Finite Waveguide Research Articles

On the sound radiation of a rolling tyre

The sound radiation from rolling tyres is still not very well understood. Although details such as horn effect or directivity during rolling have been investigated, it is not clear which vibrational modes of the tyre structure are responsible for the radiated sound power. In this work an advanced tyre model based on Wave Guide Finite Elements is used in connection with a contact model validated in previous work. With these tools the tyre vibrations during rolling on an ISO surface are simulated. Starting from the calculated contact forces in time the amplitudes of the modes excited during rolling are determined as function of frequency. A boundary element model also validated in previous work is applied to predict the sound pressure level on a reference surface around a tyre placed on rigid ground as function of the modal composition of the tyre vibrations. Taking into account different modes when calculating the vibrational field as input into the boundary element calculations, it is possible to identify individual modes or groups of modes of special relevance for the radiated sound power. The results show that mainly low-order modes with relative low amplitudes but high radiation efficiency in the frequency range around 1kHz are responsible for the radiated sound power at these frequencies, while those modes which are most strongly excited in that frequency range during rolling are irrelevant for the radiated sound power. This fact is very essential when focusing on the design of quieter tyres.

Total longitudinal momentum in a dispersive optical waveguide

Using the Lorentz force law, we derived simpler expressions for the total longitudinal (conserved) momentum and the mechanical momentums associated with an optical pulse propagating along a dispersive optical waveguide. These expressions can be applied to an arbitrary non-absorptive optical waveguide having continuous translational symmetry. Our simulation using finite difference time domain (FDTD) method verified that the total momentum formula is valid in a two-dimensional infinite waveguide. We studied the conservation of the total momentum and the transfer of the momentum to the waveguide for the case when an optical pulse travels from a finite waveguide to vacuum. We found that neither the Abraham nor the Minkowski momentum expression for an electromagnetic wave in a waveguide represents the complete total (conserved) momentum. Only the total momentum as we derived for a mode propagating in a dispersive optical waveguides is the 'true' conserved momentum. This total momentum can be expressed as PTot = -U Die/(vg) + neff (U/c). It has three contributions: (1) the Abraham momentum; (2) the momentum from the Abraham force, which equals to the difference between the Abraham momentum and the Minkowski momentum; and (3) the momentum from the dipole force which can be expressed as -UDie/vg. The last two contributions constitute the mechanical momentum. Compared with FDTD-Lorentz-force method, the presently derived total momentum formula provides a better method in terms of analyzing the permanent transfer of optical momentum to a waveguide.

Low frequency acoustic sensor or array calibration waveguides of finite length.

Calibration acoustic transducers at very low frequencies in confined and well understood environment require special equipment. The Underwater Sound Reference Division has three cylindrical tubes for low frequency calibration. This paper addresses a rectangular cross section of finite length waveguide as calibration environment. The acoustic fields in the new waveguide for standing and traveling waves are both analyzed. The mathematical model and the numerical simulation results will also be presented. [This work is supported by the U.S. Navy.]

Finite photonic crystal waveguide with an embedded cavity: optical conductance “dips” and vortices

Light transmission through a finite photonic crystal waveguide with an embedded cavity is analyzed in terms of the optical conductance (OC). Under appropriate conditions, the transmission is inhibited for any angle of incidence. The resonance condition manifests itself as a “dip” in the OC. Just at the resonance, the power flow presents strong vortices inside the cavity.

Experimental study on water-wave trapped modes

We present an experimental study on the trapped modes occurring around a vertical surface-piercing circular cylinder of radius a placed symmetrically between the parallel walls of a long but finite water waveguide of width 2d. A wavemaker placed near the entrance of the waveguide is used to force an asymmetric perturbation into the guide, and the free-surface deformation field is measured using a global single-shot optical profilometric technique. In this configuration, several values of the aspect ratio a/d were explored for a range of driving frequencies below the waveguide's cutoff. Decomposition of the obtained fields in harmonics of the driving frequency allowed for the isolation of the linear contribution, which was subsequently separated according to the symmetries of the problem. For each of the aspect ratios considered, the spatial structure of the trapped mode was obtained and compared to the theoretical predictions given by a multipole expansion method. The waveguide–obstacle system was further characterized in terms of reflection and transmission coefficients, which led to the construction of resonance curves showing the presence of one or two trapped modes (depending on the value of a/d), a result that is consistent with the theoretical predictions available in the literature. The frequency dependency of the trapped modes with the geometrical parameter a/d was determined from these curves and successfully compared to the theoretical predictions available within the frame of linear wave theory.

Accurate synthesis of linear non-resonant narrow wall inclined slotted waveguide arrays

An efficient and highly accurate network model for analysing and synthesising large but finite slotted waveguides (SWGs) is presented. The network model is tailored for arrays of linear end-fed narrow wall inclined slots. The network model accurately predicts, as function of frequency, the key electrical antenna parameters such as antenna-radiation pattern (beamwidth, inner and spurious sidelobes down to the −40 dB level, main beam squint), waveguide loss, power dissipated in the load and return loss. The network model explicitly takes mechanical tolerances into account. The model is based upon S-parameter measurements of a number of test-SWGs. The network model has been proven to be scalable from X-band to S-band waveguides and can be extrapolated to slot parameters far beyond the range of the slots of the test-SWGs. The comparison between predicted and measured results has shown that the network model is highly accurate, providing a significant improvement over full wave commercial tools in terms of prediction of the antenna parameters of interest as well as in computational speed.

Mapping local optical densities of states in silicon photonic structures with nanoscale electron spectroscopy

Relativistic electrons in a structured medium generate radiative losses such as Cherenkov and transition radiation that act as a virtual light source, coupling to the photonic densities of states. The effect is most pronounced when the imaginary part of the dielectric function is zero, a regime where in a nonretarded treatment no loss or coupling can occur. Maps of the resultant energy losses as a sub-5 nm electron probe scans across finite waveguide structures reveal spatial distributions of optical modes in a spectral domain ranging from near infrared to far ultraviolet.

EBG-Based Circular Waveguide Rod Arrays With Improved Scanning Characteristics

A finite linear circular waveguide rod array using electromagnetic band-gap (EBG) structure has been studied. Active element patterns and real radiation patterns of the finite array are investigated, instead of the reflection coefficients generally adopted in analyzing infinite phased arrays, to evaluate the effect of EBG applications. From the given results, elimination of scan blindness using EBG structure is well verified.

Image reconstruction in segmented femtosecond laser-written waveguide arrays

We present the first experimental realization of image reconstruction in finite femtosecond laser-written waveguide arrays with segmentation. The results show that arbitrary field distributions can be imaged in one-dimensional as well as in two-dimensional geometries.

A method of variation of boundaries for waveguide grating couplers

We describe a method for calculating the solution of the electromagnetic field in a non-rectilinear open waveguide by using a series expansion, starting from the field of a rectilinear waveguide. Our approach is based on a method of variation of boundaries. We prove that the obtained series expansion converges and we provide a radiation condition at infinity in such a way that the problem has a unique solution. Our approach can model several kinds of optical devices which are used in optical integrated circuits. Numerical examples will be shown for the case of finite aperiodic waveguide grating couplers.

Coordinate stretching for finite difference optical waveguide mode solvers

Numerical methods are necessary to calculate propagating modes in optical waveguides. The finite difference method is widely used because it is applicable to waveguides with arbitrary refractive index profiles and it is easy to implement. To improve the efficiency and to reduce the size of the resulting large sparse matrix, the finite difference method is often used with a variable grid size strategy. This is related to the technique of coordinate stretching. In this paper, we develop a technique for optimizing the coordinate stretching function based on discrete reflection coefficients. We demonstrate our method using a scalar model which is valid for weakly-guided optical waveguides.

PLANE WAVE DIFFRACTION BY A FINITE PARALLEL-PLATE WAVEGUIDE WITH FOUR-LAYER MATERIAL LOADING: PART I - THE CASE OF E POLARIZATION

The diffraction by a finite parallel-plate waveguide with four-layer material loading is rigorously analyzed by means of the Wiener-Hopf technique for the H-polarized plane wave incidence. Taking the Fourier transform for the unknown scattered field as well as the Helmholtz equation and applying boundary conditions in the transform domain, the problem is formulated in terms of the simultaneous Wiener-Hopf equations. The Wiener-Hopf equations are solved via the factorization and decomposition procedure together with the use of rigorous approximation procedures leading to an efficient approximation solution. The scattered field in the real space is evaluated explicitly by taking the inverse Fourier transform. Illustrative numerical examples on the radar cross section (RCS) are presented and the far field scattering characteristics of the waveguide are discussed.

Optimal design for wide-band single-mode two-dimensional photonic crystal waveguides: role of waveguide width

The propagation of counterpropagating modes in finite line-defect two-dimensional photonic crystal waveguides consisting of square lattice dielectric cylinders has been investigated by a numerical study based on multiple scattering theory. In the presence of forward propagating external light at one given frequency, two counterpropagating guided modes with the same spatial frequency can be simultaneously excited. Determined by the Fourier transform of field distribution inside waveguides, the wave vectors and lateral profiles of modes are demonstrated to coincide with theoretical results from a simple model, which only has the advantage of an energy-confining mechanism in waveguides. In addition, the spectral amplitude ratio of the backward mode to the forward mode is found to decay with a larger waveguide width and higher frequency. With an appropriate choice of waveguide width, both backward mode and higher transversal modes can be inhibited effectively, giving rise to highly efficient single-mode transmission in a wide and flat spectrum.

Analysis of Piezoelectric Ultrasonic Transducers Attached to Waveguides Using Waveguide Finite Elements

A finite-element modeling procedure for computing the frequency response of piezoelectric transducers attached to infinite constant cross-section waveguides, as encountered in guided wave ultrasonic inspection, is presented. Two-dimensional waveguide finite elements are used to model the waveguide. Conventional three-dimensional finite elements are used to model the piezoelectric transducer. The harmonic forced response of the waveguide is used to obtain a dynamic stiffness matrix (complex and frequency dependent), which represents the waveguide in the transducer model. The electrical and mechanical frequency response of the transducer, attached to the waveguide, can then be computed. The forces applied to the waveguide are calculated and are used to determine the amplitude of each mode excited in the waveguide. The method is highly efficient compared to time integration of a conventional finite-element model of a length of waveguide. In addition, the method provides information about each mode that is excited in the waveguide. The method is demonstrated by modeling a sandwich piezoelectric transducer exciting a waveguide of rectangular cross section, although it could be applied to more complex situations. It is expected that the modeling method will be useful during the optimization of piezoelectric transducers for exciting specific wave propagation modes in waveguides.

Self-Pulsed Electron Transmission through a Finite Waveguide in a Transversal Magnetic Field

The distribution of scattering delay times is analyzed for classical electrons which are transmitted through a finite waveguide. For non-zero magnetic field the distribution shows a regular pattern of maxima (logarithmic singularities). Although their location follows from a simple commensurability condition, there is no straightforward geometric explanation of this self-pulsing effect. Rather it can be understood as a time-dependent analog of transverse magnetic focusing, in terms of the stationary points of the delay time. We also discuss the possibility of singularities in the delay-time distribution for generic 2D scattering systems.

The method of waveform images for finite waveguides with resistive terminations subject to arbitrary initial conditions

Reflection at normal incidence of a plane wave can be described by imaging the incident wave profile on the opposite side of the boundary. This concept has been introduced in a few texts, but only for nondissipative conditions. In this paper the procedure to describe a purely resistive boundary is generalized, and then the concept is extended to describe the transient response of a one-dimensional, finite length waveguide. The field generated by arbitrary initial conditions is characterized by an infinite number of images, which leads to a representation of the acoustic field as oppositely propagating waves in an unbounded waveguide. Both graphical and mathematical descriptions of these waves are derived, with the former shown to provide significant insights. Mathematical analysis of the image construction leads to identification of several fundamental acoustic phenomena, including acoustic modes and reverberation time. From an instructional viewpoint the ability to explore fundamental acoustic phenomena without recourse to solving differential equations makes the waveform image concept especially useful as an introductory tool.

Modeling of tension-modulated strings using finite difference and digital waveguide techniques

Tension modulation is a nonlinear phenomenon where large-amplitude string vibrations cause the tension of the string to vary. This results in an initial pitch glide and energy coupling between modes, causing for example the generation of missing harmonics. The presentation discusses two methods for numerical simulation of the tension modulation nonlinearity from the sound synthesis point of view. The tension modulation is assumed to propagate instantaneously along the string. In the digital waveguide approach, spatially distributed fractional delay filters are used in modulating the string length during run time. Energy-preserving techniques can be used in implementing the fractional delays. In the finite difference approach, time-domain interpolation is used to artificially modulate the wave propagation velocity. The generation of missing harmonics is implemented in the finite difference model by creating an additional excitation point at the string termination. In the waveguide model, the same effect can be obtained by using suitable approximations in the string elongation calculation. Synthesis results for both techniques are presented. Also, a brief comparison of the models with a discussion on stability issues is provided. [This research has been funded by the Academy of Finland (Project No. 104934), S3TK graduate school, and Tekniikan edistamissaatio.]

A higher-order finite waveguide model for spectral analysis of composite structures

A waveguide model for spectral analysis of finite composite structures based on higher-order shear deformation theory (HSDT) is reported in this paper. The advantages of using the proposed model are attributed to the following: (1) the displacement field interpolation is carried out using the basis vector from the null space of the characteristic system, and this numerical step is a bi-product of the usual wave dispersion analysis in frequency domain, (2) the standard finite element discretization procedure involving nodal variables is employed, (3) both the frequency response and the time domain response can be obtained with the help of fast Fourier transformation (FFT) algorithm and (4) no constraint in terms of low or high frequencies is imposed, except that for a prescribed frequency band of excitation the assumed field needs to be consistent with the geometric scales in the composite material system. A novel method of embedding functionally graded array of dissimilar material phases, periodic or aperiodic, in the finite element dynamic stiffness matrix is presented, where the homogenized properties of the material system in the smallest wavelength scale can be used. Numerical simulations under impact type loading are carried out to study the effect of frequency band of excitation on the velocity response of homogeneous and inhomogeneous beam type structures.

Leaky and bound modes of surface plasmon waveguides

While theoretical studies of finite width plasmonic waveguides have focused on the bound modal solutions of metallic structures in homogeneous or near-homogeneous dielectric matrices, experimental studies have mainly probed the leaky surface plasmon modes along the air-exposed surfaces of metallic stripes on glass substrates. Combining a full-vectorial, magnetic field finite-difference method with complex coordinate stretching perfectly matched layer boundary conditions, we have solved for both the leaky and bound modes of metallic slab and stripe waveguides. Solutions for the leaky modes excited via attenuated total reflection in the Kretschmann configuration provide added insight into the results of recent near and far-field experimental studies. For these cases, an analytical approximation for the number of allowed modes as a function of waveguide width is derived based upon the guidance condition of dielectric waveguide theory. Then, consistent with a ray optics interpretation for surface plasmon-polariton propagation, a direct comparison is made between our simulations and published results with regard to field profiles and propagation lengths.

Equivalent constitutive model-based design of wave-absorbing material system and controller

A design methodology for wave-absorbing active material system is reported. The design enforces equivalence between an assumed material model having wave-absorbing behavior and a set of target feedback controllers for an array of microelectro-mechanical transducers which are integral part of the active material system. The proposed methodology is applicable to problems involving the control of acoustic waves in passive–active material system with complex constitutive behavior at different length-scales. A stress relaxation type one-dimensional constitutive model involving viscous damping mechanism is considered, which shows asymmetric wave dispersion characteristics about the half-line. The acoustic power flow and asymptotic stability of such material system are studied. A single sensor non-collocated linear feedback control system in a one-dimensional finite waveguide, which is a representative volume element in an active material system, is considered. Equivalence between the exact dynamic equilibrium of these two systems is imposed. It results in the solution space of the design variables, namely the equivalent damping coefficient, the wavelength(s) to be controlled and the location of the sensor. The characteristics of the controller transfer functions and their pole-placement problem are studied.