Dyadic Green’s Function for Multilayered Planar, Cylindrical, and Spherical Structures with Impedance Boundary Condition

The integral equation (IE) method is one of the efficient approaches for solving electromagnetic problems, where dyadic Green’s function (DGF) plays an important role as the Kernel of the integrals. In general, a layered medium with planar, cylindrical, or spherical geometry can be used to model different biomedical media such as human skin, body, or head. Therefore, in this chapter, different approaches for the derivation of Green’s function for these structures will be introduced. Due to the recent great interest in two-dimensional (2D) materials, the chapter will also discuss the generalization of the technique to the same structures with interfaces made of isotropic and anisotropic surface impedances. To this end, general formulas for the dyadic Green’s function of the aforementioned structures are extracted based on the scattering superposition method by considering field and source points in the arbitrary locations. Apparently, by setting the surface conductivity of the interfaces equal to zero, the formulations will turn into the associated problem with dielectric boundaries. This section will also aid in the design of various biomedical devices such as sensors, cloaks, and spectrometers, with improved functionality. Finally, the Purcell factor of a dipole emitter in the presence of the layered structures will be discussed as another biomedical application of the formulation.

Further assessment of a time domain impedance boundary condition for the numerical simulation of noise-absorbing materials

In regard to the mitigation of environmental noise across major industry sectors, the present study focuses on the numerical prediction of passive noise reduction devices. Here, it is further explored how the noise attenuation induced by locally reacting noise absorbing materials (also called acoustic liners) can be simulated using a time domain highly accurate Computational AeroAcoustics (CAA) method. To this end, it is assessed how a classical Time Domain Impedance Boundary Condition (TDIBC) can effectively model acoustic liners of practical interest, including when the latter are exposed to realistic conditions (grazing flow and noise excitation). The investigation consists in numerically reproducing two experimental campaigns initially performed at NASA Langley Research Center. Two different materials are considered (honeycomb superimposed with perforate or wiremesh resistive face-sheet), each being characterized by a specific noise attenuation behaviour ( e.g. dependency on the flow conditions and/or noise excitation). Each material is tested under various flow conditions ( e.g. grazing flow of Mach up to 0.5) and/or noise source excitation ( e.g. multiple tones of level up to 140 dB each). The results demonstrate the ability of the underlying CAA/TDIBC approach to simulate realistic acoustic liners in non-trivial configurations, with enough physical accuracy ( e.g. correct capture of the noise attenuation characteristics) and numerical robustness ( e.g. absence of instabilities). The study also reveals that, independent from the CAA/TDIBC approach itself, some specific pre-processing tasks (e.g. impedance eduction and subsequent TDIBC calibration) may play a bigger role than expected, in practice.

Application and Verification of Time-Domain Impedance Boundary Conditions in CAA Simulations

In computational fluid dynamic (CFD) and computational aeroacoustics (CAA) simulations, the wall surface is normally treated as a purely reflective wall. However, some surface treatments are usually applied in experiments. Thus, the simulation results cannot be validated by experimental results. In aeroacoustics analysis, impedance is a quantity to characterize reflectivity and absorption of an acoustically treated surface. One of the major numerical challenges in CAA simulations is to define acoustically well-posed boundary conditions. The impedance boundary condition is a frequency-domain boundary condition. However, CFD and CAA simulations are time-domain computations, which means the frequency-domain impedance boundary condition cannot be adopted directly. Several methods, including the three-parameter model, the z-transform method and the reflection coefficient model, were developed. In the present study, a coupling method that combines the time-domain impedance boundary condition and Large Eddy Simulations (LES) is proposed. A channel flow with wall impedance is simulated at different acoustic resistance and reactance. The approach is verified by the case with purely reflective wall impedance. For the flow with wall impedance. The effects of acoustic resistance and reactance are investigated. It is found that the wall impedance contributes to the noise reduction in the near-wall region, and with the decrease of the resistance or reactance, the sound pressure level is decreased. The method developed in this study is expected to be applied to a variety of noise-control problems.

Electromagnetic Scattering from a Graphene Disk: Helmholtz-Galerkin Technique and Surface Plasmon Resonances

The surface plasmon resonances of a monolayer graphene disk, excited by an impinging plane wave, are studied by means of an analytical-numerical technique based on the Helmholtz decomposition and the Galerkin method. An integral equation is obtained by imposing the impedance boundary condition on the disk surface, assuming the graphene surface conductivity provided by the Kubo formalism. The problem is equivalently formulated as a set of one-dimensional integral equations for the harmonics of the surface current density. The Helmholtz decomposition of each harmonic allows for scalar unknowns in the vector Hankel transform domain. A fast-converging Fredholm second-kind matrix operator equation is achieved by selecting the eigenfunctions of the most singular part of the integral operator, reconstructing the physical behavior of the unknowns, as expansion functions in a Galerkin scheme. The surface plasmon resonance frequencies are simply individuated by the peaks of the total scattering cross-section and the absorption cross-section, which are expressed in closed form. It is shown that the surface plasmon resonance frequencies can be tuned by operating on the chemical potential of the graphene and that, for orthogonal incidence, the corresponding near field behavior resembles a cylindrical standing wave with one variation along the disk azimuth.

Emitting long-distance spiral airborne sound using low-profile planar acoustic antenna

Recent years have witnessed a rapidly growing interest in exploring the use of spiral sound carrying artificial orbital angular momentum (OAM), toward establishing a spiral-wave-based technology that is significantly more efficient in energy or information delivering than the ordinary plane wave technology. A major bottleneck of advancing this technology is the efficient excitation of far-field spiral waves in free space, which is a must in exploring the use of spiral waves for long-distance information transmission and particle manipulation. Here, we report a low-profile planar acoustic antenna to modulate wavefronts emitted from a near-field point source and achieve far-field spiral airborne sound carrying OAM. Using the holographic interferogram as a 2D modulated artificial acoustic impedance metasurface, we show the efficient conversion from the surface wave into the propagating spiral shape beam both numerically and experimentally. The vortex fields with spiral phases originate from the complex inter-modal interactions between cylindrical surface waves and a spatially-modulated impedance boundary condition. This antenna can open new routes to highly integrated spiral sound emitters that are critical for practical acoustic functional devices.

On Computing Impulse Responses from Frequency-Domain Finite Element Solutions

In acoustics, knowledge of the impulse response of a system is often important. While impulse responses may be measured, they may also be predicted using numerical methods. This work considers the generation of impulse responses from frequency-domain finite element solutions. It is shown that these impulse responses, obtained by inverse Fourier transformation, are noncausal. Through error analysis, it is demonstrated that the noncausality can be reduced by increasing the duration of a source signal used to excite a simulated system. It is found that increasing the source signal duration increases the dispersion-related phase error present in the simulated impulse responses. The findings of this study are used to simulate an impulse response for a system with a nonuniform, frequency-dependent, complex impedance boundary condition.