Generalized Transfer Matrix Method Research Articles

Fiber-optic hydrophone for detection of high-intensity ultrasound waves.

Fiber-optic hydrophones (FOHs) are widely used to detect high-intensity focused ultrasound (HIFU) fields. The most common type consists of an uncoated single-mode fiber with a perpendicularly cleaved end face. The main disadvantage of these hydrophones is their low signal-to-noise ratio (SNR). To increase the SNR, signal averaging is performed, but the associated increased acquisition times hinder ultrasound field scans. In this study, with a view to increasing SNR while withstanding HIFU pressures, the bare FOH paradigm is extended to include a partially reflective coating on the fiber end face. Here, a numerical model based on the general transfer-matrix method was implemented. Based on the simulation results, a single-layer, 172 nm TiO2-coated FOH was fabricated. The frequency range of the hydrophone was verified from 1 to 30 MHz. The SNR of the acoustic measurement with the coated sensor was 21 dB higher than that of the uncoated one. The coated sensor successfully withstood a peak positive pressure of 35 MPa for 6000 pulses.

Transport effects in non-Hermitian nonreciprocal systems: General approach

In this paper, we present a unifying analytical framework for identifying conditions for transport effects such as reflectionless and transparent transport, lasing, and coherent perfect absorption in non-Hermitian nonreciprocal systems using a generalized transfer matrix method. This provides a universal approach to studying the transport of tight-binding platforms, including higher-dimensional models and those with an internal degree of freedom going beyond the previously studied case of one-dimensional chains with nearest-neighbor couplings. For a specific class of tight-binding models, the relevant transport conditions and their signatures of non-Hermitian, nonreciprocal, and topological behavior are analytically tractable from a general perspective. We investigate this class and illustrate our formalism in a paradigmatic ladder model where the system's parameters can be tuned to adjust the transport effect and topological phases.

Experimental and Numerical Analysis of Triply Coupled Vibration of Thin-Walled Beam with Arbitrary Closed Cross-Section

In this paper, a numerical experimental study about coupled vibration and natural frequency of thin-walled beams with an arbitrary closed cross-section is presented. A new thin-walled beam dynamic transfer matrix method, named TDTMM, is presented in the frequency domain for the thin-walled beam, which expands the advantages of the general dynamic transfer matrix method (GDTMM). The theory takes into account the influence of warping effect, that is, both the bimoment B and the rate of twist ϕ(x) of the beam are considered, and the TDTMM is derived by solving the governing differential equations of motion for coupled bending and torsional vibration of the thin-walled beam. Finally, two numerical examples and one experimental example are given and compared with the GDTMM and the finite element method (FEM) results to validate the developed theory.

Optical absorption in roughened silicon photovoltaic module

Photovoltaic current electric generation is directly related to the sunlight absorption in the active layers. The active layer material type and the optical losses remain the principal parameters, which have a greater effect on the amount of this absorption. This study focuses on improving the absorption in the silicon active layer of a silicon photovoltaic module by roughening the rear surface of the silicon layer. According to the Generalized Transfer Matrix Method, we derive the transmission from the incoherent multilayered module structure with a rough surface. We follow the optical model developed by Krauter and Hanitsch to derive the transmission into the silicon layer. Then the absorption is deduced from the difference between the transmission from the module and the transmission into the silicon. The effect of the incidence angles on the absorption is considered for different polarizations of light. The results of this study show a significant enhancement in the absorption in comparison to the absorption of the module with a polished rear surface. The short circuit current generated by the module with a rough rear surface silicon layer obtained is greater than that of the module with a polished rear surface.

Experimental analysis and simulation of the optical properties of gold nano-particles on sodium alginate

The reflectance and transmittance spectra of a set of thin gold films on sodium alginate are measured and simulated in the framework of the generalized transfer matrix method. In the simulation, the dielectric function for the nano-particles (NP) was modified from that of gold bulk by using a variable damping energy. A Lorentz oscillator was used to describe the localized surface plasmon resonance. The results elucidate the structural arrangement of the deposited material on the specific substrate. The collision frequency obtained from the simulation indicates that the aggregation of the NPs at the nanoscopic level correlates with the electrical properties. The intense surface plasmon resonance remains visible for film thicknesses up to 10 nm, in spite of the increasing loss of particle separation. In addition to the attained results, the developed methodology can be usefully applied on other case studies for a thorough characterization of the formation of the growing NP films on the specific substrate.

Band Structure Analysis of SH Wave Propagating in Nanoscale Layered Metamaterial Structures

This study is devoted to the analysis of the band structures of the anti-plane transverse wave (SH wave) in nanoscale layered metamaterial structures. Attention is restricted to normal incidence of waves. The localization factor is introduced to characterize the band structures. The general transfer matrix method based on the nonlocal elastic continuum theory is employed to calculate the localization factor. Based on the analysis of band structures, the influences of random disorder of the internal characteristic length and the external thickness of each sub-layer, the aperiodic arrangements, the location of different material components, the ratio of mass density, the ratio of the transverse wave velocity, the ratio of the internal characteristic length or the external thickness of each sub-layer on the band structures, the cut-off frequency, the peak points and the dense band zones are investigated and discussed in detail, which can provide some new thoughts for the designs and applications of the nanoscale wave devices.

Optical Model and Optimization for Coherent-Incoherent Hybrid Organic Solar Cells with Nanostructures.

Embedding nanostructures in organic solar cells (OSCs) is a well-known method to improve the absorption efficiency of the device by introducing the plasma resonance and scattering effects without increasing the active layer thickness. The introduction of nanostructures imposes greater demands on the optical analysis method for OSCs. In this paper, the generalized rigorous coupled-wave analysis (GRCWA) is presented to analyze and optimize the performance of coherent-incoherent hybrid organic solar cells (OSCs) with nanostructures. Considering the multiple reflections of light scattered within the glass substrate by the device, the correction vector g is derived, then the modified expressions for the field and absorption distribution in OSCs are provided. The proposed method is validated by comparing the simulated results of various structures with results obtained by the generalized transfer matrix method (GTMM) and the “equispaced thickness method” (ETM). The results demonstrate that the proposed method can reduce the number of simulations by at least half compared to the ETM while maintaining accuracy. With the proposed method, we discussed the device performance depending on the geometrical parameters of nanostructures, and the optimization and analysis are accomplished for single and tandem OSCs. After optimization based on the proposed method, the performance of OSCs are significantly improved, which further demonstrates the practicality of the method.

A novel semi-analytical approach for predicting the sound absorptions of a new underwater composite coating with transversely arranged SWCNTs

This paper presents a new underwater composite coating with transversely arranged single-walled carbon nanotubes (SWCNTs) to broaden the lower frequency limit of sound-absorbing and improve the broadband absorption bandwidth. Meanwhile, a novel semi-analytical approach integrating molecular dynamics simulation methodology and global generalized transfer matrix method (6 × 6) is proposed to predict the corresponding sound absorption characteristics. Then, the correctness and effectiveness of the present theoretical model are validated by means of an acoustic-structure fully coupled finite element simulation and theoretical predictions in turn. At last, influence laws of ten critical parameters on sound absorption coefficients are explored to reveal the multiple energy-dissipation mechanisms. The results show that the 0.5 absorption bandwidth of this coating is [0.1931, 50] kHz, which breaks the lower limit 0.5 kHz of the conventional low-frequency band and has a high-performance broadband absorption potential.

Simulation of the optical properties of gold nanoparticles on sodium alginate

In this contribution, we report on the simulation of optical reflectance and transmittance (R&T) taken on a set of gold nanoparticles thin film, deposited on sodium alginate by magnetron sputtering. The gold layer is very thin, so that the films are not continuous and the material is arranged in nanostructured layers. R&T spectra are simulated using the Generalized Transfer Matrix method applied to the film-on-substrate model. The gold NP films are simulated using the Drude-Lorentz model, by taking into account that the optical function of nanostructured gold exhibits increased collision frequency and reduced relaxation time. Moreover, the signal of localized surface plasmon, evident in the spectra, is simulated by introducing a dedicated modified Lorentz oscillator. The experimental results are well reproduced by the applied model. All trends (amplitude and energy position of the plasmon oscillator, film thickness, relaxation time) are correlated with the deposition parameters. The procedure represents a useful tool in the characterisation of such nanoparticles thin films.

A new version of the Riccati transfer matrix method for multibody systems consisting of chain and branch bodies

Computational speed and stability are two important aspects in the dynamics analysis of large-scale complex multibody systems. In order to improve both in the context of the multibody system transfer matrix method, a new version of the Riccati transfer matrix method is presented. Based on the new version of the general transfer matrix method for multibody system simulation, recursive formulae are developed which not only retain all advantages of the transfer matrix method, but also reduce the truncation error. As a result, the computational speed, accuracy and efficiency are improved. Numerical computation results obtained by the proposed method and an ordinary multibody system formulation show good agreement. The successful computation for a spatial branch system with more than 100000 degrees of freedom validates that the proposed method is also working for huge systems.

Irradiance in Mixed Coherent/Incoherent Structures: An Analytical Approach

We propose a new method for a light energy flux density (or irradiance) calculationin an arbitrary multilayer stack containing coherent and incoherent layers. Although the wellknown General Transfer-Matrix Method (GTMM) can be successfully used for the overall reflectanceand transmittance calculation, it does not allow us to obtain the corresponding irradiance depthprofile straightforwardly. We show in this paper that subsequent phase-shift integrations over theincoherent layers result in the reflectance and transmittance expressions identical to those of theGTMMformulation. However, the alternative mathematical approach allows us to derive an analyticalexpression for irradiance at an arbitrary depth of the multilayer stack, thus making it possible tocalculate the absorptance depth profile. In fact, the GTMM expressions for the overall reflectanceand transmittance turn out to be special cases of the irradiance calculation at the incident andemergent surface of the multilayer stack. Consequently, the proposed Phase-shift Integration Method(PIM) represents a continuous irradiance calculation model without any energy imbalances onlayer interfaces. In addition, since we are able to obtain analytical layer thickness derivatives,the PIM is suitable for use with gradient optimization methods. We verify the method on threecases of an encapsulated bifacial heterojunction silicon (HJ Si) solar cell, a perovskite solar cell,and a perovskite/silicon tandem solar cell, which all consist of thin and thick layers.

Effect of anisotropy on the spectral characteristics of one-dimensional porous silicon photonic crystal microcavity for optical sensing applications

We present a numerical study of the effect of anisotropy on the spectral characteristics of one-dimensional porous silicon microcavity (1D-PSMC) with single defect layer. These structures have strong potential applications in optical sensing of chemicals and bioanalytes. Bruggeman’s effective medium approximation (BEMA) and (4 × 4) general transfer matrix method are used for theoretical modeling of spectral response of anisotropic 1D-PSMC. The potential of this structure as a sensing material is illustrated by analyzing wavelength shift in the defect mode induced by infiltration of biochemical analytes of different refractive indices inside the pores. Observed wavelength shift is found to be linearly dependent on the refractive index of analytes. We propose two 1D-PSMC-based sensors with a microcavity wavelength around 800 and 1200 nm. An anisotropic sensor with an operating wavelength around 800 nm shows a maximum sensitivity of 190 while an isotropic sensor with the same design parameters displays a maximum sensitivity of 150. In the case of an anisotropic sensor designed around 1200 nm, the maximum sensitivity is 260; for the isotropic sensor with similar structure, maximum sensitivity of 210 is obtained. Increased sensitivity is observed in anisotropic structures as compared to the isotropic ones. Design parameters play an integral role to obtain desired sensitivity in 1D-PSMC structure for sensor applications. These sensors can be used for high precision optical sensing of chemical-analytes, bioanalytes, gases, and environmental pollutants.

Computational analysis of metamaterial–aluminum–silicon solar cell model

In this paper, the optical parameters of an improved waveguide structure for a more efficient silicon solar cell are studied. Despite its favorable electronic, physical, and chemical properties, silicon remains a poor absorber of light. The optical losses due to the reflection at the air/glass interface of the cell and the transmission at its back are other factors, which limit the cell conversion efficiency. Consequently, several mechanisms for light trapping capable to increase the collection of the incident photons as electrical current and to decrease the transmission loss, have been developed. In this context, we propose a multilayer waveguide structure in which the sunlight is guided by a metamaterial layer and the transmission loss is eliminated by an aluminum back reflector. The reflection and transmission coefficients are derived by using the Generalized Transfer Matrix Method. The application of the law of conservation of energy allowed the determination of the absorption coefficient. These optical parameters are examined for several angles of incidence for s-polarized light, p-polarized light and unpolarized light. Simulation results show a significant reduction of reflection and a complete suppression of transmission.

Novel Approach to The Design of Sound Insulating Composites by Means of a Non-linearly Extrapolated Master Curve

Background:The increasing use of composite structures with a high stiffness-to-weight ratio in commercial vehicles has brought about a reduction in fuel consumption but, on the other hand, has significantly increased noise transmission particularly in case of thin and lightweight structures. Noise is a primary issue for commercial vehicles, such as airplanes, helicopters and cars. The present research deals with the use of smart materials, as Shear-Thickening Fluids (STF, or dilatants) in view of manufacturing elements with increased sound insulation properties.Methods:The response of a sandwich material with the STF core was investigated both experimentally and numerically, by choosing the Sound Transmission Loss (STL) of the composite structure as the figure of merit.The experimental investigation was focused on the manufacturing of a sandwich structure made of metallic skins and a STF core that was successively characterized by sound insertion loss measurement.The numerical investigation was carried out by using a Generalized Transfer Matrix Method (GTMM) and a Statistical Energy Analysis (SEA) in view of selecting the fluid capable of granting the highest acoustic transmission loss.Results:Finally, the test results were compared to the numerical results, showing a noticeable agreement. The used STF showed increasing viscosity at increasing shear rates.

Numerical modeling of the effect of multiple incoherent layers in Cu(In,Ga)Se2solar cells based on the equispaced thickness averaging method

We investigate the effect of multiple incoherent layers on the optical characteristics of Cu(In,Ga)Se2 (CIGS) solar cells, based on the equispaced thickness averaging method (ETAM). The studied multiple incoherent layers consist of a glass cover layer, surface flattening layer, and transparent conducting layer, whose respective thicknesses are larger than the coherence length of sunlight (∼0.6 μm). An independent equispaced thickness is added to each incoherent layer and the coherent simulation results, obtained by the finite element method, are averaged over a combination of the equispaced thicknesses. By applying the proposed method, we calculated the reflectance spectra in planar and surface-textured CIGS solar cells. Considering the planar structure, the calculation results based on the ETAM are in good agreement with the exact analytical solution based on the generalized transfer matrix method. The statistical deviation from the exact solution was calculated with respect to the number of the equispaced thicknesses in each incoherent layer. When only four equispaced thicknesses are used, the calculated deviation from the exact solution rapidly decreases to 1% for planar and 10% for surface-textured CIGS solar cells, which demonstrates that the effect of the multiple incoherent layers can be efficiently calculated based on the ETAM in thin-film solar cells.

Static analysis of thin-walled space frame structures with arbitrary closed cross-sections using transfer matrix method

This paper develops a new transfer matrix method for the static analysis of thin-walled space frame structures with arbitrary closed single-cell sections, that is, thin-walled beam transfer matrix method (TBTMM), which expands the advantages of the general transfer matrix method (TMM). In this method, the bimoment B and the rate of twist of the beam φ(x) are taken into account based on the Vlasov's beam theory and Kollbrunner-Hajdin assumption, and the bending and twisting can be calculated separately combined with the characteristic of Maillart's shear center. Using this method, the transfer matrix of single beam is obtained through Laplace transform and inverse Laplace transform at first, and then gets the coupling equations of the whole structure with respect to coordinate transformation matrices and joint coupling matrices. Some numerical examples are given and compared with the general TMM and the finite element method (B-FEM and S-FEM) results to validate the developed method.

An Accurate Representation of Incoherent Layers Within One-Dimensional Thin-Film Multilayer Structures With Equivalent Propagation Matrices

We propose a novel approach of including incoherent layers into an arbitrary multilayer stack and treating them using the conventional matrix methods in the wave-optics regime. The proposed “Equivalent Matrix Method” (EMM) calculates two phase-shift additions that totally cancel out the interference terms in front of, and behind the incoherent layer. The additions are merged into an equivalent incoherent layer propagation matrix that can be used in the standard coherent calculation. The mathematical model that we describe in the paper has three important advantages. First, the exact calculation of the phase-shift additions efficiently replaces various phase-averaging approaches normally used to deal with incoherency. Second, instead of an incoherent layer, we can use an equivalent coherent layer in a rigorous simulation using the phase-matching. Last, there is no energy imbalance error caused by wave coupling in lossy incoherent layers. We verify the proposed EMM against the general transfer-matrix method (GTMM) and the combined ray optics/wave optics model (CROWM) using two cases: an arbitrary multilayer structure with four incoherent glass layers, and a thin-film hydrogenated amorphous silicon solar cell. In both cases, the EMM yielded the same results as the GTMM and CROWM, thus confirming its regularity.

Ultrathin ultra-broadband electro-absorption modulator based on few-layer graphene based anisotropic metamaterial

In this article, a few-layered graphene-dielectric multilayer (metamaterial) electro-optic modulator has been proposed in the mid and far infrared range that works on electro-absorption mechanism. Graphene, both mono layer and few layer, is an actively tunable optical material that allows control of inter-band and intra-band transition by tuning its chemical potential. Utilizing this unique feature of graphene, we propose a multilayer graphene dielectric stack where few layer graphene is preferred over mono layer graphene. Although the total thickness of the stack still remains in the nanometer range, this device can exhibit superior performances in terms of (i) high modulation depth, (ii) ultra-broadband performance, (iii) ultra-low insertion loss due to inherent metamaterial properties, (iv)nano-scale footprint, (v) polarization independence and (vi) capability of being integrated to a silicon waveguide. Interestingly, these superior performances, achievable by using few layer graphene with carefully designed metamaterial, may not be possible with mono layer graphene. Our proposals have been validated by both the effective medium theory and general transfer matrix method.

A Simple Numerical Modeling of the Effect of the Incoherent Thick Substrate in Thin-Film Solar Cells Based on the Equispaced Thickness Method

We propose a simple numerical modeling method to consider the effect of the incoherent thick substrate on the absorption characteristics of thin-film solar cells. In the proposed “equispaced thickness method” (ETM), the incoherent optical characteristics of the thick substrate are modeled by adding an additional thickness that gives an equispaced phase shift to the incoherent substrate and averaging the coherent simulation results over several equispaced thicknesses. The proposed ETM can be used to consider the effect of the incoherent glass substrate without complicated mathematical and computational procedures and is applicable to not only planar but also surface-textured thin-film solar cells. By applying the proposed method to the numerical modeling based on the finite element method (FEM), we calculate the reflectance spectra in planar and surface-textured thin-film solar cells, respectively. The simulation condition of the FEM, such as mesh size, is determined to match the numerical results based on the ETM with the analytical results obtained by the generalized transfer matrix method. For comparison, the reflectance spectra in the same structures are calculated by taking the average over coherent calculation results for a large number of random thicknesses of the incoherent layer. According to the comparison of the calculated statistical deviations from the exact solution between the ETM and the random thickness method, the ETM reduces the number of simulations by at least a factor of 50 with the same accuracy.

Bandgap extraction from quantum efficiency spectra of Cu(In,Ga)Se2 solar cells with varied grading profile and diffusion length

Quantum efficiency measurements on Cu(In,Ga)Se2 (CIGS) solar cells are widely used as a non-destructive and easy to apply method to extract the bandgap of the CIGS absorber layer. Information about the bandgap is of major relevance, e.g., for process control or parameter definition in device simulations. However, determining the bandgap from quantum efficiency measurements rely on the assumption that the quantum efficiency is solely determined by the absorption of a homogeneous absorber layer. We therefore compared different bandgap extraction models while taking into account different bandgap grading profiles and diffusion lengths, thus different bulk recombination properties. To study the effects of limited diffusion and grading in more detail, we created a one-dimensional optical simulation tool that calculates the optics by means of the generalized transfer matrix method. The tool includes models to account for roughness, thickness non-uniformity and graded layers. By fitting the model to the measured external quantum efficiency (EQE), we determine the bandgap gradient, which is compared to that calculated from the composition measured with glow discharge optical emission spectroscopy. We found that common methods to extract the bandgap overestimate the band gap value from EQE by up to 150meV depending on the slope of the grading. In contrast to this, the influence of the diffusion length on the extracted bandgap is negligible.