Optical resonators are widely used in modern photonics. Their spectral response and temporal dynamics are fundamentally driven by their natural resonances, the so-called quasinormal modes (QNMs), with complex frequencies. For optical resonators made of dispersive materials, the QNM computation requires solving a nonlinear eigenvalue problem. This raises a difficulty that is only scarcely documented in the literature. We review our recent efforts for implementing efficient and accurate QNM solvers for computing and normalizing the QNMs of micro- and nanoresonators made of highly dispersive materials. We benchmark several methods for three geometries, a two-dimensional plasmonic crystal, a two-dimensional metal grating, and a three-dimensional nanopatch antenna on a metal substrate, with the perspective to elaborate standards for the computation of resonance modes.

Electrical properties tomography (EPT) is an imaging method that uses a magnetic resonance (MR) system to non-invasively determine the spatial distribution of the conductivity and permittivity of the imaged object. This manuscript starts by providing clear definitions about the data required for, and acquired in, EPT, followed by comprehensively formulating the physical equations underlying a large number of analytical EPT techniques. This thorough mathematical overview of EPT harmonizes several EPT techniques in a single type of formulation and gives insight into how they act on the data and what their data requirements are. Furthermore, the review describes machine learning-based algorithms. Matlab code of several differential and iterative integral methods is available upon request.

Magnetic resonance electrical properties tomography (MR‐EPT) is a technique used to estimate the conductivity and permittivity of tissues from MR measurements of the transmit magnetic field. Different reconstruction methods are available; however, all these methods present several limitations, which hamper the clinical applicability. Standard Helmholtz‐based MR‐EPT methods are severely affected by noise. Iterative reconstruction methods such as contrast source inversion electrical properties tomography (CSI‐EPT) are typically time‐consuming and are dependent on their initialization. Deep learning (DL) based methods require a large amount of training data before sufficient generalization can be achieved. Here, we investigate the benefits achievable using a hybrid approach, that is, using MR‐EPT or DL‐EPT as initialization guesses for standard 3D CSI‐EPT. Using realistic electromagnetic simulations at 3 and 7 T, the accuracy and precision of hybrid CSI reconstructions are compared with those of standard 3D CSI‐EPT reconstructions. Our results indicate that a hybrid method consisting of an initial DL‐EPT reconstruction followed by a 3D CSI‐EPT reconstruction would be beneficial. DL‐EPT combined with standard 3D CSI‐EPT exploits the power of data‐driven DL‐based EPT reconstructions, while the subsequent CSI‐EPT facilitates a better generalization by providing data consistency.

Contrast source inversion – electrical properties tomography (CSI-EPT) is an iterative reconstruction method to retrieve the electrical properties (EPs) of tissues from MR data. The method is based on integral representations of the electromagnetic (EM) field and has been shown to allow EP reconstructions of small structures as well as tissue boundaries with compelling accuracy. However, to date CSI-EPT has been implemented for two-dimensional (2D) configurations only which limits its applicability. In this paper, a full three-dimensional (3D) extension of the CSI-EPT method is presented, to enable CSI-EPT to be applied to realistic 3D scenarios. Here, we demonstrate a proof-of-principle of 3D CSI-EPT and present reconstructions of a 3D abdominal body section and a 3D head model using different settings of the transmit coil. Numerical results show that the full 3D approach yields accurate reconstructions of the EPs, even at tissue boundaries and is most accurate in regions where the absolute value of the electric field is highest.

Purpose High‐permittivity materials in the form of flexible “dielectric pads” have proved very useful for addressing RF inhomogeneities in high field MRI systems. Finding the optimal design of such pads is, however, a tedious task, reducing the impact of this technique. We present an easy‐to‐use software tool which allows researchers and clinicians to design dielectric pads efficiently on standard computer systems, for 7T neuroimaging and 3T body imaging applications. Methods The tool incorporates advanced computational methods based on field decomposition and model order reduction as a framework to efficiently evaluate the B₁⁺ fields resulting from dielectric pads. The tool further incorporates optimization routines which can either optimize the position of a given dielectric pad, or perform a full parametric design. The optimization procedure can target either a single target field, or perform a sweep to explore the trade‐off between homogeneity and efficiency of the B₁⁺ field in a specific region of interest. The 3T version further allows for shifting of the imaging landmark to enable different imaging targets to be centered in the body coil. Results Example design results are shown for imaging the inner ear at 7T and for cardiac imaging at 3T. Computation times for all cases are approximately a minute per target field. Conclusion The developed tool can be easily used to design dielectric pads for any 7T neuroimaging and 3T body imaging application within minutes. This bridges the gap between the advanced design methods and the practical application by the MR community.

Purpose: Parallel RF transmission (PTx) is one of the key technologies enabling high quality imaging at ultra‐high fields (≥7T). Compliance with regulatory limits on the local specific absorption rate (SAR) typically involves over‐conservative safety margins to account for intersubject variability, which negatively affect the utilization of ultra‐high field MR. In this work, we present a method to generate a subject‐specific body model from a single T1‐weighted dataset for personalized local SAR prediction in PTx neuroimaging at 7T.Methods: Multi‐contrast data were acquired at 7T (N = 10) to establish ground truth segmentations in eight tissue types. A 2.5D convolutional neural network was trained using the T1‐weighted data as input in a leave‐one‐out cross‐validation study. The segmentation accuracy was evaluated through local SAR simulations in a quadrature birdcage as well as a PTx coil model.Results: The network‐generated segmentations reached Dice coefficients of 86.7% ± 6.7% (mean ± SD) and showed to successfully address the severe intensity bias and contrast variations typical to 7T. Errors in peak local SAR obtained were below 3.0% in the quadrature birdcage. Results obtained in the PTx configuration indicated that a safety margin of 6.3% ensures conservative local SAR estimates in 95% of the random RF shims, compared to an average overestimation of 34% in the generic “one‐size‐fits‐all” approach.Conclusion: A subject‐specific body model can be automatically generated from a single T1‐weighted dataset by means of deep learning, providing the necessary inputs for accurate and personalized local SAR predictions in PTx neuroimaging at 7T.