Acoustic Waveguide Modes Research Articles

Application of quantum graph theory to metamaterial design: Negative refraction of acoustic waveguide modes

We leverage quantum graph theory to quickly and accurately characterize acoustic metamaterials comprising networks of interconnected pipes. Anisotropic bond lengths are incorporated in the model that correspond to space-coiled acoustic structures to exhibit dispersion spectra reminiscent of hyperbolic metamaterials. We construct two metasurfaces with embedded graph structure and, motivated by the graph theory, infer and fine-tune their dispersive properties to engineer nonresonant negative refraction of acoustic surface waves at their interface. Agreement between the graph model, full-wave simulations, and experiments bolsters quantum graph theory as a new paradigm for metamaterial design. Published by the American Physical Society 2024

Spatial waveguide mode separation for acoustic waves in a meta-slab composed of subunits with graded thicknesses

A meta-slab composed of subunits with graded thicknesses is proposed for spatially separating the zeroth- and first-order acoustic waveguide modes according to the generalized Snell's law. The phase velocity for the first-order mode depends on the waveguide thickness, whereas that for the zeroth-order mode does not. This enables the required phase-shift gradients of the meta-slab to be obtained for spatially separating the two waveguide modes. To design the meta-slab, analytic solutions are derived for the transmission coefficients and phase shifts of the incident acoustic waves with the two modes propagating through the subunits. Numerical simulations with transient finite-element analyses are implemented to demonstrate the propagation of the two waveguide modes. Sinusoidal signal and tone-burst excitations are applied in the analyses. The latter case shows that the two waveguide modes can be successfully separated in space by the designed meta-slab.

Elimination of spurious modes in full-vectorial finite element method based acoustic modal solution.

Finite element method is a powerful technique for solving a wide range of engineering problems. However, the existence of the spurious solutions in full-vectorial finite element method has been a major problem for both acoustic and optic modal analyses. For emerging photonic devices exploiting light-sound interactions in high index contrast waveguides, this problem is a major limitation. A penalty function is introduced to remove these unwanted spurious modes in acoustic waveguides, which also identifies the acoustic modes more easily. Numerically simulated results also show considerably improved vector mode profiles. The proposed penalty method has been applied for the characterization of low index contrast single mode fiber and also for high index contrast silicon nanowire to demonstrate its effectiveness.

A simple approach for evaluation of cut-on condition of higher order modes in inhomogeneous uniform acoustic waveguides

Uniform acoustic waveguides in initially quiescent inhomogeneous media are governed by Bergmann’s wave equation. The transverse modes are independent of the ambient gradient, but there is a void of papers on the cut-on conditions of the higher order axial modes. This paper presents a sufficient cut-on condition and discusses its application to hard-walled ducts in which the mean temperature varies linearly and exponentially along the duct axis.

Acoustic one-way mode conversion and transmission by sonic crystal waveguides

We proposed a scheme to achieve one-way acoustic propagation and even–odd mode switching in two mutually perpendicular sonic crystal waveguides connected by a resonant cavity. The even mode in the entrance waveguide is able to switch to the odd mode in the exit waveguide through a symmetry match between the cavity resonant modes and the waveguide modes. Conversely, the odd mode in the exit waveguide is unable to be converted into the even mode in the entrance waveguide as incident waves and eigenmodes are mismatched in their symmetries at the waveguide exit. This one-way mechanism can be applied to design an acoustic diode for acoustic integration devices and can be used as a convertor of the acoustic waveguide modes.

Implementing physical constraints for noise-only mode shape estimation on real data

Many underwater acoustic tasks sample a narrowband pressure field with a vertical line array. In the absence of strong local sources, the noise sampled by an array includes both a spatially correlated and a spatially uncorrelated component. The acoustic waveguide's modes form a basis for the spatially correlated noise component generated by distant sources. This basis can be estimated from the eigenvectors of the noise sample covariance matrix. Propagation physics constrain the mode shapes to be real, but the eigenvectors are generally complex. These complex vectors require a phase rotation for each eigenvector prior to taking the real part. Previous work found that the eigenvector mode estimates' phases include spatially correlated noise. This noise correlation degrades the performance of spatial averaging and minimum variance estimates of the unknown phase rotation. The best estimate is the phase of the array element with the maximum magnitude for each mode, which is robust to the noise's spatial correlation. This research evaluates the previously developed phase rotation techniques using a real data set. The data was collected off the north coast of Elba Island by the SACLANT Centre in 1993. [This work was supported by ONR.]

Reciprocity in the scattering coefficients of acoustic waveguide modes

In this Letter, a proof is provided for the reciprocity between modal scattering coefficients of the acoustic waveguides connected by a junction enclosure. The result holds for all waveguide modes and for junction enclosures with locally reactive boundary conditions away from the interfaces between the junction and waveguides. Also provided is a physical interpretation of the reciprocity of the modal scattering coefficients. The scattering of two-dimensional waveguide modes by a right-angled bend in a rectangular duct is used as an illustrating example.

Acoustical monitoring of the second mode internal solitary wave on oceanic shelf

The possibility of monitoring second gravitational mode internal solitons using interference pattern frequency shifts is discussed. The investigation is carried out for the shelf of the northern South China Sea near the Dongsha Atoll by means of numerical modeling. We used the data of the in-situ internal solitons measurements in this area. The “vertical modes and horizontal rays” approach is implemented to calculate the low frequency sound fields in the 3d environment. Stationary acoustic path is oriented at the right angle to the preferred internal wave propagation direction. A sound source and receivers are deployed at the sea bottom. Sound receivers are located at the different ranges where horizontal refraction is pronounced, and where it is insignificant. Numerical experiments demonstrate that some of acoustic waveguide modes are focused, and others are defocused in the horizontal plane when the second mode soliton propagates across the acoustic path. It is shown that the second mode internal solitary wave parameters can be successfully reconstructed from the frequency shifts in the spectrum of received signals only if horizontal refraction effects are weak. [Work supported by Russian Foundation for Basic Research and National Science Council of Taiwan # 10-02-92005]

Existence of backward propagating acoustic waves in supported layers

Conditions for the existence of acoustic waveguide modes with the direction of the group velocity opposite to that of the phase velocity in supported layers are investigated. We begin with a study of a clamped-free layer and show that the occurrence of the negative slope in the dispersion of the second and higher order modes leading to backward propagation is a commonly encountered phenomenon related to accidental degeneracies between longitudinal and transverse thickness resonances. For a layer on an elastic substrate, the negative dispersion slope exists only when the transverse velocity of the layer is very small compared to that of the substrate, which makes backward propagation a rarely occurring phenomenon in real structures. Finally, we explain how mode-crossing in certain bi-layer structures results in the negative slope in the dispersion of the fundamental mode.

Formulation of a Complex Mode Solver for Arbitrary Circular Acoustic Waveguides

There has been a resurgence of interests in stimulated Brillouin scattering (SBS) in optical fibers recently. This is largely due to the need to overcome SBS for power scaling of single frequency fiber lasers. Complex acoustic waveguide designs have been proposed for SBS suppression in optical fibers. There is, therefore, a strong need for finding acoustic modes in complex acoustic waveguides. Furthermore, leaky acoustic modes are often ignored in recent works on SBS in optical fiber. Many leaky acoustic modes involved in SBS in optical fibers often have comparable losses to guided acoustic modes. The losses of both guided acoustic modes and many leaky acoustic modes are dominated by the extremely high material loss of acoustic waves in the GHz region in optical fibers. Therefore, it is very important to consider these leaky acoustic modes in SBS in optical fibers, especially for acoustic antiguide designs used for SBS suppressions, where those leaky acoustic modes are often responsible for the peak SBS gain and consequently SBS threshold. Even for optical fibers with guided acoustic waveguide, fine features in SBS gain spectra can be better understood by studying the additional contributions from leaky acoustic modes. In this work, we report, for the first time, a complex vector acoustic mode solver capable of finding both guided and leaky acoustic modes in arbitrary circular acoustic waveguides. The validity of the mode solver is verified by comparing simulated SBS gain spectra in two optical fibers, one with acoustic guide and one with acoustic antiguide, to measured ones. This acoustic mode solver can be used to provide highly accurate SBS gain spectrum in optical fibers. It will be a critical tool in optical fiber designs for SBS suppressions and enhancements. It will also be very important tool for understanding fine spectral details of SBS in optical fibers.

Analysis and optimization of acoustic speed profiles with large transverse variations for mitigation of stimulated Brillouin scattering in optical fibers

We derive and numerically verify a simple analytical approximation for the calculation of Brillouin gain spectra (BGS) in acoustically antiguiding optical fibers. We use our approximation to find acoustic speed profiles that minimize the peak Brillouin gain. The optimized BGS are top-hat-shaped, regardless of the optical mode distribution, with peak value inversely proportional to the effective area of the optical mode. We further investigate acoustically guiding speed profiles, in which acoustic waveguide modes lead to peaks in the Brillouin gain spectrum. However, for large cores with diameters down to 50 microm, and often even smaller, these Brillouin gain peaks are spectrally dense, and can be smeared out due to broadening in many practical systems. The Brillouin gain spectrum is then similar for waveguiding and antiguiding acoustic profiles.

Optical Generation and Characterization of Acoustic Waves in Thin Films: Fundamentals and Applications

▪ Abstract The mechanical and acoustic properties of thin films and multilayer assemblies are important both for technological applications of these materials and for basic scientific studies of their physical behavior. Techniques that use optical methods to monitor acoustic waves stimulated in thin films with short pulsed lasers are useful for accurately and nondestructively characterizing the high frequency acoustic physics of these systems. This review briefly summarizes some of these techniques and focuses on a method known as impulsive stimulated thermal scattering or transient grating photoacoustics. It describes the most advanced experimental techniques for performing this measurement and outlines its application to the study of acoustic waveguide modes in a variety of thin films. These measurements, coupled with models for the physics of the modes, can be used to determine intrinsic mechanical properties of materials and structures that occur, for example, in microelectronics and high-frequency acoustic filters. This article summarizes a selected set of existing applications and concludes with an overview of future directions that include studies of the acoustics of complex microstructures such as microfluidic networks and synthetic phononic crystals.

Trapped modes in acoustic waveguides

We consider the eigenvalue problem for the Laplacian on a cylinder perturbed by a compact obstacle (with Neumann boundary conditions) and look for eigenvalues of such a problem. In the case of a two-dimensional cylinder with symmetric obstacle we give sufficient conditions for both existence and non-existence of an eigenvalue. We also prove that in the case of a thin obstacle, parallel to the axis of the cylinder, there always exists an eigenvalue.

Higher‐order modal reflection and transmission in acoustic waveguide junctions.

Analytic expressions for the transmission and reflection coefficients of higher‐order modes in acoustic waveguides are developed and explored. When written in matrix form the equations take on the standard form of an impedance discontinutity. Numerical results for a right angle bend and a T junction show that there is significant coupling between modes, especially to the plane‐wave mode. The results indicate that modal coupling cannot be ignored in the design of active and passive attenuators that need to work at higher frequencies.

Noncontact determination of transverse isotropic elastic moduli in polyimide thin films using a laser based ultrasonic method

A transient grating laser ultrasonic method known as real-time impulsive stimulated thermal scattering is used to excite and monitor Lamb acoustic waveguide modes in free-standing thin polyimide films which are known to have transverse isotropic symmetry. The dispersion of these Lamb modes is used to accurately evaluate both the in and out-of-plane elastic moduli.

Elastic modulus and in-plane thermal diffusivity measurements in thin polyimide films using symmetry-selective real-time impulsive stimulated thermal scattering

We describe a technique for extending the utility of the real-time Impulsive Stimulated Thermal Scattering (ISTS) method for thin film characterization. Using weakly absorbed excitation pulses, we show how to selectively drive acoustic waveguide modes that are unobservable when strongly absorbed pulses are used. The ability to excite and monitor these modes is important because it allows for a significant increase in the experimental sensitivity to the film longitudinal velocity. This arrangement also greatly simplifies determination of the in-plane thermal diffusivity. The technique is illustrated through study of unsupported polyimide films with six different thicknesses.

Acoustic waveguide modes observed in electrically heated metal wires.

The steady-state resistance of small metal wires subject to an electric field is found to exhibit periodic resonances that scale with the width of the wire. The energies of the resonances have been determined using the low-temperature corrections to the resistance of the wires, and are shown to correspond to acoustic modes of the wire. We conclude that the resonances originate from increased energy relaxation that occurs when the electron system gains enough energy from the electric field to emit phonons in a higher acoustic subband of the wire.

Ultrasonic wave propagation and barrier-limited heat flow in thin films of YBa2Cu3O7-x.

Direct generation and detection of acoustic waveguide modes in thin (1000 \AA{}) films using the optical-transient-grating method are reported. The upper limit of acoustic damping in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathit{x}}$ films was measured to be \ensuremath{\sim}100 dB/cm for 1-GHz acoustic waves at room temperature. The presence of barrier-limited thermal conductivity into the supporting MgO substrate is demonstrated and a thermal diffusivity of 0.023 ${\mathrm{cm}}^{2}$/s in the a-b plane at 300 K is measured, which is consistent with previous observations.

Experimental and theoretical analysis of transient grating generation and detection of acoustic waveguide modes in ultrathin solids

A full theoretical analysis of and experimental evidence for the optical generation and detection of acoustic waveguide modes (Lamb waves) in ultrathin solids using the transient grating (TG) technique is presented. The driving force due to the TG excitation is derived for a free, isotropic plate. In contrast to a bulk isotropic material in which a single wave is excited, the TG excites a number of modes with a variety of frequencies but with the same tangential component of the wavevector. The frequencies beat, resulting in a complex time-dependent signal. Experimental results are presented for anthracene sublimation flakes. In addition to discussing the general features of Lamb wave generation, we also discuss the effects of mounting the crystal on a substrate, of varying the fringe spacing, of resonant probing, and of polarized detection. The nature of Lamb waves in anisotropic materials is illustrated, and the extent to which the isotropic theory can be applied to anisotropic systems is discussed.

Generation and detection of acoustic waveguide modes in ultrathin crystals using the transient grating technique

The generation of acoustic waveguide modes (Lamb waves) in ultrathin solids using the transient grating (TG) technique is described. The driving force due to the TG excitation is derived for a free, isotropic plate. In contrast to a bulk isotropic material in which a single wave is excited, the TG excites a number of modes with a variety of frequencies but with the same wavevector. The frequencies beat, resulting in a complex time-dependent signal. Experimental results for anthracene sublimation flakes of ≈ 1 μm thicknesses are presented. Lamb waves with frequencies that do not match the bulk frequencies are generated.