Transmission Matrix Method Research Articles

Linear-acoustic effects of asymmetrical undercutting of toneholes of woodwind instruments.

The influence of the presence and magnitude of asymmetrical undercutting of the toneholes of woodwind instruments on the change in their effective radius and the corresponding shift of the eigenfrequencies of the air duct is considered. Within the framework of the electro-acoustic analogy, a tonehole with an asymmetrical undercutting along the axis of the main bore is presented as a cascade connection of two holes with different radii (undercutting and not undercutting parts of the hole), and with a sideway undercutting-in the form of a parallel connection. Formulas for numerical calculations are given that make it possible to determine the effective radius of such holes for the open state in the low-frequency approximation. Based on the obtained dependencies, using the transmission-matrix method, the eigenfrequencies of an air duct with one hole were calculated and compared with the results of computer modeling in the COMSOL Multiphysics 5.6 program. It is shown that increasing the degree and angle of undercutting leads to an increase in the effective radius, a displacement of the "center of gravity" of the sound hole along the main bore axis, and has effect on the shift of resonant frequency.

Dispersion compensation design of high-density stacking RFSS absorbers for wideband applications

Abstract A dispersion compensation design absorber realized by high-density stacking resistive frequency selective surface (RFSS) is proposed for wideband applications. Firstly, the quantitative relationship between the equivalent impedance of RFSS and the permittivity of the effective media is constructed with the help of the transmission matrix method. The dispersion regulation of permittivity is achieved by changing the pattern and the square resistance of RFSS. In terms of absorber design, a uniform absorber with dispersion manipulation is developed as a precursor absorber. The uniform absorber has an absorption performance better than −8.5 dB above 2 GHz at normal incidence. The loss mechanism is analyzed in detail by electric field distribution and surface power loss density distribution, indicating that the uniform design cannot achieve thickness saving when extending to low frequency. Therefore, a dispersion compensation design absorber is proposed to extend −10 dB bandwidth to 1.64–28.8 GHz. Experiment results agree well with the simulation results, validating the analytic methods and design principles.

Efficient and accurate parameter extraction for quantum-well DFB lasers: a comprehensive approach integrating multiple mathematical models

This study proposes an efficient and accurate method for parameter extraction of quantum well distributed feedback (DFB) lasers by combining the rate equation model, finite element method, transmission matrix method, and traveling wave model (TWM). By fabricating and measuring the companion Fabry-Perot (FP) lasers, material and structural parameters common with the target DFB laser are extracted efficiently. All the intrinsic parameters of the DFB laser are accurately extracted by integrating multiple mathematical models, and the possibility of multiple solutions is avoided. From the extracted parameters, the output characteristics of the DFB laser are simulated using the TWM. The simulation results agree closely with the experimental results, proving the feasibility and accuracy of the proposed method.

One-dimensional acoustic modeling of the şimşal considering the external Interaction of the open finger holes

A one-dimensional model in Python was developed to analyze the acoustic behavior of the Kurdish wind instrument, the şimşal. This model was developed using the Transmission Matrix Method (TMM), which was refined by taking into account the external interactions between the open tone holes. This research focuses on the acoustic resonator part of the şimşal with the lattice of finger holes in different cross-fingering patterns. The results were validated by measurements using an impedance probe, CapteurZ, which was developed by LAUM[1] and CTTM[2] The results are in good agreement with the measurement and despite the possible sources of error, which are discussed, the deviations are within an acceptable range. [1] The Acoustics Laboratory of the University of Le Mans [2] Le Mans Technology Transfer Center.

Variation Characteristics of PM2.5 Pollution and Transport in Typical Transport Channel Cities in Winter

Taking Handan, Xingtai, Hengshui, and Cangzhou, four cities in southwest Hebei Province along the Beijing-Tianjin-Hebei typical transport route, as examples, we analyzed the variation characteristics of 3a meteorological conditions and PM2.5 concentration in winter from 2019 to 2021 and used potential source contribution analysis (PSCF) and concentration weight analysis (CWT) to identify the transport characteristics of PM2.5 in the four cities during the study period. Based on the meteorological air quality model (WRF-CMAQ) transmission matrix method and transport flux method, the contribution of PM2.5 transport between Handan, Xingtai, Hengshui, and Cangzhou and the surrounding areas was quantitatively assessed; the vertical distribution characteristics of PM2.5 net transport flux were revealed; and the two main transport routes of PM2.5 pollution were further identified. The results showed that during the study period, the PM2.5 concentration decreased by 45.85%, 49.45%, 42.40%, and 31.65%, respectively. The potential source contribution of Handan and Xingtai was mainly distributed in south-central Shanxi (Linfen, Changzhi, and Jinzhong), northern Henan (Xinxiang, Kaifeng, and Zhengzhou), and a small part of Inner Mongolia (PSCF > 0.9). The potential contribution areas of Hengshui and Cangzhou were mainly concentrated in southern Hebei (Handan and Shijiazhuang), central Shanxi (Taiyuan and Yangquan), and some Shandong regions (PSCF > 0.7), and the CWT results were similar to those of PSCF. During the study period, the local contribution (51.11%-62.99%) was slightly higher than the regional contribution (37.01%-48.89%) during winter in the four cities. Affected by horizontal turbulence and vertical diffusion, the impact of regional transmission in 2020 was slightly higher than that in other years (0.50%-9.52%). In 2021, the influence of regional transmission was slightly lower than that of other years (-2.15%--9.52%) due to low PM2.5 concentration and meteorological factors. For Handan, Xingtai, Hengshui, and Cangzhou, the total inflow (outflow) flux intensity of the four cities during winter and the surrounding areas was in 2020 > 2021 > 2019. For the total net flux, the total inflow (outflow) flux intensity of the four cities in winter was 0.094, -0.070, and 0.087 kt·d-1 (Xingtai:0.212, 0.395, and 0.544 kt·d-1; Hengshui:-0.040, -0.228, and 0.185 kt·d-1; Cangzhou:0.062, 0.126, and 0.128 kt·d-1). During the study, Handan, Xingtai, and Cangzhou were mostly used as transport receptors, whereas Hengshui was mostly used as a transport source. In the range of 0-1 260 m, the net transport flux intensity of PM2.5 increased basically with the increase in height, and the maximum net flux of the various cities in different periods was different. The maximum net flux of Handan, Xingtai, and Hengshui was 252-1 261 m, 817 m, and 252-817 m, respectively. The maximum net flux in Cangzhou was 252-359 m. By analyzing the transmission characteristics of the four cities, it was found that there were two main transport directions of PM2.5, that is, the northwest-southeast direction (Shanxi → Handan → Henan and Shandong; Shijiazhuang → Xingtai → Handan and Shandong; Baoding → Cangzhou → Shandong) and the southwest-northeast direction (Shanxi → Xingtai → Hengshui → Cangzhou → Bohai Bay).

Effect of curvature on sound propagation in the ear canal.

In this paper, we investigate the effect of the curvature and torsion of the ear canal on its resonance through a comparison between several ear canal models. Utilizing Stinson's ear canal geometries as a reference, we build and analyze several ear canal models using both transmission matrix and numerical methods for the purpose of comparative assessment. A conical transmission unit, which considers visco-thermal effects, is employed for the modeling of the human ear canal. While the transfer matrix and numerical method agree well for a straight axis model, this simplification results in up to 20% deviation from a curved canal. We propose the curve twist ratio as a metric to quantify the influence of curvature on the ear canal and find that our proposed metric can effectively express the error introduced by the simplified straight axis model. Upon this metric, an empirical equation is proposed for incorporating the curvature effect in the transmission matrix method, enabling it to generate comparable results to those of the numerical method, which considers the effect of the curvature and torsion, thus dramatically accelerating computation.

Hyperspectral imaging through scattering media via physics-informed learning

Overcoming light scattering in natural light conditions is a challenging but rewarding problem. For this problem, both physics-based and data-driven methods encounter bottlenecks to recover large amounts of hyperspectral data encoded in the scattered light spot. In this paper, we present a physics-informed learning method to solve the light scattering problem with the neural network and the incoherent light transmission matrix method. With the proposed method, we achieve single-shot hyperspectral imaging through scattering media exceeding the memory effect range. Hyperspectral images with a maximum resolution of 3.2-megapixel are recovered in 64 wavebands, which represents an order of magnitude improvement over the memory effect range. No additional imaging or dispersion elements are required in the system except for the scatter medium, thus ensuring a compact and inexpensive hyperspectral imaging system. Our recovery method outperforms other physics-based and data-driven methods in terms of recovery quality and time cost.

Analytical solution for seepage pressure of multilayered sand seabed considering interaction between wave-current action and shield tunnel

Existing theoretical studies of the seepage field around subsea shield tunnels under wave action take less account of the tunnel lining permeability, especially the effect of wave and current action on tunnel. Moreover, the solutions generally treat the sand as homogeneous and isotropic, ignoring the influence of multilayered seabed. In this paper, the analytical solutions are presented for the seepage pressure and liquefaction evaluation of sand around tunnel in multilayered seabed under wave and current action. The pore pressure response of pure seabed is obtained by the transmission and reflection matrix method. The mirror image method is introduced to establish governing equation of excess pore pressure reflected by tunnel, and the analytical solution of equation is obtained by Fourier series expansion under the condition of continuous seepage between sand and lining. Based on the superposition principle, the seepage pressure and liquefaction evaluation of sand around tunnel in multilayered seabed are obtained. Then the analytical solutions are compared with numerical and experimental results, and good agreement is obtained. In addition, the influencing factors of wave parameters (wavelength, period, current), seabed parameters (permeability, shear modulus, saturation) and tunnel parameters (lining thickness, lining permeability) are analyzed.

A Lightweight Multilayer Dissipative Material with High Acoustic Performance

A multilayer acoustic treatment constructed of fibrous acoustic absorption material combined with dissipative acoustic material achieves a low profile and is lightweight and multi-functional, with properties that are desirable for NVH (noise, vibration, and harshness) treatments. The dissipative material consists of microfibers and acoustically active particles; this material was introduced in the last SAE NVH conference: A Novel Dissipative Acoustic Material [1]. In this paper, the acoustic performance of the multilayer treatment was evaluated by using random incidence absorption and transmission loss measurements, as well as in-vehicle experiments. Absorption and transmission loss were additionally modeled using the transmission matrix method (TMM). In the in-vehicle test, an OEM wheelhouse liner with Trim, for an SUV, was evaluated utilizing this new multilayer 3M treatment.

Modelling of critical speed of railway tracks on a multi-layered transversely isotropic saturated ground

The responses of railway tracks are significantly amplified when the high-speed train travels around the speed of waves propagating in underlying soils. The dynamic amplification phenomenon corresponding to the issue of the critical speed may compromise the stability and safety of operation and increase track damage. This paper proposes an analytical model to analyze the effect of the transverse isotropy of ground on the critical speed of railway tracks on stratified saturated soils. By using the Biot's theory, the general solutions of the transversely isotropic saturated porous medium are derived by employing the potential decomposition and Fourier transform. The transmission and reflection matrix method is extended to derive the three-dimensional fundamental solution for moving point loads acting on a multi-layered transversely isotropic saturated half-space. The models for railway tracks and wheel-axle loads are subsequently coupled to the ground. The proposed model is validated through a comparison with two existing models. Numerical studies demonstrate that the material anisotropy changes the critical speed and the corresponding dynamic amplification coefficient by up to 20%. The anisotropy in the shear modulus has the most significant influence on the critical speed, followed by Young's modulus and the permeability coefficient. The material anisotropy and soil layering cannot be ignored for the assessment of the critical speed of a track-ground system.

A Highly Efficient Method for Designing Bisymmetric P‐B Phase Element Patterns of Coding Metasurfaces

AbstractThe conventional trial‐and‐error method employed in the element pattern design of coding metasurfaces lacks theoretical guidance and requires considerable time and computational resources. To overcome this problem, this paper proposes a highly efficient design method for bisymmetric Pancharatnam‐Berry (P‐B) phase element patterns. First, the equivalent impedances of the element patterns are derived from the expected reflectance and frequency range using the transmission matrix method. Subsequently, the optimal geometric parameters of the element patterns are obtained using the equivalent circuit model. For the same element pattern, the time consumption is reduced by more than 25 times compared with that required for a single full‐wave simulation. The simulation results show that metasurfaces adopting various design element patterns and the same coding sequence exhibit excellent backscattering energy homogenization performance, with a radar‐cross‐section reduction (RCSR) of less than −10 dB in the 9.47–17.57 GHz band. Two types of metasurfaces are fabricated using a meshed pattern, a sodium–calcium glass and a metallic mesh. The measured RCSR is less than −10 dB for a broadband of 7.74 GHz, and the normalized optical transmittance is 85% within 380–2500 nm, which is favorable for optical windows used in aerospace, medical, and precision instrumentation.

Dynamic response of a multi-scale layered saturated porous half-space due to seismic dislocation source by using a revised dynamic stiffness matrix method

The study investigating the dynamic response of seismic dislocation source in a layered saturated porous half-space, particularly the multi-scale characteristic of half-space, from crustal to geotechnical scale, is still lacking in the literature. particularly in will lead to the computation bottlenecks for multi-scale seismic wave propagation. Based on Biot's theory of wave propagation in a fluid-saturated porous solid, a dynamic stiffness matrix method is proposed to investigate the dynamic response of a multi-scale layered saturated porous half-space due to the seismic dislocation source. Assembling each layer stiffness matrix in the frequency-wavenumber domain, the global dynamic stiffness matrix is constructed to avoid errors accumulative compared to the reflection and transmission matrix method. The divergent index terms of the stiffness matrix with respect to thickness and wavenumber are extracted to revise the dynamic stiffness matrix adapted for multi-scale half-space. The seismic dislocation source action is equal to the external forces imposed on the total saturated porous half-space, which can obtain the dynamic response by using revised dynamic stiffness matrix method. The accuracy of the proposed method is verified via the comparison between the calculated results and of three published literatures. The multi-scale model with realistic near-surface fine structure is selected to investigate the effects of superficial fine structures on the dynamic responses. The numerical simulations results show that the presence of low-velocity saturated porous layers has a prominent impact on ground motion. The dynamic response seems to be sensitive to the porosity conditions, especially for high frequency, which cause the difference in variation of peak displacement value.

Design and optimization of a half-wavelength ultrasonic bone scalpel

Compared with traditional orthopedic surgical instruments, the ultrasonic bone scalpel (UBS) has obvious advantages in both safety and effectiveness. Based on the structure of the sandwich piezoelectric transducer, a design of half-wavelength UBS with a longitudinal vibration frequency of 22.5 kHz is proposed in this study. Firstly, the dimensions of each component of the UBS are calculated by the transmission matrix method, the initial design is verified by modal analysis, and the error is optimized by the response surface method. Then the harmonic response analysis is used to calculate the UBS’s tip amplitude, impedance and stress distribution. In addition, the influence of bolt pre-tightening force on the vibration characteristics of the UBS is analyzed. When the bolt pre-tightening force is 50-90MPa, the vibration performance of the UBS is stable, and the tip amplitude is large, which provides a reference for selecting appropriate tightening torque when the UBS is assembled. Finally, the bone-cutting experiment shows that the UBS has good cutting performance.

Spectra reconfiguration of a silicon microring resonator via double injection with different angles.

A reconfigurable silicon microring filter, which is constructed by cascading a tunable Mach-Zehnder interferometer and a double injected silicon microring resonator with a variable input angle, is proposed and investigated. The spectra reconfigurations of the optical filter were simulated and analyzed using the transmission matrix method. The results show that when keeping the perimeter of the microring constant, the free spectral range (FSR) of the filter can be multiplied by adjusting the angle between the two injections. Moreover, by changing the coupling coefficients of the microring and the optical power ratio between the two injections, different types of spectral responses such as square, sinusoidal, and flat-top interleaver can be obtained. The device is simple and easy to integrate, and its capabilities to expand the FSR and spectral reconfiguration may have great potential in reconfigurable integrated optic chips.

A 2.5D low-profile wideband frequency selective structure with high-selectivity performance

In this paper, a low-profile high-selectivity 2.5D FSS based on the dislocation patch structure is proposed and discussed. The dislocation patch structure is used to construct the low-profile transmission line, and a second-order band- pass FSS with a controllable transmission zero is realized by introducing a series LC structure to the dislocation patch structure. The effects of the geometrical parameters on the frequency response of the proposed second-order bandpass FSS are analyzed based on the transmission matrix method and the equivalent circuit simulation. Then, two proposed second-order bandpass FSSs with different transmission zeros are combined and placed crossly to construct two propagation paths, and a high-selectivity third-order FSS is obtained. Finally, the prototype is fabricated and measured to prove the effectiveness of the proposed FSS. The measured results show that the proposed high-selectivity FSS has a wide working bandwidth, proper selective performance, and a thinner profile than other high-selectivity 2D/3D FSSs.

A bandwidth enhanced multilayer electromagnetic bandgap structure to reduce the simultaneous switching noise

<abstract> <p>A bandwidth enhanced multilayer Electromagnetic Band Gap (EBG) structure to reduce the simultaneous switching noise (SSN) in high frequency operating circuits, which useful for the satellite communication application, is presented in this paper. A proposed stack structure is mathematically analyzed by the dispersion method and transmission matrix method. Simulation results show good mitigation of SSN in scattering parameters and signal integrity in terms of eye diagrams. We have also checked for power integrity analysis using self-impedance. The proposed structure gives a good SSN suppression at -30 dB from 817 MHz to 26.32 GHz, around 25.50 GHz bandwidth and also reduces the cavity mode resonance within the stopband range. The proposed multilayer structure is compared with planar EBG plane and reference board. It is also compared with published results.</p> </abstract>

The Absorption Properties of One‐Dimensional Spherical Photonic Crystals Based on Magnetized Ferrite Materials

AbstractBased on a spherical coordinate system and Maxwell's set of equations, the calculation formulas of one‐dimensional (1‐D) magnetized ferrite spherical photonic crystals (MFSPCs) are obtained and treated with the solution method of the spherical Bessel equations. Combined with the conventional transmission matrix method, expressions for the absorptance, reflectance, and transmittance of the 1‐D MFSPCs are given. 1‐D MFSPCs consisting of the general dielectric and Yttrium iron garnet (YIG) are also designed to verify the correctness of the conclusions. Variables such as external magnetic field, incidence angle, initial radius, and YIG thickness effects on the features of such 1‐D MFSPCs are also discussed. The transformation of the external magnetic field has a linear relationship with the position of the absorption band (AB). The three variables of incidence angle, initial radius, and YIG thickness have a substantial influence on the width and position of the AB, which can be adjusted according to the actual demand and are of high application significance. The results of this study can be helpful for the design of multifunctional absorbers and radome.

Imaging through scattering media using differential intensity transmission matrices with different Hadamard orderings.

A transmission matrix (TM) is a powerful tool for light focusing and imaging through scattering media. For measuring it, the normal way requires establishing a multiple-step phase-shifting interferometer, which makes the TM measurement not only complex and sensitive but also time-consuming. Imaging through scattering media using an intensity TM method can make the setup for TM measurement without the phase-shifting interferometer, thus it is much simple, more stable, and several times faster. Here, based upon a differential intensity TM method, we demonstrated it to do imaging through scattering media using different Hadamard orderings. To accelerate the TM measuring speed while degrading as little as possible of the imaging quality, a relatively reasonable strategy to plan Hadamard orderings for the TM measurement is designed since it can suggest us to preferentially measure the components in TM that are more important to the imaging quality. Thanks to the different Hadamard orderings, their influences on the imaging quality at different measuring ratios are investigated, thus an optimal measuring ordering for accelerating the TM measurement can be obtained, while only sacrificing as little as possible of the image fidelity. Simulations and experiments verify the effectiveness of the proposed method.

Impedance modeling and analysis of multi-stacked on-chip power distribution network in 3D ICs

An accurate impedance modeling of a multi-stacked on-chip power distributed network (PDN) based on through-silicon-vias (TSVs) is vitally important to estimate the electrical performance in three-dimensional integrated circuits (3D ICs). This paper proposes a method for calculating the impedance matrix of the multi-stacked on-chip PDN, which mainly consists of arbitrarily distributed TSVs and grid-type on-chip PDNs. First, a real stack-up structure of a multi-stacked on-chip PDN is separated into discrete components intentionally. Then, the equivalent lumped circuit models of all discrete components are assembled into a whole to build the transmission matrix of the multi-stacked on-chip PDN through the relationship between the nodal voltage and the nodal current. Finally, the impedance matrix can be derived through the transmission matrix. In this paper, the coupling of the arbitrarily distributed TSVs and the distributional effect of the on-chip PDN are considered in the impedance matrix through the transmission matrix method (TMM). The proposed method replaces the simulation of the complex equivalent circuit model with the matrix calculation. The verification results show that the deviation of resonant frequency is about 6 $$\%$$ and the conversation of the simulation time is about 99.9 $$\%$$ compared with the HFSS model. It can accurately and quickly calculate the impedance of the multi-stacked on-chip PDN.

Particle manipulation behind a turbid medium based on the intensity transmission matrix

Although optical tweezers can manipulate tiny particles, the distortion caused by the scattering medium restricts their application. Wavefront-shaping techniques such as the transmission matrix (TM) method are powerful tools to achieve light focusing behind the scattering medium. In this paper, we propose a method to focus light through a scattering medium in a large area based on the intensity transmission matrix (ITM). Only relying on the intensity distribution, we can calculate the ITM with the number of measurements equal to that of the control segments. Free of the diffraction limit, our method guarantees high energy usage of the light field. Based on this method, we have implemented particle manipulation with a high degree of freedom on single and multiple particles. In addition, the manipulation range is enlarged more than 20 times (compared to the memory effect) to 200 μm.