Ideal Waveguide Research Articles

Elastodynamic shape derivative: focus on the sampling of a circular distribution

The detection and quantification of defects plays a crucial role in several industries. Assessing the severity enables to schedule maintenance appropriately, optimizing costs and reducing risks. Guided elastic waves are particularly suitable for Structural Health Monitoring applications on thin structures thanks to their long range and high sensitivity. Guided wave tomography, based on an acoustic propagation hypothesis, has been studied over the last decade to quantitatively image defects in waveguides. The acoustic approximation of this family of methods allows fast computation and good estimation of defects for simple geometries such as plates or pipes. However, this hypothesis induces that a single guided mode is considered, without mode conversion, which limits its use to defects larger than two wavelengths in structures close to ideal waveguides. Hence the need of new imaging algorithms for smaller defects in less ideal structures such as pipes with welded supports. We present here an adaptation of the shape derivative method to ultrasounds in order to reconstruct surface defect on structures with complex geometries. The physical model used is the full elastodynamic problem. It allows taking into account all physical phenomena occuring during wave propagation. Iterative methods such as shape derivative are well known to give precise results but at a high computational cost as the method needs to solve the full elastodynamic problem at each iteration, and a sensitivity to local minima, which may prevent convergence toward the true defect. To suppress these two drawbacks, a spectral finite element method is used to reduce the computation and memory costs. The result of acoustic guided wave tomography is also used as a first guess to reduce the number of iterations and the sensitivity to local minima. After explaining the principle of the shape derivative, validations on simulated and experimental data will be presented in this talk.

Hollow-core terahertz Bragg waveguide based on a helical support structure.

A helical structural support scheme is proposed to mechanically support dielectric layers in a hollow-core terahertz Bragg waveguide by means of an axially rotating wrap-around strip structure. The helical-strip supported waveguide samples are fabricated using 3D printing technology, and the waveguide samples are experimentally tested using a terahertz time-domain spectroscopy system. The results show that choosing a suitable helix period can obtain loss characteristics close to those of an ideal Bragg waveguide, with a low transmission loss of less than 0.097dB/m in the range of 0.57-0.58THz.

Depth distribution law of polarization characteristics of vector acoustic field in shallow sea (Retracted)

The polarization of the acoustic field in the ocean waveguide environment is a unique property that can be measured by using a particle velocity sensor in the water column. It can provide new ideas for locating and detecting the underwater target, so it is interesting to study the polarization. The polarization of a monochromatic signal has been described by the Stokes parameters, a set of four real-valued quantities in previous work. In this work, the Stokes parameters are extended to the broadband form, and the expression is simplified by using the nonstationary phase approximation, which reduces the complexity of the theoretical derivation and reveals the physical mechanism behind the significant variations in polarization with source depth and symmetrical depth. Theoretical analysis shows that the polarization characteristics in the ideal waveguide vary significantly in the sea surface, the sea bottom, the depth of the sound source and symmetrical depth. In this work the numerical simulation is used to verify the theoretical analysis and study the relationship between range and integral bandwidth when nonstationary phase approximation method is effective. The numerical results demonstrate that the simplified expression using the nonstationary phase approximation is effective and can better characterize the depth distribution characteristics of the polarization. Additionally, by normalizing the broadband Stokes parameters, the effect of range on the depth distribution characteristics of polarization can be removed. It means that the normalized broadband Stokes parameters are in theory free of the range and depend on the environment, the receiver depth and the source depth, which have the potential to be used for source depth estimation. Subsequently, focusing on normalized broadband Stokes parameters, we analyzes the effects of parameters such as source frequency, source depth, sound speed profile and water depth on the depth distribution characteristics of polarization. The analysis results show that environmental factors have great influence on the depth distribution characteristics of polarization. In the end, the validity of the nonstationary phase approximation and the range-independent property of the normalized broadband Stokes parameters are verified by the results of the RHUM-RUM experimental data processing. The findings provide a theoretical basis for passive target depth estimation based on polarization.

Performance comparison of conventional and striation-based beamformers for underwater bearing detection of pulse sources.

The multi-path and dispersion properties of shallow water waveguides make conventional beamforming (CBF) face issues such as beam shift, broadening, splitting, output distortion, and array gain reduction. In this paper, the striation-based beamforming (SBF) is investigated to address these issues. SBF differs from CBF by utilizing frequency-shift processing along interference striations. The performance difference between CBF and SBF is compared. It demonstrates that under ideal waveguide modeling with pulse sources, SBF can achieve a beam output response that is close to the plane wave condition. The speed term of SBF's response is approximately independent of modal indexes, which equips SBF to form a unique beam output and guarantee the beam resolution. The processing of consistent signals along the striation maintains the optimal signal correlation, which makes SBF ensure the output fidelity and array gain. To shift the mainlobe of SBF to the source azimuth, the time delay related to the waveform truncation point can be introduced to pre-compensate the array signals. There exist two theoretical accuracy limits to using the truncation. First, truncation time corresponds to the waveform point at r0/c (r0 is the source range), and the mainlobe of SBF is directed to the source azimuth. Second, truncation corresponds to the pulse peak point, and the azimuth estimation accuracy of SBF gets close to CBF. Simulations and experimental results are given as illustrations.

Particle Filtering for Source Depth and Water Depth Joint Tracking in Shallow Water

Environmental mismatch degrades the performance of source localization and tracking methods in shallow water. One solution is to estimate source parameters and the key environmental parameters simultaneously from the acoustic data. In this paper, an unconventional approach of joint tracking source depth and water depth parameters by a particle filter is proposed. This approach is free of prior environmental knowledge and numerical calculation of any forward model. First, a state-space model based on modal nature behavior is established driving the shallow-water propagation, instead of modeling in time or space, as was done previous works. Subsequently, particle filtering is employed for joint tracking, in which the evolution with mode-order of vertical wavenumbers and the relationship between state parameters and beam-wavenumber outputs transformed from the data are exploited. Final, the particle smoother reduces the uncertainty of state parameters at initial steps, and improves the overall tracking accuracy. Our approach is demonstrated using simulated data in an ideal waveguide and applied to shallow-water SWellEx-96 experimental data to substantiate its superior performance.

Singular Points Location Pattern Analysis based on Modes Interference

<p>Given the lack of research on the regularity of distribution of singular points, the singular points under different influence factors are analyzed. The location of singular points for adjacent modes group (AMG) generated by the interference modes is derived using normal modes theory in the far field of the ideal shallow waveguide. The singular points are verified by simulation, which compares the distribution of the acoustic field and singular points. Moreover, it is concluded that the number and distribution of singular points in the period of the interference structure of the field (PISF) has a relationship with order (lower order of AMG) and adjacent order (difference between two orders of AMG). The arrangement of upper-lower-two-points increases by 2 with each increase of order and is distributed at both ends of PISF. The arrangement of rhombic-four-points increases by 1 with each increase of adjacent order and increases alternately at both ends of PISF. Meanwhile, there is a periodic relationship between the depth of the source and the location of singular points.</p> <p> </p>

Research on anti-resonant terahertz hollow waveguides with cascaded bridges

A low loss terahertz waveguide based on anti-resonant parameters is proposed to construct a periodic support structure of an arch bridge in Bragg air layer. Simulation results show that terahertz waves can be transmitted with low loss in the anti-resonant band. After numerical simulation to determine the parameters of the waveguide, the waveguide samples are manufactured by 3D printing technology and experimental tests are carried out. Experimental results demonstrate that the terahertz wave within the 0.84–0.887 THz band can be transmitted with a low loss of only 0.245dB/m, which is nearly ten times lower than that of the conventional multi-support structure terahertz Bragg waveguide, and comparable to that ofthe ideal air-core Bragg waveguide.

Ideal Phase-Free Wave Propagation in Air Channel

Despite many intriguing approaches to realize zero-index media by metamaterial, a more common and attractive way to observe phase-invariant phenomenon at finite frequency is actually by the photonic waveguide mode at the cutoff frequency, which can reside in air channel surrounded by photonic band gap media. However, the group velocity of the gap-confined waveguide mode goes to zero (∂ω/∂k = 0) for k = 0 at the cutoff frequency, making it extremely difficult to excite and transport information by the phase advance-free propagation. In this work, we propose a dielectric photonic crystal platform for realizing an ideal air-concentrated phase-free waveguide. The waveguide is designed as a sandwiched structure like a photonic crystal (PC) line defect (e.g., PC-air-PC), which supports a pair of bound states in the continuum (BICs) at the PC-air domain, as well as multiple orders of gap-confined waveguide modes (WMs) inside the air channel. It is shown that the two BIC field distributions are allowed to be of symmetric and antisymmetric characteristics and are respectively coupled to the first- and second-order waveguide mode around k = 0. The interaction between these modes results in a linear band crossing (Δω ∼ k) at finite frequency, leading to the ideal phase-free wave propagation. We numerically and experimentally show the ideal phase-free propagation of the first- and second-order waveguide modes in the air channel. Our work provides an alternative way toward ideal phase-free waveguide, and the results may be of potential application for on-chip communication, qubit entanglement, precise signal processing, etc.

Reducing ambiguities in single-hydrophone matched-field processing by exploiting source motion

Matched-field processing for localizing an underwater acoustic source in range and depth from power-spectrum measurements obtained at a single hydrophone receiver often suffers from high side-lobes and ambiguities when the signal is narrowband or signal bandwidth is small. In this paper we review how source motion can be utilized to reduce side-lobes in depth and range via an incoherent synthetic-aperture-like approach and explain the mechanisms responsible for side-lobe reduction relative to the height of the main-lobe by using a normal-mode expansion for the pressure field. We also derive an approximation for the depth main-lobe width when the true source range is known for the ideal rigid-waveguide case. Numerical results are presented corroborating the analytical analysis along with some matched-field localization ambiguity surface examples for (a) an ideal shallow-water waveguide with a pressure-release top boundary and a rigid bottom boundary and (b) a more realistic shallow-water Pekeris environment, to demonstrate how side-lobes and ambiguities are reduced when source motion is exploited in the matched-field processing.

Microstructure realization of a lattice-based polar solid for arbitrary elastic waveguiding

The ability to precisely directing and controlling longitudinal (P) and transverse (S) waves in 2D solids along an arbitrary trajectory has attracted significant research interest and is crucial for practical applications such as imaging, cloaking, and wave focusing. Here, we report, design and examine an inhomogeneous lattice-based polar medium for ideal elastic waveguide, whose microstructures are inversely determined by the discrete transformation elasticity (DTE). Microstructures of the suggested medium, which are realized through global linear transformation and local affine transformation, enables arbitrary waveguides to transport elastic waves with minimal energy loss. Numerical simulation is then conducted to demonstrate that the lattice-based polar waveguide can efficiently steer both in-plane P and S wave modes over a broad frequency band. We also leverage the medium for Rayleigh wave control on curved surfaces. The constructed polar surface can break the conventional limit of the Rayleigh wave propagation on both concave and convex surfaces with extreme curvatures. This study is not only a concrete manifestation of the polar material, discrete transform elasticity, and their advantages but also provides a great potential in engineering applications such as signal detection, vibration control, and earthquake protection.

Resolution of matched field processing for a single hydrophone in a rigid waveguide.

This paper studies resolution of matched field processing for locating, in range and depth, a broadband underwater acoustic source from data measured at a single hydrophone receiver. For the case of an ideal rigid shallow-water waveguide with a pressure-release top boundary and a rigid bottom boundary, the paper derives approximations for the main-lobe widths of the ambiguity surface. The two cases studied in this paper are (1) when coherent measurements of the pressure are available, with the transmitted source waveform precisely known, and (2) when only measurements of the received-signal pressure magnitude-squared are available, such as might occur when the transmitted signal is random and unknown. The analysis uses the normal-mode expansion for the pressure field to derive approximate expressions for the ambiguity-surface main-lobe widths, as a function of the number of modes and frequency band, for both range and depth. Numerical results are presented corroborating the analytical analysis. Finally, the paper argues that this ambiguity analysis can also give insights into Pekeris waveguides under appropriate conditions and shows numerical simulations of matched-field localization ambiguity surfaces for some realistic shallow-water Pekeris environments.

Training physics-informed neural networks to directly predict acoustic field values in simple environments

As acousticians turn to machine learning for solutions to old and new problems, neural networks have become a go-to tool due to their capacity for model representation and quick forward computations. However, these benefits come at the cost of obscurity; it is difficult to determine whether the proficiency of a trained neural network is limited by training effort, training dataset size or scope, or compatibility of the network’s design with the data’s underlying pattern of interest. For neural networks trained to provide solutions to the point-source Helmholtz-equation in axisymmetric single-path, two-path, and multi-path (ideal waveguide) environments with constant sound speed, the key limitations are the dataset composition and network design. This study examines the effects on performance and explainablity which result from providing physical information (governing equation and boundary conditions) to these neural networks, instead of only acoustic-field solutions generated from well-known analytic solutions. The outcome of using physics-informed neural networks (PINNs) for these simple environments informs their possible extension to more complex, realistic environments. This study emphasizes source frequencies in the 100’s of Hz, depths up to 500 m, and ranges up to 10 km for sound speeds near 1500 m/s. [Work supported by the NDSEG fellowship program.]

An overview of array invariant for source-range estimation in shallow water.

Traditional matched-field processing (MFP) refers to array processing algorithms, which fully exploit the physics of wave propagation to localize underwater acoustic sources. As a generalization of plane wave beamforming, the "steering vectors," or replicas, are solutions of the wave equation descriptive of the ocean environment. Thus, model-based MFP is inherently sensitive to environmental mismatch, motivating the development of robust methods. One such method is the array invariant (AI), which instead exploits the dispersion characteristics of broadband signals in acoustic waveguides, summarized by a single parameter known as the waveguide invariant β. AI employs conventional plane wave beamforming and utilizes coherent multipath arrivals (eigenrays) separated into beam angle and travel time for source-range estimation. Although originating from the ideal waveguide, it is applicable to many realistic shallow-water environments wherein the dispersion characteristics are similar to those in ideal waveguides. First introduced in 2006 and denoted by χ, the dispersion-based AI has been fully integrated with β. The remarkable performance and robustness of AI were demonstrated using various experimental data collected in shallow water, including sources of opportunity. Further, it was extended successfully to a range-dependent coastal environment with a sloping bottom, using an iterative approach and a small-aperture array. This paper provides an overview of AI, covering its basic physics and connection with β, comparison between MFP and AI, self-calibration of the array tilt, and recent developments such as adaptive AI, which can handle the dependence of β on the propagation angle, including steep-angle arrivals.

Resolution of matched field processing for a single hydrophone in a rigid waveguide

This paper studies resolution of matched field processing for locating, in range and depth, a broadband underwater acoustic source from data measured at a single hydrophone receiver. For the case of an ideal rigid shallow-water waveguide with a pressure-release top boundary and a rigid bottom boundary, we derive approximations for the main-lobe widths of the ambiguity surface. The two cases studied in this paper are (1) when coherent measurements of the pressure are available, with the transmitted source waveform precisely known, and (2) when only measurements of the received signal power spectral density (PSD) are available, such as occur when the transmitted signal is random and unknown. The analysis uses the normal-mode expansion for the pressure field to derive approximate expressions for the ambiguity surface main-lobe widths, as a function of the number of modes and frequency band, for both range and depth. Numerical results are presented corroborating the analytical analysis. Finally, we argue that this ambiguity analysis also gives insights into real ocean waveguide localization characteristics under appropriate conditions, and show numerical simulations of matched field localization ambiguity surfaces for some realistic shallow-water Pekeris environments.

Bend-Imitating Theory and Electron Scattering in Sharply-bent Quantum Nanowires

The concept of bend-imitating description as applied to the one-electron quantum mechanics in sharply-bent ideal electron waveguides and its development into a self-consistent theory are presented. In general, the theory allows one to model each particular circular-like bend of a continuous quantum wire as some specific multichannel scatterer being point-like in the longitudinal direction. In an equivalent formulation, the theory gives rise to rather simple matching rules for the electron wave function and its longitudinal derivative affecting only the straight parts of a wire and thereby permitting one to bypass a detailed quantum mechanical consideration of elbow domains. The proposed technique is applicable to the analytical investigation of spectral and transport properties related to the ideal sharply-bent 3D wire-like structures of fixed cross-section and is adaptable to the 2D wire-like structures, as well as to the wire-like structures in the magnetic field perpendicular to the wire bending plane. In the framework of bend-imitating approach, the investigation of the electron scattering in a doubly-bent 2D quantum wire with S-like bend has been made, and the explicit dependences of the transmission and reflection coefficients on geometrical parameters of a structure, as well as on the electron energy, have been obtained. The total elimination of the mixing between the scattering channels of a S-like bent quantum wire is predicted.

The waveguide invariant for a Pekeris waveguide.

A closed-form waveguide invariant β for a Pekeris waveguide is derived. It is based on the modal Wentzel-Kramers-Brillouin (WKB) dispersion equation and implicit differentiation, in conjunction with the concept of the "effective boundary depth," ΔH(θ), where θ is the propagation angle. First, an explicit formula for β(m,n) between mode pairs is obtained assuming an ideal waveguide of the effective waveguide depth, H+ΔH(θ), and provides an excellent agreement with the reference value for the Pekeris waveguide of depth H obtained using the normal mode program kraken. Then, a closed-form expression for a group of adjacent modes is derived: β=(H+ΔH(θ))/(H/ cos2 θ-ΔH(θ)), which can be approximated by β=cos2 θ as ΔH(θ)/H≪1, the analytical expression for an ideal waveguide.

Analysis and Implementation of Self-Packaged Multi-Layer Suspended Coplanar Waveguide and its Applications in Filtering Circuits

In this paper, ideal suspended coplanar waveguide model is analyzed by using conformal mapping method, and the characteristic impedance is formulated and verified. A self-packaged suspended coplanar waveguide (SCPW) using multi-layer PCB technique is proposed and implemented with a experimental insertion loss of no more than 0.5dB, and return loss of better than 15.8dB from DC to 10GHz, which eliminates the drawbacks of the traditional suspended circuits such as bulky size, heavy weight and difficult to be integration because of their indispensable metal cavity and mechanical assemble. Both self-packaging and inside/outside end connection are used to reduce the wave leakage. Based on the self-packaged multi-layer suspended coplanar waveguide, a high frequency selective and high isolated multi-resonator coupled diplexer with measured isolation of no less than 42.5dB, and out-of-band suppression of more than 37dB as well as multiple transmission zeros have been implemented. A reflectionless bandstop filter with a measured S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> attenuation of more than 13.8dB is also implemented for demonstrating the availability of the self-packaged multi-layer SCPW.

Transverse components of the electromagnetic field in a waveguide with modulated in space and in time magnetodielectric filling

The propagation of transverse magnetic (TM) and transverse electric (TE) electromagnetic waves in a regular ideal waveguide of arbitrary cross section is considered. It is assumed that the permittivity and permeability of the magnetodielectric filling of the waveguide are functions that depend on the coordinate and time. Analytical expressions for the transverse components of the magnetic and electric vectors of the TM- and TE-fields in the waveguide are obtained from the system of Maxwell equations. They are expressed in terms of the longitudinal components of the electric and magnetic vectors, which describe the transverse magnetic and transverse electric fields in the waveguide. For the above longitudinal components of the electric and magnetic vectors, the wave equations are given, which are also obtained from the system of Maxwell's equations. Keywords: Maxwell equations, propagation of electromagnetic waves, waveguide with modulated filling, transverse components, Helmholtz equations, Dirichlet and Neumann problems.

Transition Effects of THz Helical Undulator Radiation in a Waveguide

The radiation of a particle instantly injected into an infinite ideal cylindrical waveguide and implementing a helical motion is considered. Additionally, the problem of the radiation of a time-varying point charge moving stationary along a helical orbit in the same waveguide is also solved. Additionally, an explicit expression is obtained for the longitudinal component of the electric field of radiation with a wavefront moving together with the particle. The basic properties of radiation are determined: the conditions for its forward propagation are obtained, and its angular directivity is determined. A formula is given that describes radiation upon gradual introduction of a bunch into a waveguide (modeling the injection process) and during its subsequent propagation.

A Vector Wavenumber Integration Model of Underwater Acoustic Propagation Based on the Matched Interface and Boundary Method

Acoustic particle velocities can provide additional energy flow information of the sound field; thus, the vector acoustic model is attracting increasing attention. In the current study, a vector wavenumber integration (VWI) model was established to provide benchmark solutions of ocean acoustic propagation. The depth-separated wave equation was solved using finite difference (FD) methods with second- and fourth-order accuracy, and the sound source singularity in this equation was treated using the matched interface and boundary method. Moreover, the particle velocity was calculated using the wavenumber integration method, consistent with the calculation of the sound pressure. Furthermore, the VWI model was verified using acoustic test cases of the free acoustic field, the ideal fluid waveguide, the Bucker waveguide, and the Munk waveguide by comparing the solutions of the VWI model, the analytical formula, and the image method. In the free acoustic field case, the errors of the second- and fourth-order FD schemes for solving the depth-separated equation were calculated, and the actual orders of accuracy of the FD schemes were tested. Moreover, the time-averaged sound intensity (TASI) was calculated using the pressure and particle velocity, and the TASI streamlines were traced to visualize the time-independent energy flow in the acoustic field and better understand the distribution of the acoustic transmission loss.