This paper first extends an integral equation (IE) based zero-thickness metasurface forward solver known as the implicit (IMP) IE-GSTC method to account for composite metasurface problems consisting of multiple metasurfaces and additional dielectric scattering objects. This extension is followed by the development of a unified mathematical framework that is used to analyze and compare the formulation of different IE-based zero-thickness metasurface forward solvers. It is shown that all of these IE-based zero-thickness metasurface forward solvers are analytically equivalent. Despite this analytical equivalence, we demonstrate that there exist key numerical differences between the formulations, which can affect the computational performance of each method. We conclude the paper by first comparing the performance of the extended IMP IE-GSTC method, applied to composite metasurface problems utilizing zero-thickness metasurface models, to that of a commercial full-wave forward solver that utilizes finite-thickness metasurface models. Finally, we conduct a comparison between the numerical performance of the IMP IE-GSTC and those of the other IE-based zero-thickness methods.

We analytically demonstrate how the properties of local cascaded metasurface pairs can be mapped to those of single non-local metasurfaces such that their external field scattering remains identical regardless of the particular incident field. This mapping is obtained for two-dimensional problems by exploiting Love's equivalence principle and fundamental linear operations. We verify the mapping with simulated data and show that the mapping preserves the losslessness, passivity, and reciprocity characteristics of the original local cascaded metasurface pair.

In this paper, we consider two design procedures for a cascaded metasurface pair. For a particular application, we present and evaluate data from simulations and experiments. We discuss the details and limitations of the two design algorithms, the fabrication process, and the measurement procedure. In particular, we highlight difficulties with respect to the measurement and analysis, as well as the techniques used to address these difficulties.

This paper reviews some of our recent works on how electromagnetic metasurfaces could be advantageously used for microwave imaging applications. In particular, it discusses some possibilities for augmenting the information content of the data and enhancing the achievable signal-to-noise ratio.

We investigate how the performance of a cascaded metasurface system can change when it is designed with physically realizable unit cells as opposed to unit cells based on impedance boundary conditions. In the provided example, we have observed that the performance of the physically realizable metasurface system has degraded significantly close to its edges.

This paper reviews some of our recent research progress in the area of electromagnetic inverse metasurface design. In particular, the scope of this paper is on the inverse design of omega-bianisotropic transmitting metasurfaces.

We present the formulation of a novel integral-equation (IE)-based algorithm to solve for the scattered fields of a metasurface problem. The metasurface is assumed to be a thin sheet behaving according to the susceptibility model from the generalized sheet transition conditions (GSTCs). The proposed (implicit) IE-GSTC algorithm differs from other IE-GSTC methods by solving for the average scattered fields (by utilizing the mathematical properties of the IE operators) and only indirectly using the GSTC equations, which results in a reduced number of fundamental unknowns when compared to other methods. In addition, we show how the average scattered fields can be used in order to find the scattered fields everywhere. The proposed method is used to simulate two cases under the two-dimensional transverse-electric assumption. In particular, the results of the second case are compared to those obtained by a full-wave simulation in ANSYS HFSS.

Electromagnetic forward and inverse solvers are considered for the analysis and design of electromagnetic metasurfaces. This paper reviews (i) a forward solver that takes the surface susceptibilities of metasurfaces and calculates their scattered fields and (ii) an inverse solver that takes user-defined desired power patterns and outputs the required metasurface properties. An omega-bianisotropic transmitting metasurface is then fabricated and measured to evaluate the performance of these forward and inverse solvers.

The formulation and implementation of the Love’s condition constraint for the source reconstruction method (SRM) in near-field antenna measurements is analyzed in the context of inverse problems. To this end, the SRM is first analyzed to identify the non-unique or non-radiating current sources which may be present. Next, the advantages and disadvantages of general regularization techniques, which may address the non-radiating currents, are presented which serve to motivate the use of the Love’s condition constraint. The main methods of formulating the constraint are then presented, one of which is a novel technique developed for this paper. Following this, the formulation methods are analyzed in order to predict the similarities and differences of the methods in the context of addressing the non-radiating currents of the SRM. This analysis is reinforced by simulated antenna measurements. In particular, the novel formulation method is demonstrated to provide greater reconstruction accuracy (in the examples considered), at the cost of computational complexity.

Microwave imaging (MWI) systems are usually enclosed within casings, e.g., in order to contain the utilized coupling liquid or to help mount the antenna system. On the other hand, inverse scattering algorithms, which are used to process the measured microwave scattering data, often assume that the background medium of the imaging system extends to infinity (i.e., unbounded background medium assumption). Thus, they do not consider the reflections occurring at the system enclosure. For such algorithms to yield successful images, these reflections need to be minimized, e.g., via the use of a lossy coupling liquid. As an alternative to a lossy background medium which also reduces the desired signal level, this paper investigates the use of metallic-backed absorbing metasurfaces as the MWI system enclosure in order to (i) reduce these reflections, and also (ii) to shield the MWI system from external interference. Using simulated data, we then show that standard inverse scattering algorithms, employing the free-space assumption, can successfully process the data collected under the metasurface enclosure and yield acceptable permittivity images. The advantages and disadvantages of absorbing metasurface enclosure, along with the limitations of this study, will also be discussed. Finally, an absorbing metasurface is fabricated and its reflectivity is experimentally evaluated.

This paper presents an electromagnetic inversion algorithm for the design of cascaded metasurfaces that enables the design process to begin from more practical output field specifications such as a desired power pattern or far-field performance criteria. Thus, this method combines the greater field transformation support of multiple metasurfaces with the flexibility of the electromagnetic inverse source framework. To this end, two optimization problems are formed: one associated with the interior space between two metasurfaces, and the other for the exterior space. The cost functionals corresponding to each of these two optimization problems are minimized using the nonlinear conjugate gradient algorithm with analytic expressions for the gradient operators. A total variation regularizer is incorporated into the optimization procedure to favour smooth field variations from one unit cell to the next. The numerical implementation of the developed design procedure is presented in detail along with several two-dimensional (2D) simulated examples to demonstrate the capabilities of the method.

The standard weighted L2 norm total variation multiplicative regularization (MR) term originally developed for microwave imaging algorithms is modified to take into account structural prior information, also known as spatial priors (SP), about the object being imaged. This modification adds one extra term to the integrand of the standard MR, thus, being referred to as an augmented MR (AMR). The main advantage of the proposed approach is that it requires a minimal change to the existing microwave imaging algorithms that are already equipped with the MR. Using two experimental data sets, it is shown that the proposed AMR (i) can handle partial SP, and (ii) can, to some extent, enhance the quantitative accuracy achievable from microwave imaging.