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Sprays generated by atomization processes have been used in a wide range of fields. The size and spatial distribution of volumetric droplets in a spray are critical parameters in industrial applications. Astigmatic interferometric particle imaging (AIPI), an extension of the traditional interferometric particle imaging (IPI), is developed to simultaneously measure the size and 3D position of volumetric droplets in a sparse spray. Based on the generalized Huygens–Fresnel integral and the transfer matrix, the size and depth position of droplet can be respectively extracted from the fringe spacing and orientation of interferogram in AIPI. An AIPI setup is established to characterize droplets in a sparse spray generated by a nozzle with the AIPI calibration procedure adopted. The measured parameters by AIPI are compared with those obtained synchronously by digital inline holography, which is regarded as a standard measurement technique. Results show that the average deviation values of droplet size and depth position are respectively 3.8% and 6.8%. AIPI has been demonstrated with high accuracy in simultaneous 3D positions and size measurements.

International audience; The optical properties of chiral plasmonic metasurfaces depend strongly on their architecture, in particular the orientation and spacing between the individual building blocks assembled into large arrays. However, methods to obtain chiral metamaterials with fully tunable chiroptical properties in the UV, visible and near infrared range are scarce. Here, we show that the chiroptical properties of silver nanowires assembled in helical nanostructures by Grazing Incidence Spraying and Layer-by-Layer assembly can be finely tuned over a broad wavelength range using simple design principles. The angle between the oriented nanowire layers controls the intensity of the circular dichroism, reaching ellipticity values higher than 13° and g-factor values up to 1.6, while the shape of the circular dichroism spectra depends strongly on the spacing between the layers which can be tuned at the nm-scale. The structure-dependent optical properties of the assembly are successfully modeled using a transfer matrix approach.

In this article, the frequency coupling of weak grid-connected doubly fed induction generator (DFIG) based wind turbines (WT) during asymmetric faults have received little attention. To analyze the frequency coupling phenomenon of the system during asymmetric faults, this article established the complex transfer function model in αβ frame based on the transformation relationship between complex transfer function and transfer matrix. According to the complex transfer function, the frequency coupling mechanism of the DFIG system during asymmetric faults is revealed, and the transfer evolution law of coupling frequencies is described in detail. Finally, the correction of theoretical analysis and the validity of proposed complex transfer models are verified by the simulation and experiment.

A binary superconductor–dielectric photonic crystal (PC) is proposed. The PC has the structure (AB)N with layer A representing the superconducting layer and layer B the dielectric material. The transfer matrix technique is used to deduce the transmission coefficient through the PC. The properties of photonic bandgaps (PBGs) arising in the transmission spectra are studied with the angle of incidence and with all parameters of the superconductor such as thickness, London penetration length, and critical temperature. Many interesting findings were reached: The PBG width decreases with increasing the incidence angle until it disappears for high incidence angles. There is an optimum superconducting layer thickness at which the PBG shows a maximum. The critical temperature has the lowest effect on the PBG width among the superconductor parameters, whereas London penetration length has the topmost effect.

A $\\boldsymbol d$ - $\\boldsymbol q$ frame impedance model of modular multilevel converter (MMC), which is suitable for high-frequency resonance (HFR) analysis under the condition that the number of submodules in MMC reaches hundreds level, is presented in this work. A 10th-order dynamic phasor model for the MMC is linearized and combined with a control subsystem model. A modular modeling approach based on transfer matrix is applied to the overall linearized model to derive the impedance model. The validity and accuracy of the model are verified using a 501-level MMC aggregated model in SIMULINK. Results show that the impedance model has satisfactory accuracy in the frequency ranging from 1 to 3000 Hz. Then, the impedance model is used to analyze an HFR accident in a realistic MMC project. Therefore, a high time delay in controller is proved can provide negative resistance in high frequency and cause instability.

International audience; We have designed and experimentally studied several systems of standard coaxial cables with different impedances which mimic the operation of so-called photonic structures like coupled photonic crystal microcavities. Using elementary cells of half-meter long coaxial cables, we got resonances around 100 MHz, a range of frequencies that can be easily studied with standard teaching laboratory apparatus. Resonant mode frequency splitting has been obtained in the case of double and triple coupled cavities. Good agreement between experimental results and the transfer matrix model has been observed. The aim here is to demonstrate that a standard coaxial cable system is a very cheap and easy to implement structure to explain to undergraduate students complex phenomena that usually occur in the optical domain. © 2021 Author(s).

This paper proposes a novel displacement–strain transfer (DST) matrix method to estimate the local bending deformation of bridge deck using the measured strain. The DST matrix of the bi-dimensional plate with various boundary conditions is derived theoretically, and the local bending deformation of the plate can be further estimated. A plate with four simply supported edges, two simply supported edges, and one clamped edge under various load cases is simulated. The DST matrix is calculated, and the local bending deformation is finally estimated. The proposed method is also verified by the experimental test of a simply supported plate. Both the numerical and experimental results indicate that the proposed method can effectively estimate the local bending deformation of a bi-dimensional plate. Finally, a steel–concrete composite girder bridge is simulated, and the local bending deformation of the bridge deck is also effectively estimated based on the proposed method.

Industry is moving towards more data-oriented design and analyses to solve complex analytical problems. Solving complex and large finite element models is still challenging and requires high computational time and resources. Here, a modular method is presented to predict the transmission of vehicle body vibration to the occupants’ body by combining the numerical transfer matrices of the subsystems. The transfer matrices of the subsystems are presented in the form of data which is sourced from either physical tests or finite element models. The structural dynamics of the vehicle body is represented using a transfer matrix at each of the seat mounting points in three triaxial (X–Y–Z) orientations. The proposed method provides an accurate estimation of the transmission of the vehicle body vibration to the seat frame and the seated occupant. This method allows the combination of conventional finite element analytical model data and the experimental data of subsystems to accurately predict the dynamic performance of the complex structure. The numerical transfer matrices can also be the subject of machine learning for various applications such as for the prediction of the vibration discomfort of the occupant with different seat and foam designs and with different physical characteristics of the occupant body.

In this work, a symmetric one dimensional quinary photonic crystal structure is proposed. The unit cell of the proposed structure is composed of materials chosen in such a way that the refractive i...

Mode-by-mode impulse responses, or spectral transfer matrix (STM) of birefringent fibers are measured by using linear optical sampling, with assist of polarization multiplexed probe pulse. By analyzing the STM, differential mode delays are estimated.

Purpose Crack damage detection for aluminum alloy materials using fiber Bragg Grating (FBG) sensor is a kind of structure health monitoring. In this paper, the damage index of full width at half maximum (FWHM) was extracted from the distorted reflection spectra caused by the crack-tip inhomogeneous strain field, so as to explain the crack propagation behaviors. Design/methodology/approach The FWHM variations were also investigated through combining the theoretical calculations with simulation and experimental analyses. The transfer matrix algorithm was developed to explore the mechanism by which FWHM changed with the linear and quadratic strain. Moreover, the crack-tip inhomogeneous strain field on the specimen surface was computed according to the digital image correlation measurement during the experiments. Findings The experimental results demonstrated that the saltation points in FWHM curve accorded with the moments of crack propagation to FBG sensors. Originality/value The interpretation of reflected spectrum deformation mechanism with crack propagation was analyzed based on both simulations and experiments, and then the performance of potential damage features – FWHM were proposed and evaluated. According to the correlation between the damage characteristic and the crack-tip location, the crack-tip of the specimen could be measured rapidly and accurately with this technique.

A frequency conversion mixer or single side band modulator using two cascaded MZM is proven experimentally. The operation of the circuit is modelled by a transfer matrix approach and verified by simulation in support of the experiment. A 10 GHz shift of the optical carrier in both left and right direction is demonstrated. The residual sideband suppression relative to the enhanced sideband is 22 dB for the best cases. Numerical analysis shows that the circuit has 3-dB optical and 3-dB electrical intrinsic advantage over the functionally equivalent DP-MZM.

In this work we present a simple transfer-matrix based modeling tool for arbitrarily layered stacks of resonant plasmonic metasurfaces interspersed with dielectric and metallic multilayers. We present the application of this model by analyzing three seminal problems in nanophotonics. These are the scenario of perfect absorption in plasmonic Salisbury screens, strong coupling of microcavity resonances with the resonance of plasmon nano-antenna metasurfaces, and the hybridization of cavities, excitons and metasurface resonances.

In the present study, the transmission characteristics of ultrashort pulses through coupled-cavity waveguides in one-dimensional photonic crystals were investigated theoretically, using finite-difference time-domain and transfer matrix methods. By controlling the configuration of the waveguides, a flat defects’ band can be obtained in the transmission spectra, which can be used for passing ultrashort pulses. The conditions for achieving a flat defects’ band are derived by optimization geometrical parameters of the waveguides. The optimized structure is able to transmit ultrashort pulses, up to 30 fs, with negligible distortion and attenuation. Unlike the previously designed waveguides with the same application, we designed our system without using graded index materials or many thin film layers.

The propagation properties of waves in Timoshenko beams resting on flexible supports and with periodically attached harmonic locally resonant oscillators are studied by the transfer matrix methodology. Through calculating the differential equations of the beam for the flexible vibration and the dynamic equations of the oscillators in series, the matrix of dynamic stiffness and the resulting transfer matrix are derived. Accordingly, the band gap in infinite system characterized by the propagation constant can be verified by comparing to the curve of transmission property, determined with the finite element method for the finite system. The mechanism of each band gap formation is further explored. Numerical results show that different from the single degree-of-freedom mass-spring model, one more locally resonant band gap is generated in the system of two oscillators in series. The introduction of flexible supports, allowing for variable internal coupling between the adjacent cells, produces an extra band gap with a minimum frequency of zero. It is also found that the starting frequencies of the locally resonant gaps are related to the spring stiffness and mass of the oscillator. Therefore, the positions and widths of the band gaps can be tuned by properly adjusting the four parameters of the oscillators and also the stiffness of the flexible supports.

Dielectric materials play a supporting role for electronic circuits. With the development of 5G millimeter wave communication, precision measurement of dielectric property becomes increasingly important. This paper introduces a free-space quasi-optical spectroscopy for complex dielectric property measurement. This spectroscopy can work in both transmission and reflection modes to accommodate both low-loss and high-loss materials. By applying the transfer matrix theory, both solid and liquid samples can be characterized using this system. In addition, the system employs a Gaussian telescope design, giving a possibility of broadband operation. Furthermore, this system is much simpler in calibration compared to other systems. A detailed description of the quasi-optical system is presented. Four materials are measured in the E-band (60–90 GHz). De-ionized water is also measured to represent liquid substrates in electronic circuits. The measurement is in good agreement with published data within a discrepancy of 5%.

Surface Plasmon Resonance (SPR) technique has been of recent interest in many fields such as biological and chemical sensing, defense-related applications, etc. The introduction of graphene sheet (metal-like optical properties) over a thin-film layers plays a significant role in generating SPR. Different nanoplasmonic structures like Coupled Waveguide SPR (CWSPR) and Long Range SPR (LRSPR) are considered with modified Kretschmann-Raether configurations for different wavelengths in visible range for plasmonic sensors application. Characteristic Transfer Matrix (CTM) method in MATLAB environment is employed to obtain the theoretical results of LRSPR-based nanoplasmonic structures. Based on different compositions, minimum reflectivity as obtained is reported here. Due to the incorporation of additional graphene thin layer, keeping the angle of incidence constant, the percentage of reflectivity is being increased significantly, thereby reducing the transmission within the layers. With the variation of thickness, refractive index of different layers as well as wavelength of the LASER source, one may optimize the structures to obtain best possible performance.

This work investigates voltages on overhead distribution lines produced by direct strokes, protected by shield wires, placed both above and below phase conductors. An improved formulation based on transfer matrix method and theory of multiconductor transmission lines with periodic grounding allows to eliminate the need of two characteristic wave impedance matrices. Based on the theoretical formulation developed in the first part of this work, as well as on the models there presented for the pole and grounding systems, we report here a wealth of simulation results concerning the line overvoltages subsequent to a pole being hit by lightning. Results are discussed considering a variety of factors, namely, position of the victim pole, type of load at both ends of the line, presence or absence of underbuilt shield wires, waveform of the lightning current, soil parameters and parameters of the frequency-dependent impedance of the pole grounding system. The good performance of the developed method is assessed by comparing our results with some EMTPRV simulations. The transfer matrix method is then used to show the effect of shield wires in conjunction with periodic grounding: we assess the effects of terminations, frequency dependent models of the pole footing and grounding systems and frequency dependent models of lossy ground.

In this study, a new simulation method is proposed and verified for fiber Bragg grating patterned on polarization maintaining fiber(PM-FBG) using the transfer matrix approach. The method is designed to solve the twisted PM-FBG simulation. The four mode matrix element of a period grating is derived from the S matrix element and the method only involves the torsion-induced shear strain entry e x y which can be considered as the rotation of the principal axis of the polarization maintaining fiber and ignores the torsion-induced shear strain entries e x z and e y z . The validity of the method is confirmed by numerical simulation of the twisted PM-FBG. The novel method provides the ability to analyze any type of PM-FBG.

Fiber Bragg Gratings or FBGs have achieved significant attention towards sensing and communication applications due to their outstanding advantages. Due to its high sensitivity towards various design parameters, it is now widely used to measure different physical and chemical parameters in various industrial sectors, including harsh environment applications. This review presents a comparative study of different FBG-based temperature and strain sensors reported in recent years. The analytical formulation for such sensors is also presented in brief. Necessary numerical simulation results are incorporated. For FBG based temperature sensors, both low and high range are considered. Similarly, for FBG-based strain sensors, both uniform and non-uniform strain are considered and discussed in brief. Apart from the sensing applications, new variants of FBG like secondary gratings and Random Optical Grating by Ultraviolet or ultrafast laser Exposure (ROGUE) gratings are also discussed.

Given the wide range of applications of time-domain spectroscopy, and particularly THz time-domain spectroscopy, the modelling of a probe pulse propagating through a multilayered structure is often required. Due to the fact that the multilayers are usually grown on a substrate much thicker than the other layers, the transmission of a probe pulse includes a series of echo pulses caused by the multiple reflections at the substrate interfaces. Experiments often measure the time profile and construct the transmitted spectrum only from the first transmitted pulse. Due to the fact that typical substrates lead to times of crossing comparable to the spectral bandwidth, the first transmitted pulse's spectrum and the full transmitted spectrum can be importantly different. It is therefore important to theoretically model the transmission without the echo, to be able to directly compare with experimental results. Here we propose a method to elegantly and easily theoretically remove the echo from the transmission spectrum, without Fourier transforming the signal twice. The spectrum of the transmitted pulse without echo will be produced analytically without additional numerical steps, reducing computational time and program complexity when dealing with larger scale computing.

In this paper, we give a spatial frequency analysis of polarization imaging system and study the effects of rotational alignment errors of the polarizer from their ideal orientations. With the help of newly proposed Optical Transfer Matrix (OTM) for a diffraction-limited polarization imaging system, we investigate the effects of polarization-sensitive aberrations from the generalized pupil matrix at the exit pupil plane. Here, polarization aberrations stemming from the angular alignment errors of a linear polarizer has been demonstrated. The performance of a polarization imaging system with rotational alignment error has also been evaluated based on a cost function based on OTM.

As an advanced technology, polarization imaging has attracted widespread interests in recent years due to its unique ability to detect the polarization information of objects. With illumination of partially coherent and partially polarized light, the polarization imaging systems are in generally nonlinear systems because they do not possess a transfer matrix in the usual sense. Nonetheless, it is possible to apply a sinusoidal amplitude object at the input and to measure a periodic output. However, unlike the linear case, knowledge of the response of the polarization system to a sinusoidal input does not allow one to predict what the output will be for other types of inputs. To address the fundamental nonlinearity in evaluation of the Stokes images, we provide a frequency- domain calculation of Stoke images of a sinusoidal amplitude grating under partially polarized and partially coherent illumination, and propose a new concept referred to as transmission cross coefficients to describe its frequency response of polarization imaging system. Some of the implications of such analysis are also given for polarization imaging evaluation.

We present e-mulate, an user-friendly software developed to calculate the electronic states of quantum well heterostructures. e-mulate was designed with a graphical user interface for users without previous coding skills. The unidimensional Schrodinger equation is numerically solved using transfer matrix and Numerov algorithms in the back-end. Essential figures of merit of optoelectronic devices, such as photodetectors are provided by the software: optical transition energies with their respective oscillator strengths, the absorption and the electronic transmission spectra. A comparison between the calculated absorption and experimental results of an In 0.53 Ga 0.47 As/In 0.52 Al 0.48 As quantum Bragg mirror photodetectors is presented as validation of the software.

In this work we developed an extension to the Transfer Matrix method (TMM) to include a current source term, with the aim of describing both the transmission and emission of THz pulses in spintronics THz emitters. The TMM with source is derived from the Maxwell equations with a volume free current term. This extension to the TMM allows for the study of realistic spintronics THz emitters as multilayers of different materials with different thicknesses. We use this to prove that, in spite of a common misconception, the drop rate of the THz emission amplitude at higher heavy metal layer thicknesses is not related and does not provide information about the spin diffusion length. It is instead the effect of the increase in the parasitic absorption of the generated radiation by the conducting parts of the spintronics THz emitter itself.

Land use change is an important driving force factor affecting the river water environment and directly affecting water quality. To analyze the impact of land use change on water quality change, this study first analyzed the land use change index of the study area. Then, the study area was divided into three subzones based on surface runoff. The relationship between the characteristics of land use change and the water quality grade was obtained by grey correlation analysis. The results showed that the land use types changed significantly in the study area since 2000, and water body and forest land were the two land types with the most significant changes. The transfer rate is cultivated field &gt, forest land &gt, construction land &gt, grassland &gt, unused land &gt, water body. The entropy value of land use information is represented as Area I &gt, Area III &gt, Area II. The shift range of gravity center is forest land &gt, water body &gt, cultivated field. There is a strong correlation between land use change index and water quality, which can be improved and managed by changing the land use type. It is necessary to establish ecological protection areas or functional areas in Area I, artificial lawns or plantations shall be built in the river around the water body to intercept pollutants from non-point source pollution in Area II, and scientific and rational farming in the lower reaches of rivers can reduce non-point source pollution caused by farming.

In photonics, the study of wave propagation in scattering media is limited by the inherent challenges in detecting the time-varying electric field oscillations, as detectors and cameras are only sensitive to the optical intensity. In the Terahertz (THz) domain, however, Time-Domain Spectroscopy (TDS) is an established technique capable of directly measuring the electric field and provide full-wave characterisation (amplitude and optical delay) in time. The combination of THz time-resolved measurements with the theory of wave propagation in scattering media is a rapidly emerging subject. It opens a promising route to gain coherent control over multiple-scattering phenomena in ways not previously accessible in optics [1] . Besides, the combination of broadband excitation and coherent, field-sensitive detection could allow investigating the transmission properties of a scattering medium in unprecedented detail and retrieve its coherent transfer-matrix representation, a task out-of-reach at optical frequencies. In this work, we theoretically demonstrate spatiotemporal refocusing of THz waves following a direct measurement of the transfer matrix of the scattering medium. Our approach combines the advantages offered by field-sensitive detection with the nonlinear wavefront shaping of THz waves. Wavefront shaping represents the state-of-the-art in the control of complex wave propagation at optical frequencies, as it allows to sequentially retrieve the transfer matrix elements of the scatterer [2] . To overcome the limited availability of THz Spatial Light Modulator (SLM) devices, we employ a recently proposed technique based on the nonlinear conversion of structured optical beams to THz patterns [3] . Specifically, we take inspiration from nonlinear Ghost-Imaging techniques and project a complete set of orthogonal Hadamard patterns on the scatterer [4] . This technique allows us to retrieve the complex-valued elements of the transfer matrix by numerical inversion ( Fig. 1a,b ). We apply the direct knowledge of the transfer matrix elements to identify the optimal focusing pattern in a deterministic fashion ( Fig. 1c,d ). Unlike iterative optimisation techniques [2] , our deterministic approach takes advantage of the full amount of spatiotemporal information encoded in the transfer matrix elements. Under this view, the task of identifying the optimal input wavefront is rewritten into an inverse problem that can be solved via constraint least-square optimisation methods. An exemplary result is shown in Fig. 1c,d , where our technique is employed to achieve spatiotemporal refocusing (i.e., focusing in space and compression in time) of a single cycle THz pulse.

Chalcogenide Glasses are of recent interest in the field of chemical and bio-sensing applications. These are considered either in stored memory devices or in optical domain. The involvement of such material in the bio-sensing application for the development of SPR (Surface Plasmon Resonance) Sensors is very essential and thus, has been considered in this manuscript. In a Kretschmann SPR configuration, a thin-film layer of such Chalcogenide material has been incorporated which is further accompanied with a Graphene layer. The optical properties of both the materials viz. chalcogenide and graphene have been portrayed and presented in this paper by taking the assistance of MATLAB environment and Characteristic Transfer Matrix (CTM) Method.

In this study, the dynamic response of beams resting on two-parameter elastic foundation subjected to moving load is investigated by using the transfer matrix method (TMM). The Timoshenko beam theory (TBT) which considers shear deformation and rotational inertia is used to model the beam. The two-parameter elastic foundation model is selected as Pasternak foundation that takes into account a shear layer at the end of linear springs of Winkler foundation. The TMM which uses the relation between analytically obtained state vectors of each end of the beam is applied to solve the free vibration problem. After performing the free vibration analysis, the mathematical model is simplified into an equivalent single degree of freedom (SDOF) system by using the exact mode shapes to obtain dynamic responses. The generalized displacement is calculated for each mode by using the Runge-Kutta algorithm. A numerical case study is presented for a simply-supported Timoshenko beam on the Pasternak foundation subjected to a concentrated load. The natural frequencies obtained from finite element method (FEM) results of SAP2000 are presented with the results of TMM for comparison purposes using the Winkler foundation. The effects of shear layer on the natural frequencies of the model are revealed. The mode shapes are plotted. The proposed approach for calculating dynamic responses is validated by using the results of FEM for Winkler foundation model. Then, the effects of Winkler springs and shear layer of the foundation model on the dynamic responses are presented in figures. The effects of modal damping are discussed. Finally, the critical velocities for the model are calculated for various elastic foundation scenarios and the effects of elastic foundation parameters on the dynamic response of beam model subjected to moving load with high velocity are observed.

In this paper, a theoretical analysis of a flat-top microring resonator (FTMRR) is undertaken. The intensity and group delay responses of the FTMRR are derived from a transfer matrix formalism, which shows that flat-top resonance is possible in this single-ring cavity by stimulating and manipulating slow light in the counterclockwise (CCW) mode and fast light in the clockwise (CW) mode. The analytical solutions required for achieving the flat-top responses are obtained by assuming that the slope around the resonant wavelength equals zero. In addition, an improvement in the bandwidth of the FTMRR (in comparison with the MRR), the tunable and reconfigurable optical responses for filtering/switching, and the small variation in intensity during the tuning of the flat-top group delay observed in the previous experiments are all proved through theoretical analysis.

Huazhong University of Science and Technology has been developing a proton therapy facility based on a superconducting cyclotron. As an important section of the facility, the gantry beamline has been designed using TRANSPORT code with simplified fringing field model and linear transfer matrix. However, realistic magnetic fringing field and second-order terms of particle motion cannot be precisely described in this approach, which may deviate the actual result from the design value and thereby increase uncertainties for radiation therapy during beam delivery. For this consideration, the specific effects of fringing field and second-order aberrations have been investigated using OPERA code and ODE solvers. For the potential problems of the designed gantry beamline, COSY INFINITY code, which can calculate transfer matrix of any order under the realistic fringing field represented by Enge function, was used to optimize the optics of present gantry beamline. The final results suggest the beam analysis and optimization methods mentioned in this paper are effective and valuable for relevant applications.

Dynamics modelling and simulating are the significant process to improve the machining accuracy of the machine tool. This paper is aimed to model and simulate the ultra-precision fly-cutting machine tool (UFMT) and find the relations between structure parameters and machined surface. In this paper, the multi-rigid-flexible-body dynamics model of the UFMT is firstly built by using transfer matrix method for multibody systems. After deducing overall transfer equation, overall transfer matrix, eigenfrequency equation and dynamics equations, the vibration characteristics and dynamics response of tool-tip are simulated and validated by tests. The machined surface is simulated by transferring displacement between the fly-cutting tool-tip and the workpiece into 3D curve. According to the simulation results, both the air-bearing stiffness of the flying-cutting head and cutting process parameters have effects on the machined surface.

Surface plasmon resonance has many applications in designing biosensors. In this paper, an easy fabrication liquid crystal-based surface plasmon resonance (LC-SPR) biosensor is simulated and presented which can determine reflectance and sensitivity via liquid crystal structure, gold structure, and silver structure. The powerful transfer matrix was applied for calculating the reflectance and sensitivity of the biosensor. The alignment of liquid crystal molecules and the concentration of biological analytes have a remarkable impact on biosensor’s sensitivity enhancement. The results indicated that, after including analytes, the birefringence of liquid crystal changes; consequently, performance parameters are enhanced. Maximum performance parameters of the proposed LC-SPR biosensor obtained for the homogeneous condition of S = 0 and silver-based structure parameters are better than those of other structures.

An effective method for the calculations of stress and residual strength of complex spatial pipelines at static and dynamic loading with taking into account the vibration of internal liquid and Puasson coupling is presented. It based on the well-known transfer matrix approach. The method utilizes the exact mechanical equations for the stress-strained state of straight beam with distributed mass, which connect unknown parameters of forces and displacements at the end of beam calculation element with the parameters at the beginning of the element. At a general level, the solution scheme and calculation models are the same for static and dynamic calculations, the only difference – are the equations. Two different methods are used to find natural vibration frequencies of the distributed mass system: straightforward (“brute force”) and quick, based on Williams-Wittrick frequencies counter. Within such counter a special procedure is developed for taking into account fluid vibration with consideration of volumetric balance condition at T-nozzles. The excellent accuracy of the method is demonstrated by the modeling of thin-walled, water filled pipe behavior after the rod impact. Two seismic analysis procedures are implemented on the base of developed method: standard response spectrum procedure and normal-mode summation procedure (“exact” dynamical), which uses accelerograms. These methods and procedures have been already implemented in calculation software for pipeline strength assessment with the possibility of building of arbitrary complexity models by the user-friendly, visual way. Their effectiveness is demonstrated by the seismic calculation for primary circuit pipings of Zaporizhia NPP.

"Ternary photonic crystals have shown a superior performance over the binary ones. In this work, a ternary photonic crystal which has the structure dielectric/plasma/ dielectric is considered. Transmission through the proposed photonic crystal at oblique incidence on a specific PC structure is analyzed using the transfer matrix technique. The effect of the plasma layer of the photonic band gap is investigated. The use of the proposed photonic crystal as an optical sensor for detection of small changes within the plasma electron density or the index of refraction of the dielectric layers is investigated." "Ternary photonic crystals have shown a superior performance over the binary ones. In this work, a ternary photonic crystal which has the structure dielectric/plasma/ dielectric is considered. Transmission through the proposed photonic crystal at oblique incidence on a specific PC structure is analyzed using the transfer matrix technique. The effect of the plasma layer of the photonic band gap is investigated. The use of the proposed photonic crystal as an optical sensor for detection of small changes within the plasma electron density or the index of refraction of the dielectric layers is investigated."

A planar DC-blocker suitable for differential mode signalling applications is designed and fabricated. The theory of this component is explained in a new form which utilises the wave scattering transfer matrix. The proposed interpretation of the transfer matrix is most suitable for series (cascade) elements like DC-blockers. In addition to the theoretical enhancement, design of a compressed balanced DC-blocker inserted through a shielded broadside coupled stripline (SBCSL) transmission line (TL) is presented. The return loss of better than 10 dB is obtained at 50-ohm differential-mode input ports of the fabricated DC-blocker in the entire frequency range of 5.6–8.4 GHz. The other achievement of this paper is design and fabrication of a wideband substrate-integrated waveguide (SIW)-mediated balun structure for single-ended measurement of a balanced SBCSL component. The fabricated balun exhibits a nearly perfect coaxial-mode to coupled-stripline differential-mode conversion in the full range of 5–9 GHz. The presented balun is successfully utilised to derive the scattering parameters (S-parameters) of the fabricated balanced SBCSL DC-blocker.

The orientation of a transparent spheroidal particle can be obtained from the speckle orientation of a given out-of-focus image. In this paper, we present a method for obtaining the speckle orientation of the out-of-focus image. Based on optical transfer matrix theory, we study the effect the number, phase difference, internal distribution, and dimension of the emitting points and the relative position of the outermost emitting points have on the speckle orientation of out-of-focus images. We acquired out-of-focus images with different speckle orientations and applied both a Fourier transform and autocorrelation to process the simulative and experimental out-of-focus images. We found that the orientation of the Fourier transform of an out-of-focus image is perpendicular to the speckle orientation of the image. Further, the orientation of the autocorrelation of an out-of-focus image is parallel to the speckle orientation of the image. We therefore propose a method for obtaining the speckle orientation of an out-of-focus image using either a Fourier transform or autocorrelation. The method can be used to acquire the orientation of a transparent spheroidal particle.

This paper presents the development of a three-dimensional (3-D) displacement sensor based on one fiber Bragg grating (FBG). In order to obtain higher sensitivity and dynamic range, the FBG is inscribed in low-loss, multimode, cyclic transparent amorphous fluoropolymers using the direct-write, plane-by-plane femtosecond laser inscription method. The proposed sensor is based on the influence of each displacement condition, namely, axial strain, torsion, and bending on the FBG reflection spectrum. Such influence is analyzed with respect to the FBG wavelength shift, reflectivity, and full width half maximum. The operation principle and theoretical background of the proposed approach is numerically analyzed by means of finite element analysis for the strain along the grating length and coupled-mode theory with a modified transfer matrix formulation for the FBG spectrum. The sensor is experimentally characterized and validated in which the results show good agreement between the applied axial strain, bending, and torsion with relative errors below 5.5%. Thus, the proposed sensor is an interesting alternative for measuring displacements in 3-D applications, such as movement analysis and the instrumentation of novel soft robots.

We proposed a numerical method, which is based on the RCWA method combined with T matrix. It is applied as an effective method to design controllable-reflection metallic microstructures from wide incidence angles. The specific structures were fabricated by laser processing, and were analyzed and compared with simulation. Their optical characters showed low-reflection features and was verified in experiments.

In order to obtain an integrated structure achieving controllable circular polarization and laser output at 1310 nm, the gain and loss microcavities, magnetic microcavity, and metal layers are used to form a compound structure system, and the 4 × 4 transfer matrix is used to study transmission characteristics of the structure. The strong Faraday rotation effect and gain transmission modes are found through external pump energy, which leads to a circular polarization laser output. The output of circular polarization laser can be controlled by the modulation of external magnetic field. The structure can be functioned as a magnetic switch of circular polarization lasing.

In this letter, we deduce the approximate analytical formula for the finite Airy beam propagating in the misaligned slab system with a rectangular aperture by using the generalized Huygens-Fresnel integral equation, the light transfer matrix and expanding the hard-edged rectangular function into a finite sum of complex Gaussian function. The particular cases of this beam propagating in the apertured aligned slab system, unapertured misaligned slab system and unapertured aligned one are further illustrated through numerical examples as well. The effects of aperture size and misaligned factors on beam evolution in these slab structures are developed, which can provide a fast and effective method for investigating other kinds of pseudo non-diffracting laser beams through the rectangularly apertured misaligned slab system because most of the optical devices are slightly misaligned more or less in the practical application. Keywords: Finite Airy beam, Transfer matrix, Generalized Huygens-Fresnel integral equation, Misalignment, Rectangular aperture

The study of the temporal and spatial evolution of wetland landscapes and its driving factors is an important reference for wetland ecological restoration and protection. This article utilized seven periods of land use data in Henan Province from 1980 to 2015 to extract the spatial distribution characteristics of wetlands and analyze the temporal and spatial changes of wetlands in Henan Province. Transfer matrix, landscape metrics, correlation analysis, and redundancy analysis were applied to calculate and analyze the transformation types and area of wetland resources between all consecutive periods, and then the main driving factors of wetland expansion/contraction were explored. First, the total wetland area in Henan Province increased by 28% from 1980 to 2015, and the increased wetland area was mainly constructed wetlands, including paddy field, reservoir and pond, and canal. Natural wetlands such as marsh, lake, and floodplain decreased by 74%. Marsh area declined the most during 1990–1995, and was mainly transformed into floodplain and “Others” because of agricultural reclamation, low precipitation, and low Yellow River runoff. The floodplain area dropped the most from 2005 to 2010, mainly converted to canals and “Others” because of reclamation, exploitation of groundwater, the construction of the South–to–North Water Transfer Project, and recreational land development. Second, the results of correlation analysis and redundancy analysis indicated that economic factors were positively correlated with the area of some constructed wetlands and negatively correlated with the area of some natural wetlands. Socioeconomic development was the main driving factors for changes in wetland types. The proportion of wetland habitat in Henan Province in 2015 was only 0.3%, which is low compared to the Chinese average of 2.7%. The government should pay more attention to the restoration of natural wetlands in Henan Province.

In this paper, an all-optical plasmonic switch based on the metal-insulator-metal (MIM) waveguide configuration is proposed. The structure uses a Kerr-type nonlinear material (Au:SiO2 Composite) and Fano resonance to achieve all-optical switching. It is shown that adding two stubs to a MIM waveguide creates a Fano resonance which can be used for switching applications. A pump signal is used for this purpose. The two dimensional finite difference time domain (FDTD) method is employed to numerically simulate the proposed switch. In order to verify the FDTD simulation results, the basic MIM structure is also analyzed using the scattering matrix theory and a transfer matrix combination. At the wavelength of 1455 nm, the transmission changed from 0.52 to 0.03 by launching an optical pump. Moreover, the proposed all-optical switch has many advantages such as its compact size, lower pump intensity (which is equal to $145\ mW/\mu m^{2}$ ), and a fast switching time.

In this study, glasses were used as substrates and an e-beam was used the method to deposit MgF2 and Nb2O5 single-layer films, and the optical properties, including extinction coefficients (k values) and refractive indices (n values), were measured by using the light wavelength as variable. The equation d = λ/(4n) was used to calculate the thickness (d) of 1/4 wavelength (λ) for each layer of the MgF2-Nb2O5 bilayer films in distributed Bragg reflectors (DBRs) with a designed reflective wavelength at blue light (~450nm). Each MgF2-Nb2O5 bilayer film was called a period, and the glass substrates were used to deposit the films with two, four, and six periods for fabricating the DBRs. The field emission scanning electron microscope equipped with a focused ion beam was used to measure the thickness of each MgF2-Nb2O5 layer in the DBRs with different periods. The measured maximum reflective ratios were compared with Sheppard’s approximate equation, which calculates only the maximum reflective ratio at a specific wavelength. An overall transfer matrix was investigated to calculate the reflective spectra by incorporating the variable n values and thicknesses of the MgF2-Nb2O5 films in each layer. We show that the measured results of the fabricated DBRs matched the results simulated using Sheppard’s approximate equation and the overall transfer matrix.

With the increasing number of electric vehicles in urban power grid, the random characteristics of charging and discharging behavior make the distribution network power flow distribution complex and changeable. At the same time, the electric vehicle has the characteristics of discreteness and randomness in the space-time distribution, which makes the electric vehicle's discharge behavior difficult to describe. This paper proposes a distributed generation equivalent method based on the discharge behavior of electric vehicles. Firstly, the vehicle transfer matrix based on Markov chain is used to simulate the travel behavior of electric vehicles; Secondly, combined with the travel behavior and charging and discharging rules of electric vehicles, the charge and discharge state of electric vehicles is studied, and the discharge behavior of electric vehicles is equivalent to a distributed generation with a change in output; Finally, the validity of the proposed equivalent method is verified by an example analysis, and the influence of electric vehicle discharge behavior on distribution network power flow distribution is discussed.

In this paper, a new method for measuring the refractive index of seawater based on the V-shaped cavity is proposed. MATLAB software is used to simulate the V-shaped cavity based on the optical thin film transfer matrix. By changing the refractive index of the liquid in the glassware placed in the cavity, the filtering characteristics of the V-shaped cavity are changed. The change of refractive index can be demodulated by monitoring the shift of transmission wavelength of V-shaped cavity. In this paper, the refractive index detection sensitivity is 217nm/RIU, and the refractive index high resolution measurement can be up to 10-8 RIU. In this paper, the empirical formula of the change of refractive index with the change of transmission wavelength shift is given. When the change of refractive index is 10-7 RIU, the accuracy of demodulation using the empirical formula is 0.03%. The outcomes indicate that the new method proposed in this paper has a strong application prospect in the field of high resolution ocean optical sensing.