase transitions, we accounted for inter-chains interactions, treated in the mean-field approach. Hysteretic multi-step transitions, recalling experimental observations, are then achieved. Overall, the present model not only suggests new landscapes of interaction configurations between SCO molecules but also opens new avenues to tackle the complex behaviors often observed in the properties of SCO materials.

Broadband low-transmission study of ventilation metasurfaces based on Archimedean spirals

The primary objectives of acoustic material design include ensuring indoor ventilation and isolating external noise. This study introduces a ventilation metamaterial surface based on Archimedean spirals (ASVM) and calculates its energy transmission coefficient using simulation and the Transfer Matrix Method (TMM). Experimental validation confirms the accuracy of the proposed model, highlighting ASVM’s potential as an effective ventilation metamaterial surface. Subsequently, ASVM is integrated with Helmholtz resonators (HR) to create two new metasurfaces: HR-ASVM without a neck and N-HR-ASVM with a neck. The former exhibits a power transmission coefficient below 0.2 across the broadband range of 1300 Hz to 2500 Hz, while the latter demonstrates superior sound insulation performance (power transmission coefficient below 0.1) from 639 Hz to 2500 Hz, with complete transmission suppression at 710 Hz. Notably, the thickness of N-HR-ASVM at this frequency is only 1/13 of the wavelength. Simulations of the acoustic pressure field and energy flow analyze the mechanisms responsible for low transmission. Finally, the energy transmission coefficient of N-HR-ASVM is experimentally measured and found to align closely with simulation results. This study provides valuable insights into the research on spiral ventilation metamaterial surfaces.

Asymptotic solutions for heat transfer and stresses in functionally graded porous sandwich pipes subjected to nonuniform pressures and thermal loads

In this work, thermomechanical behaviors of temperature-dependent (TD) functionally graded porous (FGP) sandwich pipes subjected to nonuniform pressures and thermal loads are studied. Because the material properties are variable across the wall of the pipe, seeking exact solutions for the pipe is almost impossible. We use a slice model where the pipe is partitioned into plenty of annular slices and each slice is assumed to have uniform material properties. First, the nonlinear heat transfer along the pipe wall thickness is obtained by introducing an iterative procedure. Then, by using the Fourier series, the mechanical problem is decomposed into axisymmetric and nonaxisymmetric parts. Both the parts can be treated by the state space method and transfer matrix method, and then the superposition principle is used to obtain the displacement and stress distributions. The model results are in good consistency with those obtained from the numerical simulation and those reported in the literature. Finally, an FGP sandwich pipe is considered to discuss the effects of the temperature dependence of material properties (TDMP), power-law index, porosity, and pressure distribution on its thermomechanical behaviors.

Structured acoustic materials for mitigating low-frequencybroadband aircraft noise: transfer matrix method

This study investigates, by numerical modeling, the mitigation of low-frequency broadband aircraft noise using a structured assembly of acoustic materials using the Transfer Matrix Method. The prevalence of low-frequency aircraft noise poses challenges to environmental sustainability and passenger comfort. The investigation focuses on an approach that employs strategically arranged structured acoustic materials to attenuate undesirable noise frequencies. The Transfer Matrix Method is used to model the acoustic behavior of the structured assembly, enabling a comprehensive analysis of sound transmission and absorption properties. This method supports the design and optimization of the assembly. The performance of the structured assembly to selectively attenuate low-frequency broadband noise is assessed through numerical simulations. The paper discusses implications for aircraft design, considering factors such as weight and cost. The benefits for environmental impact and passenger experience are also explored. Challenges and limitations in the implementation of structured acoustic materials are examined. The configuration studied presents an assembly of structured metamaterials arranged in series and in parallel which are integrated into a layer of glass wool. Present research contributes to the development of sustainable solutions for low-frequency aircraft noise. The structured assembly analyzed shows promise for significant noise reduction while considering practical constraints.

Sound absorption of slit resonator with embedded aperture in linear and nonlinear regimes

This paper presents a slit resonator with embedded aperture (SREA) by embedding the slit-type neck into the cavity, and investigates its sound absorption characteristics in linear and nonlinear regimes. The theoretical acoustic impedance model of the SREA is established through transfer matrix method. The theoretical, simulation and experimental results demonstrate that the SREA enhances oscillating mass without altering acoustic capacity through the embedded slit-type neck, enabling it to achieve quasi-perfect absorption at lower frequencies with the same external geometry as traditional slit resonator. The formation and shielding of acoustic vortex caused by the high sound intensity increase the normalized acoustic resistance and decreases the acoustic reactance, causing the peak sound absorption coefficient to decline. This paper introduces a nonlinear correction expression for the normalized acoustic resistance of SREA by analogy with cylindrical neck.

Characterization and estimation of the acoustical and elastic parameters in stone wool samples

Mineral wool is widely used in acoustic applications. The properties of glass wool have been broadly investigated, thus resulting in a good knowledge of its structure and parameters. This information is used to describe mineral wool in general. Nevertheless, other types, such as stone wool, involve a different production process and therefore have a different fibre structure. e.g. stone wool is not transversally isotropic as glass wool. These differences can have important effects depending on the use of the material; therefore, assuming the same parameter values for both materials may lead to inaccurate results in simulations and calculations. Currently there are few studies that characterize both the acoustic and elastic properties of stone wool. This contribution reports on the characterization of two stone wool samples with different densities (~70 kg/m3 and ~140 kg/m3). The characterization aimed at obtaining the parameters that are required for the description of the propagation of sound in the material through the Biot poroelastic model, i.e. the acoustic and elastic parameters. The obtained knowledge enables the adequate modelling of the investigated poroelastic materials in different configurations by numerical methods such as finite elements and the transfer matrix method.

Accounting of imperfect interfaces in multilayer modeling

Multilayer systems are widely used in industry for their performances as compared with homogeneous materials. The layers are usually glued together but the bonding may be imperfect (air bubble, detachment). The interfaces are generally modeled as sliding or bonded. These two behaviors can be significantly different and the actual behavior is generally somewhere in between. The vibroacoustic behavior of the structure is thus modified by the imperfect interface. Several models have been implemented to describe the dynamic behavior of multilayer systems with imperfect interfaces. In this paper, we propose an analytical model of imperfect interfaces based on the Transfer Matrix Method (TMM). Two computations are performed in parallel (one with a perfectly bonded interface and the other with a sliding interface). Instead of mixing impedances or admittances matrices, a mixing law on the state variables is applied, resulting in an equivalent global matrix which can be coupled in any multi-layer. The model is compared in terms of the sound absorption or sound transmission loss with the existing ones and is applied on different classical multilayer systems with multi-layered solid plates and a multilayer composed of a porous layer with a heavy layer which is widely used in the automotive industry.

Hierarchical porous metamaterial for sound absorption

Absorption of sound is of great importance in several engineering applications, from room acoustics to engine noise reduction. Porous media are practical and commonly used to address this issue. However, their performance is limited at large wavelengths, where more material is required. Inspired by recursive patterns at multiple scale lengths, typical of many biological systems, we propose here a new design based on hierarchical multilayered porous materials. Two hierarchical designs are investigated: periodic and gradient. In both cases it is found that the increase of the hierarchy level allows to simultaneously (i) increase the absorption, and (ii) reduce the quantity of porous material required. Both the cases of normal and oblique incidences are examined. The absorption coefficient is calculated via the transfer matrix method and the finite element method, supporting measurements in an impedance tube. The porous media are described through the JCA model. An optimization algorithm based on the metaheuristic Greedy Randomized Adaptive Search Procedure is developed to optimize the organization of the porous layers, and practical tips are given on the most suitable choice of parameters (static air-flow resistivity, angle of incidence) to obtain the highest absorption amplification at desired low frequencies.