Volume Integral Formulation for the Calculation of Material Independent Modes of Dielectric Scatterers

In the frame of volume integral equation methods, we introduce an alternative representation of the electromagnetic field scattered by a homogeneous object of arbitrary shape at a given frequency, in terms of a set of modes independent of its permittivity. This is accomplished by introducing an auxiliary eigenvalue problem, based on a volume integral operator. With this modal basis the expansion coefficients of the scattered field are simple rational functions of the permittivity of the scatterer. We show, by studying the electromagnetic scattering from a sphere and a cylinder of dimensions comparable to the incident wavelength, that only a moderate number of modes is needed to accurately describe the scattered far field. This method can be used to investigate resonant scattering phenomena, including plasmonic and photonic resonances, and to design the permittivity of the object to pursue a prescribed tailoring of the scattered field. Moreover, the presented modal expansion is computationally advantageous compared to direct solution of the volume integral equation when the scattered field has to be computed for many different values of the dielectric permittivity, given the size and shape of the dielectric body

Magnetoquasistatic resonances of small dielectric objects

A small dielectric object with positive permittivity may resonate when the free-space wavelength is large in comparison with the object dimensions if the permittivity is sufficiently high. We show that these resonances are described by the magnetoquasistatic approximation of the Maxwell's equations in which the normal component of the displacement current density field vanishes on the surface of the particle. They are associated to values of permittivities and frequencies for which source-free quasistatic magnetic fields exist, which are connected to the eigenvalues of a magnetostatic integral operator. We present the general physical properties of magnetoquasistatic resonances in dielectrics with arbitrary shape. They arise from the interplay between the polarization energy stored in the dielectric and the energy stored in the magnetic field. Our findings improve the understanding of resonances in high-permittivity dielectric objects and provide a powerful tool that greatly simplifies the analysis and design of high-index resonators

Synthesis of resonant modes in electromagnetics

Resonant modes determine the response of electromagnetic devices, including dielectric and plasmonic resonators. Relying on the degrees of freedom that metamaterials provide, this contribution shows how to design, at will, the resonant modes of a dielectric object placed in an unbounded space. Specifically, the proposed method returns in analytical form the spatial distribution of the dielectric susceptibility tensor for which the object exhibits resonances at prescribed frequencies and spatial distribution of the polarization. Together with the synthesis of the material, two key concepts are introduced: the controlled tunability of the resonant modes and the number of essential modes, i.e. the number of modes that uniquely characterize the spatial distribution of the dielectric susceptibility. Moreover, this approach can be applied to design the resonant modes of any system where the constitutive relationship is linear and local

An Eddy-Current Testing Method for Measuring the Thickness of Metallic Plates

Thickness measurements of metallic plates are mandatory in many industrial scenarios. Methods based on eddy-current testing (ECT) are ideal for fast and accurate online contactless thickness measurements, making them very attractive in the Industry 4.0 scenario. This contribution is focused on a specific and robust ECT technique proposed in the past by the scientific community. The main limitation is its applicability to thin materials only, where the thickness of the material is much smaller than the overall size of the ECT probe. Extending the range of applicability to thicker materials introduces a progressive and severe degradation of the measurement accuracy. In this article, we analyze the theoretical foundation of this method with an entirely original approach based on the celebrated Buckingham π theorem. In doing this, we draw the complete theoretical picture of the method, providing a simple, clear, and rigorous view of its performance and intrinsic limitations. Moreover, we propose two solutions, one analytical and the other iterative, to accurately estimate the thickness of the materials from thin to thick values. Finally, a numerical analysis combined with an experimental campaign confirms the effectiveness of the proposed solutions, making the method suitable for industrial and other applications

Differential vulnerability of retinal layers to early age-related macular degeneration: evidence by SD-OCT segmentation analysis.

PURPOSE We evaluated layer-by-layer retinal thickness in spectral-domain optical coherence tomography (SD-OCT), determined by automated segmentation analysis (ASA) software in healthy and early age-related maculopathy (ARM) eyes. METHODS There were 57 eyes (specifically, 19 healthy eyes under 60 years old, 19 healthy eyes over 60, and 19 ARM eyes) recruited into this cross-sectional study. The mean ages were 36.78 (SD, ±13.82), 69.89 (SD, ±6.14), and 66.10 (SD, ±8.67) years, respectively, in the three study groups. The SD-OCT scans were transferred into a dedicated software program that performed automated segmentation of different retinal layers. RESULTS Automated layer segmentation showed clear boundaries between the following layers: retinal nerve fiber layer (RNFL), ganglion cell layer plus inner plexiform layer (GCL+IPL), inner nuclear layer plus outer plexiform layer (INL+OPL), outer nuclear layer (ONL), and RPE complex. The thickness of the RNFL, ONL, and RPE layers did not show a statistically significant change across the three groups by ANOVA (P = 0.10, P = 0.09, P = 0.15, respectively). The thickness of GCL+IPL and INL+OPL was significantly different across the groups (P < 0.01), being reduced in the ARM eyes compared to healthy eyes, under and over 60 years old. CONCLUSIONS The early morphologic involvement of the GCL+IPL and INL+OPL layers in ARM eyes, as revealed by the ASA, could be related to early anatomic changes described in the inner retina of ARM eyes. This finding may represent a morphologic correlation to the deficits in postreceptoral retinal function in ARM eyes

A Fast Matrix Compression Method for Large Scale Numerical Modelling of Rotationally Symmetric 3D Passive Structures in Fusion Devices

This paper illustrates the development of a recursive QR technique for the analysis of transient events, such as disruptions or scenario evolution, in fusion devices with three-dimensional conducting structures using an integral eddy current formulation. An integral formulation involves the solution, at each time step, of a large full linear system. For this reason, a direct solution is impractical in terms of time and memory consumption. Moreover, typical fusion devices show a symmetric/periodic structure. This can be properly exploited when the plasma and other sources possess the same symmetry/periodicity of the structure. Indeed, in this case, the computation can be reduced to only a single sector of the overall structure. In this work the periodicity and the symmetries are merged in the recursive QR technique, exhibiting a huge decrease in the computational cost. Finally, the proposed technique is applied to a realistic large-scale problem related to the International Thermonuclear Experimental Reactor (ITER)