Modified Transfer Matrix Method Research Articles

Investigation of an annular photonic crystal sensor for real-time monitoring of calcium carbonate scales in water distribution systems

This research exhibits a new configuration of photonic crystals known as annular photonic crystals (APCs) for real-time detection of calcium carbonate (CaCO3) scale in the water pipeline. The proposed sensor features a circular arrangement of porous silicon materials with varying levels of porosity. A central defect layer is incorporated into the design to capture the target analyte, allowing it to detect changes in the refractive index caused by scale formation. To analyze the reflectance spectrum of this structure, a modified transfer matrix method is utilized. An extensive optimization process is conducted based on the characteristics of the defect mode, focusing on various geometric parameters, including layer thickness, porosity levels, core circle radius, and structural periodicity, to achieve optimal sensor performance. The simulation outcomes revealed that at the optimized structure parameters, the sensor offers a remarkable QF, sensitivity, and FoM of 1215, 176.85 nm/RIU, and 350.5 1/RIU, respectively. Moreover, the proposed structure is simple, cost-effective, and compact, which makes it an ideal candidate for the detection of calcium carbonate scales formed in pipes and devices in water supply networks.

Optical properties of cylindrical topological photonic crystal heterostructures

This paper uses a modified transfer matrix method to investigate the optical properties of a cylindrical topological photonic crystal heterostructure composed of two cylindrical photonic crystals. Topological photonic crystals are novel structures with topological edge states capable of field confinement and robust propagation. Numerical results showed that when the sum of the phases of the reflection coefficients of the two cylindrical photonic crystals is zero, a topological edge state occurs inside their overlapping band gaps. In the linear regime, the peak frequency of the topological edge states undergoes a redshift as the incidence angle increases. An increase in the incidence angle leads to a decrease (increase) in the Full width at half maximum of the E-polarized (H-polarized) topological edge states. As the incidence angle increases, the frequency separation between the E-polarized and H-polarized topological edge states increases, causing the cylindrical heterostructure to work as a polarizer. The performance of the cylindrical topological photonic crystal heterostructure as a polarizer is evaluated in the linear and nonlinear regimes. We showed that the peak frequency of the topological edge states undergoes a redshift irrespective of their polarization state as the intensity of the input light increases. We found that the structure has a good performance in the nonlinear regime due to the higher displacement in E-polarized topological edge states compared to H-polarized topological edge states. The findings of this paper might be beneficial in the construction of polarization-maintaining optical fiber, which has specific applications in telecommunications, fiber optic sensing, interferometry, and quantum key distribution.

Modification of the transfer matrix method for the sonic black hole and broadening effective absorption band

Sonic black hole (SBH) is capable of the concentration for the sound energy by the shrinking duct and appropriate wall admittance. However, the concentrated energy cannot be dissipated due to the weak air damping. Meanwhile, when the inserted rings are insufficient, the accuracy of the conventional transfer matrix method (TMM) is less than satisfactory for the simulation of the original SBH. In this study we commit to modify this simulation method and broaden the effective absorption band by using porous materials. First, we derived the acoustic transfer relationship of the conical cavity and the acoustic admittance of the toroidal cavity, via formulating the basic equation. After combining with the two method, the modified TMM (MTMM) results show excellent agreement with the finite element results. The applicability of the derived wall admittance is analyzed in detail. The MTMM has also been applied to obtain the sound absorption of a SBH configuration with embedded porous materials (PMSBH). The proposed PMSBH can effectively dissipate the concentrated sound energy, leading to the ultra-low cut-on frequency of near-perfect absorption. Specifically, the cut-on frequency of the PMSBH is 387 Hz, with the corresponding wavelength being 8.8 times than the structural length. In addition, the parametric analysis shows the near independence of the absorption performance of the PMSBH on the damping loss, so that the PMSBH can achieve excellent absorption without adding other acoustic materials. These appealing characteristic could promote the application of the PMSBH in noise control.

Recent Developments in Using a Modified Transfer Matrix Method for an Automotive Exhaust Muffler Design Based on Computation Fluid Dynamics in 3D

The present work aims to investigate the newly modified transfer matrix method (MTMM) to predict an automotive exhaust muffler’s transmission loss (AEMTL). The MTMM is a mixed method between a 3D-CFD (Computation Fluid Dynamics in 3D), namely AVL FIRETM M Engine (process-safe 3D-CFD Simulations of Internal Combustions Engines), and the classic TMM for the exhaust muffler. For all the continuous and discontinuous sections of the exhaust muffler, the Mach number of the cross-section, the temperature, and the type of discontinuity of the exhaust gas flow were taken into consideration to evaluate the specific elements of the acoustic quadrupole that define the MTMM coupled with AVL FIRETM M Engine for one given muffler exhaust. Also, the perforations of intermediary ducts were considered in the new MTMM (AVL FIRETM M Engine linked with TMM) to predict the TL (transmission loss) of an automotive exhaust muffler with three expansion chambers. The results obtained for the TL in the frequency range 0.1-4 kHz agree with the experimental results published in the literature. The TMM was improved by adding the AVL FIRETM M Engine as a valuable tool in designing the automotive exhaust muffler (AEM).

A Modified Transfer Matrix Method for Static and Dynamic Analysis of Beams that Eliminates the Need to Compute the Inverse of the Zero Matrix

A Modified Transfer Matrix Method for Static and Dynamic Analysis of Beams that Eliminates the Need to Compute the Inverse of the Zero Matrix

Sound Absorption Characteristics of Unsaturated Porous Material Calculated by Modified Transfer Matrix Method

Porous materials have emerged as one of the most widely employed sound-absorbing materials in practical applications, owing to their excellent sound absorption properties and lightweight nature. Unsaturated porous materials have the potential to achieve superior sound absorption effects and significantly reduce mass. However, current research on the sound absorption performance of unsaturated porous materials is limited. This paper used a modified transfer matrix method (MTMM), which relies on matrix dimensionality reduction, to analyze the sound absorption characteristics of unsaturated porous materials under various boundary conditions. The study also examines the impact of different parameters, such as material thickness and saturation, on sound absorption performance and compares the results. The findings indicate that when a solid elastic plate is attached to an unsaturated porous elastic plate, the absorption coefficient decreases while the transmission loss increases. Additionally, reducing the thickness of the plate and increasing its porosity and saturation levels lead to an increase in the absorption coefficient and a decrease in the transmission loss.

Planar piezoelectric metamaterials: Sound transmission and applicable frequency range in oblique incidence

Frequency limit and applicable frequency range of planar piezoelectric metamaterials connected to external circuits have not been well defined in estimating the sound transmission loss. This article extends the classical transfer matrix method for use in evaluating the sound transmission of thin-plate piezoelectric metamaterials in oblique incidence. Using the Kirchhoff thin plate theory, a modified transfer matrix method that takes factors of external circuits into consideration is developed for attenuation and control of acoustic waves. Several vibro-acoustic analytical models are compared, including the Kirchhoff thin plate theory, the Reissner–Mindlin thick plate theory and the theory of wave propagation in elastic solids. These theories are used to determine the dispersion relation, coincidence and transition frequency of thin and thick plate theories in analysing piezoelectric acoustic metamaterials, alongside a validation using the finite element method. Then acoustic properties of piezoelectric plates connected to passive external circuits are studied parametrically with both dimensional and dimensionless variables based on an equivalent Kirchhoff plate approximation. The findings show that external electrical impedance alone can be used to adjust the resonance frequency over a broad range and thereby control sound transmission loss. This provides considerable flexibility in modifying the acoustic properties of the piezoelectric metamaterial in comparison to traditional, fixed-structure metamaterials. The study indicates a straightforward and powerful analytical approach for the optimization of acoustic insulation using thin-plate piezoelectric metamaterials.

Wide tuning of epsilon-near-zero plasmon resonance in pulsed laser deposited ITO thin films

Oxygen vacancies in indium tin oxide (ITO) thin films provide a direct route to effectively tune the free electron density and thereby, controlling the epsilon-near-zero (ENZ) cut-off wavelength, the wavelength at which the real part of permittivity crosses zero of the permittivity axis. In this report, oxygen vacancies in pulsed laser deposited ITO thin films are systematically tuned using different background gases (O2, N2, Ar, and He). ENZ cut-offs are observed for the films deposited under He and Ar gases. In contrast, no such cut-offs are observed in the case of other two gases. An ITO thin film deposited under He gas exhibits deeper resonance signal than the one deposited under Ar gas. As expected, no such dip in the resonance spectra is observed for the films deposited under O2 and N2 gases. This observation is directly correlated to the change in the number of oxygen vacancies under different ambient gases. A modified transfer matrix method which incorporates surface roughness as an effective medium layer is developed to describe the experimentally observed resonance spectra numerically. Angular invariancy of ENZ plasmon resonance and the difference in absorption values for ITO films deposited under different gases is understood in terms of local field intensity enhancement factor. The study presented here will certainly be very useful in understanding the ENZ plasmon resonance phenomena as a whole. Additionally, ITO films deposited under an inert gas environment could be excellent material platforms for realizing several exotic ENZ applications.

Multi-directional strain measurement under thermomechanical loading using embedded phase-shifted fiber Bragg grating

This study presents a multi-directional strain measurement technique under thermomechanical loading, utilizing the sensitive birefringence of an embedded phase-shifted fiber Bragg grating. The spectral response of the phase-shifted fiber Bragg grating to temperature and multi-directional strains is mathematically elucidated and simulated using a modified transfer matrix method considering the polarization state. Strain decoupling and reconstruction algorithms are newly proposed based on thermomechanical analysis, which relate the spectral characteristics, strains in the sensor, and strains in the host material. After calibration of the temperature and multi-directional strain responses, a phase-shifted fiber Bragg grating is embedded into a polyetherimide specimen and subjected to thermomechanical loading, achieving the measurement of pressure as well as three-directional strains in the sensor and polyetherimide. The presented technique is demonstrated to be reliable for accurate multi-directional strain measurement under thermomechanical loading with minimal errors and shows potential for in-situ measurement of advanced structures.

A Novel Generalized Sandwich Beam for Global Stability Analysis of Tall Buildings with Shear Walls Using a Modified Transfer Matrix Method

This research presents the study of the global buckling analysis of tall buildings with shear walls of significant length, where it is not possible to neglect the stiffness due to local shear. In order to correctly idealize the tall building, this research proposes a novel generalized sandwich beam replacement resulting from the generalization of the classical sandwich beam by including an additional mechanism due to the consideration of the local shear stiffness. The association of mechanisms of model shows that the proposed beam results from the series coupling of the classic sandwich beam and the local shear beam. Four characteristic stiffnesses and three kinematic fields associated with the model are considered. The differential equations and boundary conditions governing equilibrium are obtained by applying a variational approach using Hamilton’s principle to the relevant Lagrangian function. A modified transfer matrix method is proposed that diagonalizes the inverse of the zero transfer matrix and reduces the computational cost to solve the equilibrium equations numerically. The modified transfer matrix method allows the analysis to be generalized to buildings with uniform and non-uniform properties along their height considering a constant or variable compressive load along the height of the building. A parametric analysis is presented to evaluate the importance of the inclusion of the local shear mechanism of the shear walls. The results of the numerical examples are encouraging and show that at a reduced computational cost, the presented numerical procedure can greatly help engineers in the preliminary and final structural analysis of tall buildings.

An Investigation of High-Performance Pressure Sensor Employing a Polymer-Defect-Based 1D Annular Photonic Crystal

This study aims to theoretically address the design and analysis of an efficient pressure sensor designed using a polymer-based defective 1D annular photonic crystal (APC). The 1D APC comprises an alternate arrangement of Si and SiO2 in a cylindrical fashion, incorporating a central defect layer. The investigation of the reflectance characteristics of the proposed structure is conducted by separately considering the polystyrene (PS) and the polymethyl methacrylate (PMMA) polymer materials as the defect layer. The pressure-sensitive refractive index of the polymers and the constituent materials of the APC play a vital role in envisaging the pressure-sensing application. The cornerstone of this study is represented by the shift analysis regarding the wavelength of the defect mode inside the band gap using different applied pressures, employing the modified transfer matrix method (MTMM). Various geometrical parameters like the defect polymer layer’s thickness and the APC period were carefully optimized to achieve an improved sensing performance. The proposed design demonstrated a remarkable pressure sensitivity and FoM of 51.29 nm/GPa and 301.7 GPa−1, respectively, which is considerably high in the current research scenario. It is believed that the proposed structure can be an apt candidate for an innovative high-performance pressure sensor, and could play a key role in photonic integrated circuits.

Detection of wide variety of pathogens by using one-dimensional biosensor based on annular photonic crystal

A novel way of identifying the bacillus anthracis spore and various bacteria cells present in the water samples by means of one-dimensional biophotonic sensor design (PQ)5D(PQ)5 is studied in this manuscript. The proposed biophotonic sensor is designed by associating two 1D annular photonic crystals (APCs) PQ5 through a defect layer D. The alternate cylindrical layers P and Q of both APCs are made up of materials TiO2 and SiO2 respectively. The present study has been carried out in the visible region of electromagnetic (EM) spectrum. First, the proposed biosensor is loaded separately with different water samples containing various bacteria cells and spore into the region marked by defect layer D of the structure. The modified transfer matrix method (MTMM) in cylindrical coordinate system has been used for obtaining simulation results with the help of MATLAB software. The sensitivity of the proposed biosensor varies between maximum of 472.794 nm/nmol/L to minimum of 450.549 nm/nmol/L depending upon the water samples under investigation. Also, the additional parameters like figure of merit (FoM), quality factor (Qf) and limit of detection (LoD) have been evaluated to examine the overall performance of the proposed biosensor. The analysis opens a new pathway to prefer 1D APCs based biophotonic sensors over biosensors made up of 1D planar PCs because APC biosensors are more sensitive than the biosensors based on planar PCs.

Biophotonic sensor design for the detection of reproductive hormones in females by using a 1D defective annular photonic crystal

Abstract In this research work, we have proposed a one-dimensional (1D) defective annular photonic crystal (DAPC) (AB)5 CDC(AB)5 to identify the presence of reproductive progesterone and estradiol hormones in women. The periodicity of the proposed biosensing design made up of 1D annular photonic crystal (APC) has been broken by introducing a cylindrical cavity D of porous gallium nitride (GaN) material. The inner and outer faces of cylindrical cavity D are surrounded by concentric cylindrical buffer layers of magnesium fluoride (MgF2) material. We have used a modified transfer matrix method with the help of MATLAB software to carry out investigations pertaining to the proposed theoretical work. The two distinct categories of blood samples containing reproductive hormones of different concentrations have been used in this work. The sensitivity of proposed 1D DAPC varies between 159.673 nm nmol−1 L−1 to 170.1525 nm nmol−1 L−1 when a cavity is infiltrated with a blood sample having progesterone hormone whose concentration varies between 0 and 200 nmol L−1. Moreover, the sensitivity of the structure varies between 158.7816 nm nmol−1 L−1 to 170 nm nmol−1 L−1 under the influence of blood samples having estradiol hormones of different concentrations. In order to evaluate the performance of the proposed biosensor in the true sense we have also computed quality factor (Q) and figure of merit (FoM) values of the biosensor corresponding to both categories of blood samples of different concentrations. Our study shows that biosensors made up of 1D annular photonic structures are more efficient in comparison to the biosensors made up of planar 1D photonic crystals. Apart from detecting the reproductive hormones in females such kind of APC-based specialized biosensing devices may be very useful in the field of medical engineering and technology.

Modeling spintronic terahertz emitters as a function of spin generation and diffusion geometry

Spintronic THz emitters (STE) are efficient THz sources constructed using thin heavy-metal (HM) and ferromagnetic-metal (FM) layers. To improve the performance of the STE, different structuring methods (trilayers, stacked bilayers) have been experimentally applied. A theoretical description of the overall THz emission process is necessary to optimize the efficiency of STE. In particular, geometry, composition, pump laser frequency, and spin diffusion will be significant in understanding the pathways for further research developments. This work will apply a generalized model based on a modified Transfer Matrix Method (TMM). We will consider the spin generation and diffusion in the FM and HM layers and explain the spintronic THz emission process. This model is suitable for calculating emitted THz signal as a function of FM and HM thicknesses for different geometrical configurations. We will investigate a bilayer geometry as a test case, but the extension to a multi-layer configuration is straightforward. We will show how the different configurations of the sample will influence the THz emission amplitude.

Nonlinear operation of an FP laser with PT symmetry active medium.

In this paper, an analysis of the nonlinear laser operation in an active medium made of a parity time (PT) symmetric structure placed in a Fabry-Perot (FP) resonator is demonstrated for the first time. The FP mirrors' reflection coefficients and phases, the PT symmetric structure period, primitive cell number, and the gain and loss saturation effects are taken into account in a presented theoretical model. The modified transfer matrix method is used to obtain characteristics of laser output intensity. Numerical results show that the selection of the appropriate phase of the FP resonator's mirrors makes it possible to obtain different levels of the output intensity. Moreover, for certain value of a ratio of the grating period to the operating wavelength, it is possible to obtain the bistability effect.

Study on the Low-Frequency and Broadband Sound Absorption Performance of an Underwater Anechoic Layer with Novel Design

To further improve the low-frequency broadband sound absorption capability of the underwater anechoic layer (UAL) on the surface of marine equipment, a novel sound absorption structure with cavities (NSSC) is designed by adding resonators and honeycombs to the traditional sound absorption structure with cavities (SSC). Based on the principle of shear dissipation, the original intention of the design is to allow more parts of the viscoelastic material to participate the dissipation of acoustic energy. The approximate multilayer sound absorption theoretical model based on the modified transfer matrix method is used to verify the accuracy of finite element calculations. In the frequency range of 1100 Hz–10,000 Hz, the sound absorption coefficient (α) of NSSC can reach 0.8. The effects of the presence and size of cylindrical oscillators and honeycomb structures on sound absorption are discussed in detail. The results show that expanding the effective sound absorption range of the damping area of the structure is the key to improve the wideband sound absorption effect. This design concept could guide the structural design of the UAL.

Modified transfer matrix method for vibration analysis of beam structures including branches and rigid bodies

Beam frames can be found in many application scenarios, ranging from big-scale structure engineering of buildings, bridges to small systems of micromachines, sensors, robotics and metamaterials. However, several challenging issues, e.g. serial-parallel configurations, beam and rigid body coupling along with inconsistent dimension of state variables, often lead to a complicated dynamic modeling. In this paper, we show that the free vibration analysis of a class of beam structures with serial-parallel branches and rigid bodies can be significantly streamlined by modifying the transfer matrix method in a graphic manner. Treating general beam structures as a topological graph with standard building blocks enables a modular modeling process and hence offers a new way to divide the complex modeling issue into much easier steps. The transfer matrix of typical building blocks, such as a beam connected to rigid bodies, tree branches and parallel clamped sub-chains, are derived and standardized providing new perspectives and distinct forms in contrast to previous studies. The transfer matrix method exhibits several advantages of easy programming, accurate solution and small degrees-of-freedom for serial structures. The presented approach extends these characteristics to a range of multi-body systems consisting of rigid bodies and beams. Comparative validation with four application case studies confirms these advantages.

Waveguide demultiplexer based on Helmholtz-resonator mediated extraordinary acoustic transmission

The design of an acoustic demultiplexer based on in-line Helmholtz resonators is demonstrated analytically via a modified transfer matrix method and computationally through finite element simulations. The modeled system consists of a single input waveguide that splits in a Y-configuration into two output waveguides. Each output arm has a single tuned Helmholtz resonator embedded in-line along the length of the guide. The Helmholtz resonators in each arm consist of a single cavity with two necks—one directed towards the input and output sides of the guide. The phenomenon of extraordinary acoustic transmission results in near perfect transmission of sound along each output arm in a small frequency interval about the Helmholtz resonant frequency. The demultiplexed frequencies are determined by the physical dimensions of the Helmholtz resonator. Using a single Helmholtz resonator in each output arm means that the system is more compact compared to other proposed schemes using either side-loaded Helmholtz resonators or stubs.

Film thickness dependency and refractive index sensing capabilities of lossy mode resonances in metallic indium-rich ITO thin films

Film thickness plays a crucial role in determining the position and depth of lossy mode resonance (LMR). Herein, we explore the overall film thickness dependency of LMR properties of pulsed-laser-deposited metallic indium-rich indium tin oxide (ITO) thin films by employing a simple Kretschmann–Raether geometry. It is observed that the depth of LMR is increased monotonically with increasing film thickness. Extremely high attenuation values of − 20 d B for transverse electric and − 10 d B for transverse magnetic polarizations are achieved for the film with the greatest film thickness. Also, the LMR positions are considerably redshifted with increasing thickness. A numerical simulation algorithm based on the modified transfer matrix method, where surface roughness is taken into account with the application of anisotropic Bruggemann effective medium approximation, is used to simulate the experimental LMR spectra for all vacuum-deposited ITO thin films effectively. As an application of this study, refractive index (RI) sensing is demonstrated in the RI range of 1.3325–1.4459, and highest sensitivity values of 3840 nm/RIU and 2542 nm/RIU are accomplished for transverse electric and transverse magnetic polarizations, respectively. This study will help in attaining a deep level of understanding of the film thickness effect on thin film based LMR and elevate metallic indium-rich ITO as an excellent material template for LMR studies.

A Modified Transfer Matrix Method for Modal Analysis of Stepped Rotor Assembly Applied in the Turbomolecular Pump

An accurate modal analysis of the stepped rotor assembly is significant in the design process of rotors. The transfer matrix method (TMM) is widely used in the modal analysis of the rotor. However, the influences of the step and the assembling modes are not considered in the traditional TMM. In this paper, a modified transfer matrix method is presented for the modal calculation of the rotor in the turbomolecular pump. The stiffness reduction of stepped segments and the effect of assembled components are considered in this modified method. First of all, the traditional transfer matrix model is built. Then, the stepped segments of the rotor are changed into conical segments and the lumped mass model of conical segments is calculated. Next, the conicities of conical segments are analyzed and relations between conicities and dimensions of the rotor are discovered. Finally, the stiffness factors which can describe the effects of different assembling modes are introduced and optimized. The optimized stiffness factors are analyzed and explained from the perspective of contact stress. The modal of the stepped rotor assembly could be computed with high accuracy by using this method.