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This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. This paper presents new advances in the arbitrary Lagrangian–Eulerian modal method (ALEM) recently developed for the systematic simulation of the dynamics of general reeving systems. These advances are related to a more convenient model of the sheaves dynamics and the use of axial deformation modes to account for non-constant axial forces within the finite elements. Regarding the sheaves dynamics, the original formulation uses kinematic constraints to account for the torque transmission at the sheaves by neglecting the rotary inertia. One of the advances described in this paper is the use of the rotation angles of the sheaves as generalized coordinates together with the rope-to-sheave no-slip assumption as linear constraint equations. This modeling option guarantees the exact torque balance at the sheave without including any nonlinear kinematic constraint. Numerical results show the influence in the system dynamics of the sheave rotary inertia. Regarding the axial forces within the finite elements, the original formulation uses a combination of absolute position coordinates and transverse local modal coordinates to account for the rope absolute position and deformation shape. The axial force, which only depends on the absolute position coordinates, is constant along the element because linear shape functions are assumed to describe the axial displacements. For reeving systems with very long rope spans, as the elevators of high buildings, the constant axial force is inaccurate because the weight of the ropes becomes important and the axial force varies approximately linearly within the rope free span. To account for space-varying axial forces, this paper also introduces modal coordinates in the axial direction. Numerical results show that a set of three modal coordinates in the axial direction is enough to simulate linearly varying axial forces. Unión Europea - Horizon 2020 Marie Skłodowska-Curie No 860124, THREAD.

At the ultrahigh frequencies common to portable radios, tunnels such as mine entries are often modeled by hollow dielectric waveguides. The roughness condition of the tunnel walls has an influence on radio propagation, and therefore should be taken into account when an accurate power prediction is needed. This paper investigates how wall roughness affects radio propagation in tunnels, and presents a unified ray tracing and modal method for modeling radio propagation in tunnels with rough walls. First, general analytical formulas for modeling the influence of the wall roughness are derived, based on the modal method and the ray tracing method, respectively. Second, the equivalence of the ray tracing and modal methods in the presence of wall roughnesses is mathematically proved, by showing that the ray tracing-based analytical formula can converge to the modal-based formula through the Poisson summation formula. The derivation and findings are verified by simulation results based on ray tracing and modal methods.

A new method whose basis function expressed by that of a interface is proposed to analysis the grating diffraction, which can solve the physical defects of the Rayleigh method and avoid the coordinate transformation of the Coordinate transformation method. This method is named as the Huygens modal method. At the same time, the Huygens modal method can simplify the eigen matrix equation and the traditional Fourier modal method can be summarized as a special case of the Huygens modal method. In the end, a general form of the H-method of a grating diffraction is derived.

We propose the generalization of the Fourier modal method aimed at calculating localized eigenmodes of integrated optical resonators. The method is based on constructing the analytic continuation of the structure's scattering matrix and calculating its poles. The method allows one to calculate the complex frequency of the localized mode and the corresponding field distribution. We use the proposed method to calculate the eigenmodes of rectangular dielectric block located on metal surface. We show that excitation of these modes by surface plasmon-polariton (SPP) results in resonant features in the SPP transmission spectrum. The proposed method can be used to design and investigate optical properties of integrated and plasmonic optical devices., 13 pages, 4 figures

Deep-etched rectangular fused-silica transmission gratings used as orthogonal polarizing beam combiners at the wavelength of 532 nm are designed based on the modal method. The fabrication tolerances and the properties of the orthogonal polarizing beam combiners are analyzed by rigorous coupled-wave analysis. It is shown that these gratings have large fabrication tolerances and good properties when the diffraction efficiencies are greater than 90%. The optimal grating is highly efficient (>95%) over broad incidence condition and also has large fabrication tolerances.

A two-channel system of stabilization of pressure in a fire chamber of a boiler unit is considered. Regulation of pressure is carried out by means of an automated electric drive by changing the speeds of rotation of the smoke exhauster and fan. It is suggested that smoke exhausters (the first channel of regulation) and fans (the second channel of regulation) be controlled. This increases the stability of depression in transitional regimes. It also reduces the time of transients and leads to a more efficient operating regime of the boiler unit. Regulators for the first and second control paths are synthesized. Synthesis is carried out by a modified modal method. The regulator of the first channel contains two components: a regulator of statics and a regulator of dynamics. It works in two regimes: established and transitional. The regulator of dynamics contains the regulator of the second channel only, and it works only in transitional regimes. This strategy allows not interfering with the main process of burning in the fire chamber of a boiler unit with quasi-established regimes. It also reduces the time of transients, when the process burning is not optimal. Regulation systems operating on one and two channels of influences are compared.

A modal method for designing the one-dimensional (1-D) dielectric multilevel antireflection gratings (ARGs) used for TE polarized waves is proposed based on the effective refractive indices concept of the modal method (MM). In this method, the effective refractive index (ERI) for each level is determined by the effective mode index of the modal method. The refractive indices under and above the grating region are equivalent to their effective refractive indices that is determined by the 0th order propagating wave vector of the Fourier expansion of the electric fields under and above the grating region, which are different from the conventional effective medium theory (EMT), and the relationship between the ERI in MM and that in EMT are also revealed. As an example, we designed and analyzed the fused-silica multilevel ARGs by using the MM and the commonly used second-order effective medium theory (SEMT). The designed results are numerically verified by using the rigorous coupled-wave analysis method (RCWA) and the thin-film theory.

A rigorous and efficient grating-analysis method with a piece-wise function is presented and the total reflection phase grating is studied. Some results show that the rigorous theory method is several times faster and more accurate than the previous work. And the condition and physical mechanism of total reflection of phase gratings are also discussed too.

A two-port beam splitter is presented to obtain the 50/50 output based on the two-layer grating. The previously reported beam splitter grating can work only at the special prescribed incident angle. The deviation of incident angle introduces the effect on the splitting ratio uniformity. The proposed two-layer beam splitter grating is aimed to obtain the broad incident angular bandwidth. To optimize the beam splitter, a simplified modal method and rigorous coupled-wave analysis are employed to analyze the propagation process and to calculate the efficiency. Based on the optimized grating parameters, the 50/50 output can be obtained with the polarization-independent property. Most importantly, good splitting ratio uniformity can be exhibited within the broad angular bandwidth for both TE and TM polarizations. The polarization-independent property and the broad incident angular bandwidth are significant for practical applications.

An efficient and accurate technique based on a modal method of moments (MoM) is introduced to evaluate shielding effectiveness (SE) of a rectangular enclosure with apertures at opposing walls. The perforated walls are obliquely illuminated by arbitrary polarized incident plane waves. This technique takes the effect of the perforated wall thickness into account as well. The method is validated by comparing the results with measurements and fully numerical methods for an enclosure with various apertures illuminated by an arbitrary incident plane wave. It is shown that wall thickness affects SE for different polarized incident waves.

Antireflective sub-wavelength structures (SWSs) combined a Ge1−xCx coating on Zinc sulfide (ZnS) can enhance the long-wave infrared transmission and durability of ZnS, which have the potent for practical applications. We have investigated the antireflective characteristics of Ge1−xCx sub-wavelength periodic hole structures on ZnS through the Fourier modal method (FMM) for application with normally incident, randomly polarized, 10.6 μm wavelength. Then according to the results, we have successfully fabricated the sub-wavelength periodic square hole structures with Ge0.05C0.95 films on one side of ZnS. A substantial transmittance improvement for bare ZnS in the 8–12 μm spectral region was obtained.

The optical design of a beam splitter that has a 50/50 splitting ratio regardless of the polarization is presented. The non-polarizing beam splitter (NPBS) is based on the fused-silica rectangular transmission gratings with high intensity tolerance. The modal method has been used to estimate the effective index of the modes excited in the grating region for TE and TM polarizations. If a phase difference equals an odd multiples of π/2 for the first two modes (i.e. modes 0 and 1), the incident light will be diffracted into the 0 and −1 orders with about 50% and 50% diffraction efficiency for TM and TE polarizations, respectively.

In this paper, we propose a broad band 1 × 3 beam splitter operating in the telecommunication wavelength band under normal incidence, this device consisting of a double-groove fused silica grating layer is designed with using the inverse mathematical method and rigorous vector diffraction theory. It is shown from our calculations that the device presents excellent beam splitter ability for TE polarization light with the average diffraction efficiencies is more than 95% over ∼100 nm wavelength range, moreover, the uniformity of our beam splitter is better than 2% in the whole wavelength band. Furthermore, the physical understanding of the diffraction behaviors taking place inside the beam splitter gratings can be explained by the modal method.

We propose a method for calculating the monostatic radar cross section of a two-dimensional complex-shaped cavity, which contains a plane-layered medium in the form of a loaded metal diaphragm placed on a dielectric layer. The method is based on the combined boundary-integral/modal method and the variational Galerkin method with the use of dyadic Green’s functions. The results of calculating the angular dependences of the radar cross section for various parameters of the plane-layered medium are presented. Restrictions of the applicability and potential for further development of the method are indicated.

The eigenvalue problem discussed in Noponen and Turunen [Eigenmode method for electromagnetic synthesis of diffractive elements with three-dimensional profiles, J. Opt. Soc. Am. A 11 (1994) 2494–2502] for crossed gratings is analyzed in a different way using the three components of the electric field instead of the components E x,y , H x,y . As a result, half as many eigenvectors are needed.

MODALMETHODANALYSISOFMULTILAYEREDCOATEDCIRCULARWAVEGUIDEUSINGAMODIFIEDCHARACTERISTICEQUATIONF.-G.Hu,C.-F.Wang,Y.Xu,andY.-B.GanTemasekLaboratoriesNationalUniversityofSingapore10KentRidgeCrescent,Singapore119260Abstract—In this paper, the modal method is applied to analyzecoated circular waveguide terminated by a perfect electric conductor(PEC) plate. The key to this method is the accurate calculationof the propagation constants of modes in coated circular waveguide.To overcome numerical difficulties, such as overflow, encountered insolvingcharacteristicequation,thecharacteristicequationismodifiedusing Hankel function of the second kind instead of Bessel functionof the first kind in the coated layers. The modified characteristicequationcanbeaccuratelysolvedtoobtainthepropagationconstantseven for very large circular waveguide with highly lossy coatings.To verify the modified characteristic equation, the attenuationand scattering property of circular waveguide structure have beensimulated. Simulationresultsagreewellwiththereferenceresults.1 Introduction2 CharacteristicEquationanditsModification3 ScatteringAnalysisofCircularCoatedWaveguide4 NumericalResults5 ConclusionsReferences

The continuously increasing complexity of opto-electronic devices and the rising demands of simulation accuracy lead to the need of solving very large systems of linear equations making iterative methods promising and attractive from the computational point of view with respect to direct methods. In particular, iterative approach potentially enables the reduction of required computational time to solve Maxwell’ s equations by Eigenmode Expansion algorithms. Regardless of the particular eigenmodes finding method used, the expansion coefficients are computed as a rule by scattering matrix (S-matrix) approach or similar techniques requiring order of M 3 operations. In this work we consider alternatives to the S-matrix technique which are based on pure iterative or mixed direct–iterative approaches. The possibility to diminish the impact of M 3 -order calculations to overall time and in some cases even to reduce the number of arithmetic operations to M 2 by applying iterative techniques are discussed. Numerical results are illustrated to discuss validity and potentiality of the proposed approaches. Keywords: iterative approach, scattering matrix, modal method, opto-electronic simulations, Maxwell’s equations solver

We present a modal method for the analysis of integrated optics structures. The presented technique, called Radiation Spectrum Method (RSM), is based on the analysis of the radiation mode spectrum generated at each waveguide discontinuity in the structure. The full wave capabilities of the RSM are demonstrated by its application for several non-paraxial tests as tilted waveguide and bent waveguide tests. We also demonstrate the method capability to correctly analyse components using abrupt index changes.

Wood's anomalies of resonance type are investigated by means of a rigorous modal method. Single modal coefficients are used to characterize strength and position of the resonances. With the concept of effective grating periods a formula for the position of resonances with respect to wavelength and angle of incidence is achieved. The influence of varying grating parameters is discussed.

In a recent paper [J. Opt. Soc. Am. A 29, 2038 (2012)], we proposed a generalized high spatial resolution zonal wavefront reconstruction method for lateral shearing interferometry. The test wavefront can be reconstructed with high spatial resolution by using linear interpolation on a subgrid for initial values estimation. In the current paper, we utilize the difference between the Zernike polynomial fitting method and linear interpolation in determining the subgrid initial values. The validity of the proposed method is investigated through comparison with the previous high spatial resolution zonal method. Simulation results show that the proposed method is more accurate and more stable to shear ratios compared with the previous method. A comprehensive comparison of the properties of the proposed method, the previous high spatial resolution zonal method, and the modal method is performed.

Three terahertz (THz) GaAs/AlGaAs quantum-well photodetectors with different 1-D metal gratings are fabricated for front-incident detection of THz waves. Photocurrent spectra are acquired and compared with 45 ° incident facet samples (without grating), and peak responsivities are determined with a calibrated blackbody radiation source. The results show that these gratings can couple THz waves into detectors effectively, resulting in good detector responsivities. The modal method is employed to simulate the light coupling efficiency and the optimization conditions of the gratings. © 2011 IEEE.

A modal method is used for the determination of the near field weighting functions related to the power transmitted from a rectangular waveguide aperture towards a lossy material and, by reciprocit...

International audience; We present two mode solvers applied to a very thin long-range plasmonic waveguide. We compare the guided mode complex effective index obtained either applying a Fourier modal method or calculating density of guided modes using the Green's dyad technique. We achieve good agreement for both effective indices and mode profiles. We also observe a different behaviour compared to long-range surface plasmon supported by thicker films.

Maxwell equations are solved in a layer comprising a finite number of homogeneous isotropic dielectric regions ended by anisotropic perfectly matched layers (PMLs). The boundary-value problem is solved and the dispersion relation inside the PML is derived. The general expression of the eigenvalues equation for an arbitrary number of regions in each layer is obtained, and both polarization modes are considered. The modal functions of a single layer ended by PMLs are found, and their orthogonality relation is derived. The present method is useful to simulate scattering problems from dielectric objects as well as propagation in planar slab waveguides. Its potential to deal with more complex problems such as the scattering from an object with arbitrary cross section in open space using the multilayer modal method is briefly discussed., 17 pages, 4 figures

[1] The second part of this two-piece paper applies the method developed in part 1 to show some interesting features for the practical analysis and design of leaky-wave antennas. Novel analytical formulas based on the propagation and radiation discrete Parallel-Plate Waveguide (PPW) spectrum coefficients described in the first part are presented, in order to calculate some interesting propagation and radiation aspects of leaky-wave modes. These formulas will be used in the design of a slot-line millimeter-wave band leaky-wave antenna, measuring parameters such as reflection and radiation losses, polarization purity, and coupling with undesired channel-guide leaky modes. Comparisons with previous works for slot-line leaky-wave modes are presented, together with novel and interesting results, showing the usefulness of the proposed approach for the design of practical leaky-wave laterally shielded planar printed antennas.

The antireflective characteristics of Si nanocone (NC) arrays were estimated using a theory devised for an inhomogeneous antireflection layer, and further verified by the Fourier modal method (FMM). Considering a better impedance matching from air to Si, a minimum depth of 400 nm is essentially required. Although Si NC arrays have usually been suggested to be at a base diameter of ∼300 nm for infinitely thick Si wafers, as wafers become thinner than 50 μm, the optimal base diameter of the NCs is suggested to be ∼500 nm so as to excite more resonant modes. Our simulation work indicates that geometrical parameters such as the top diameter and filling ratio of the NCs are much more sensitive in terms of optimizing the optical performance on ultrathin (∼5 μm) wafers, suggesting the need for strict control of the surface morphology in the nanostructure fabrication process.

Using a full-vector modal method, the authors have identified a region of nearly zero flattened chromatic dispersion in a specially designed photonic crystal fibre. The approach permits an accurate control of the dispersion features of these fibres in terms of their structural parameters.

This paper researches on the control laws of synchronised switch damping on inductor technique (SSDI). The SSDI shunt damping is adaptive to the excitation frequency, and no precise tuning of the shunt parameters is necessary. With this property, the SSDI technique is very adept in handling broadband multimodal and random excitation. The triggering of the switch is decided by a decision algorithm, normally called switching control law, which plays an important role in damping performance. In the original control law, the switch is triggered on each extremum deformation of the shunted piezoelement. It is shown that this switching law maximises the dissipated energy only for monomodal excitation, therefore various control laws were proposed for improving the damping performance in the case of complex multimodal excitation. In this paper, all of the proposed control laws are reviewed and classified. Besides, an enhanced switching law base on modal method is presented and highlighted. Measurements are conducted on a clamped-free beam test rig to validate the theoretical results.

The problem of scattering of Rayleigh waves at a rectangular groove is addressed. Grooves are known to excite bulk waves upon scattering and, hence, are potential sources (albeit secondary) in bulk-acoustic-wave (BAW) devices. The groove is formulated as a volume perturbation of the geometry. A modal method is used, and the results of Rayleigh wave reflection as well as bulk wave radiation are obtained and compared with the results available in the literature. The method is compared with the boundary perturbation formulation. The equivalence of the boundary perturbation method and the volume perturbation method is shown. >

The spot size of the focus in a very lossy medium is discussed with relevance to creation of local temperature increase in muscle tissue by means of electromagnetic waves. A slot in a cylinder is used as a source for heating a lossy cylinder and the internal fields are analyzed by a modal method and a fast Fourier transform (FFT) method.