Incorporating Meta‐Atom Interactions in Rapid Optimization of Large‐Scale Disordered Metasurfaces Based on Deep Interactive Learning

Surface symmetry breaking and disorder have been recently explored to overcome operation bandwidth, unwanted diffraction, and polarization dependence issues in the conventional metasurface designs thanks to their increasing degrees of design freedom. However, efficient full‐wave simulation and optimization of electrically large electromagnetic structures have been a longstanding problem. Herein, an interactive learning approach is developed to build new meta‐atom datasets which include the effect of mutual coupling. A deep learning‐based model is developed to extract features of incident/reflection waves and their neighboring interaction responses from a limited number of known meta‐atoms. Finally, the deep neural network is incorporated with optimization algorithms to design, as an example, large‐scale metasurfaces for beam manipulation and wideband scattering reduction. The results demonstrate that the proposed architecture can be successfully applied to rapidly design aperture‐efficient metasurfaces or metalenses at large scales of over tens of thousands of meta‐atoms.


Introduction
The emergence of metasurface has broken the tradition of electromagnetic (EM) designs, of which subwavelength meta-atoms are closely packed in a structured and unstructured manner on thin material substrates. [1] It has become possible through the design of various metasurface structures to manipulate and control all kinds of EM waves with arbitrary refractive indices, transmission, and reflection properties. Based on its unique EM properties and low-cost manufacturing processes, abundant applications have been proposed, such as vortex beam generation, [2] polarization conversion, [3,4] scattering reduction, [5] and antenna performance enhancement. [6] More recently, nonlinear devices and active materials have been incorporated with the design of metasufaces. For instance, Cui et al. reported a novel structure through integrating programmable active components to metasurface in order to digitally control the phase state (0°or 180°) of meta-atoms at microwave frequencies. [7] Indeed, programmable metasurfaces like this have great potential for applications including microwave imaging, [8,9] information modulation in wireless communication, [10,11] and secured wave manipulation. [12,13] In contrast to the conventional metasurface with "unit cell" boundaries, the nonperiodic metasurface has the advantage of possessing more degrees of design freedom, which can be applied to further improve device performance. [14][15][16] Nevertheless, one of the strategies in these designs is to "unwillingly" neglect the influence of meta-atoms interactions, which will significantly decrease the efficiency. [17] Alternatively, one may adopt heuristic approaches based on experimental and numerical tools to straightforwardly try out different topologies and arrangements of meta-atoms, [18,19] which leads to the requirement of excessive computing resources and manpower for metasurfaces scale-up design and optimization.
However, due to the diversity of meta-atoms permutations in the nonidentical metasurface, research on the subject has been mostly restricted to small-scale metasurface designs. Optimizing very large-scale metasurfaces with the consideration of interaction among meta-atoms, i.e., unwanted mutual coupling effects, still can become extremely difficult. [20,21] To account for the interaction among meta-atoms, some researchers have combined "brute force" optimization methods with numerical simulations. [22] Nevertheless, such processes require extensive computational power and are time-consuming, when it comes to designing very large-scale metasurface structures. Although a "supercell" approach may be proposed to partially alleviate the problem, it is only limited to the design of quasiperiodic metasurfaces, which is unhelpful for random or inhomogeneous metasurfaces, such as metalens. [23] Alternatively, one may rely on high-performance computing with graphics processing units (GPUs) to realize hardware acceleration on full-wave modeling of DOI: 10.1002/adpr.202200099 Surface symmetry breaking and disorder have been recently explored to overcome operation bandwidth, unwanted diffraction, and polarization dependence issues in the conventional metasurface designs thanks to their increasing degrees of design freedom. However, efficient full-wave simulation and optimization of electrically large electromagnetic structures have been a longstanding problem. Herein, an interactive learning approach is developed to build new meta-atom datasets which include the effect of mutual coupling. A deep learningbased model is developed to extract features of incident/reflection waves and their neighboring interaction responses from a limited number of known meta-atoms. Finally, the deep neural network is incorporated with optimization algorithms to design, as an example, large-scale metasurfaces for beam manipulation and wideband scattering reduction. The results demonstrate that the proposed architecture can be successfully applied to rapidly design apertureefficient metasurfaces or metalenses at large scales of over tens of thousands of meta-atoms.
metasurfaces. [18] Despite all efforts, rapid optimization of large-scale disordered metasurfaces by incorporating meta-atom interactions remains to be challenging, especially with a moderate computing power and conventional computational electromagnetics (CEM) tools.
To overcome the bottleneck, machine learning (ML) approaches have been introduced to CEM in recent years. [24][25][26][27][28][29][30][31][32][33] As one of the mainstream approaches nowadays in data classification and regression problems, the deep learning (DL) technique can efficiently and accurately solve EM inverse problems where scattering EM fields are used as the input and the ground-truth scatterer as the output. [24,26] Moreover, it can also be used to solve both forward and backward problems of metasurface design. [27,32] In the forward design, the corresponding S-parameters can be predicted from its geometric configuration, and the complex EM environment can also be replaced by multiple convolution neural networks (CNNs) and nonlinear activation functions. [28,29] Meanwhile, it has been reported that the mutual coupling of arbitrarily shaped metaatoms can be considered using the wavelength-scale-based 1D training dataset, and calculated with a well-trained DL model. [17] Additionally, the deep neural network (DNN)-based method of resolving optical coupling on aperiodic nanostructures of arbitrary size is also investigated. [30] Another novel DL architecture, which is widely used in the design of metasurfaces, is the generative adversarial network (GAN). [31] Coupled with the inverse modeling problem is metasurface optimization using traditional algorithms, such as genetic algorithm (GA) and particle swarm optimization (PSO), against spectral or radiation requirements. [25,29] Meanwhile, a benchmarking DL-based structures investigation on the performance of the accuracy, diversity, and robustness has been elaborated to assist researchers appropriately to pick up suitable models. [34] Although ML algorithms have successfully been applied for the design of metasurfaces, they still face several challenges in this field. First, currently proposed ML solutions are not easily generalizable or scalable to large EM structures. For example, Zhang et al. applied Resnet-101 Network and successfully predict its reflection phase responses with 90.05% accuracy, and the average phase error is 1.4933°. [29] However, as soon as the coding sequence is changed, the proposed neural network will be totally invalid and it becomes inevitable to restart the whole ML process cycle by building the dataset and training the network again with hyperparameters optimization, which is time-consuming and computationally inefficient. Second, it is very difficult to connect the weights in the neural networks with physical interpretation of EM properties in the design of metasurfaces. [28,29,35,36] A neural network architecture in these applications can be considered as a "black box" in the sense, [37] and, therefore, in the design of metasurface, although one may be able to build a robust network with multiple hidden layers to predict spectrum information or radiation pattern from the structures of metasurface, it is difficult to anticipate EM properties of meta-atoms under the influence of mutual coupling.
In this article, we propose and demonstrate a deep interactive learning approach to develop a semianalytical model for rapid calculation and optimization of metasurfaces incorporating meta-atom interactions. Specifically, in the hidden layers of our DL model, we employ two respective blocks to train corresponding weights of reflection phase and amplitude for different meta-atoms, to "quantify" the mutual coupling of each atom. We will then assign the weighted coefficients to the conventional analytical formula for array synthesis. Having validated our approach, we demonstrate its effectiveness and versatility by the inverse design of large disordered metasurfaces for optimizing antenna radiation and radar cross-section (RCS) reduction with GA. Two samples which based on RCS optimization are fabricated and measured to demonstrate the correctness of our approach.

Approximate Analytical Formula
An antenna array consists of a group of similar antennas that may be placed in a pattern (line, plane, circle, etc.). Although it is theoretically possible to calculate the far-field scattering pattern based on formulation of antenna arrays, [7] the difference between the theoretical and experimental results can be quite large due to the effect of mutual coupling. To take into account the effect of mutual coupling among meta-atoms, the hypothesis is that we can deploy a coupling coefficient matrix to approximate real reflection responses of different meta-atoms which are closely packed. That is, if we can obtain the actual EM responses of the meta-atoms, the analytical equation can directly calculate the RCS of the metasurface accurately. Then, the field scattering pattern from the metasurface F true ( f, θ, φ) under a plane wave incident illuminates can be simplified as where |E m,n ( f, θ, φ)| is the amplitude of scattering pattern for (m,n)th element in the numerical simulation with the Bloch theorem, f is the frequency of interest, θ and φ are the elevation and azimuth angles for an arbitrary scattering direction, respectively, D is the side length of a single element, λ is the wavelength, ϕ m,n ( f ) is the reflection phase of (m,n)th lattice extracted from numerical simulation with the Bloch theorem, F true ( f, θ, φ) is the scattering pattern of metasurface in which the mutual coupling effect is taken into account, and ΔA m,n ( f ) and Δϕ m,n ( f ) are the amplitude and phase weights for (m,n)th element, respectively. In the conventional design of a fully reflective metasurface, the reflection amplitude is set to 1, and the reflection phase is equal to ϕ m,n ( f ) which is obtained assuming a periodic array of identical meta-atoms under periodic boundary conditions. It has, however, reported that nonidentical neighbors of the meta-atom have an impact on the actual reflection amplitude and phase, different from those under the assumption of periodic array. [38] By simply introducing the correction weights ΔA m,n ( f ) and Δϕ m,n ( f ), we can quantify the amplitude and phase errors of (m,n)th element to account for the effect of mutual coupling. We can then apply analytical formula to replace the time-consuming and computationally inefficient numerical simulations on any nonidentical metasurface structures, which can dramatically accelerate the numerical simulation and optimization. Moreover, our approach can be easily scaled up for larger structures without any extra numerical effort. The detailed explanation for the approximate formula can be seen in Supporting Information 1.

Deep Learning Model Propagation and Learned Parameters Design
According to Equation (1), the scattering pattern F true ( f, θ, φ) of a metasurface can be calculated if we know the actual reflection amplitude [1 þ ΔA m,n ( f )] and reflection phase [1 þ Δϕ m,n ( f )] ϕ m,n ( f ) of meta-atoms. In Equation (1), the amplitude weights ΔA m,n ( f ) and phase weights Δϕ m,n ( f ) are unknowns introduced to account for the mutual coupling effect and are dependent on the type of meta-atom and its neighboring meta-atoms. Therefore, estimating ΔA m,n ( f ) and Δϕ m,n ( f ) accurately would enable us to apply the proposed analytical Equation (1) for precise calculation of the scattering pattern F true ( f, θ, φ) of a metasurface of arbitrary size with little to no increase in computational cost.
In order to obtain the ΔA m,n ( f ) and Δϕ m,n ( f ) of different types of meta-atoms, we propose a DNN-based approach to efficiently predict the elements' real reflection amplitude and phase responses under the influence of mutual coupling. The key idea here is to implement an analytical layer that mimics Equation (1) within the DNN while letting the DNN to learn unknown weights (vectors) ΔA m,n ( f ) and Δϕ m,n ( f ) automatically from data. We trained our proposed network using 450 simulated samples with 10 Â 10 dimensions, which consists of 350 training and 100 validation patterns. The detailed information about the dataset can be seen in Section 4.1. The input of the DNN is a binary representation of the metasurface and the target output is the corresponding RCS as simulated in CST Microwave Studio Suite. Because ΔA m,n ( f ) and Δϕ m,n ( f ) are extracted from a neural network trained with full wave simulation data, ΔA m,n ( f ) and Δϕ m,n ( f ) can be substituted in Equation (1) to obtain results that agree well with time-consuming full wave simulations. The overview of the new design is shown in Figure 1. Considering that the nearest neighboring meta-atoms contribute to major coupling effects, [39] as well as the computational cost on the DL model, the mutual coupling effects on the 3 Â 3 neighboring environment of meta-atoms are studied in the proposed structure. At the beginning of the process, the 10 Â 10 scale binary coding matrix representing the nonidentical metasurface structure is first converted into an integer coding matrix by using a 3 Â 3-dimensional sliding window with a step size of 1. The numbers 0-8, and numbers 9-17, are used to present the number of surrounding "Unit 1" elements for the "Unit 0" and "Unit 1" in the 3 Â 3 region, respectively. For instance, in a 3 Â 3 area, if the center element is "Unit 0", and there are two "Unit 1" elements in the eight neighboring lattices, this position is then converted to digital "2" in the integer coding sequence, and if the center element is "Unit 1", and the eight neighboring lattices exist three "Unit 1" elements, this position is then converted to digital "12" in the integer coding sequence. Additionally, elements of "Unit 0" are padded when the center element is at the edge. Likewise, the proposed integer coding matrix representation of the metasurface encodes details about the neighborhood of each meta-atom. It is worth noting that although the introduction of the virtual "Unit 0" at the edge of the metasurfaces allows for the projection of the metasurface to an integer coding matrix without loss of dimensionality, extra errors may appear on the meta-atoms that are adjacent to the border because those virtual elements are not physically present. After the 10 Â 10 integer coding matrix is flattened into an integer sequence with a dimension of 100 Â 1, one-hot encoding features are then created based on the type of the center meta-atom and its surrounding elements. As there are 18 possible unique arrangements around a single element, the array size is 100 Â 18 after one-hot encoding. One-hot encoding is a process of converting categorical data into a set of binary vectors in which each vector has only a single digital "1" and all the others are digital "0". Afterward, the onehot encoding matrix with size of 100 Â 18 is input into the proposed DL modules consisting of two respective dense layers to calculate the actual reflection amplitude [1 þ ΔA m,n ( f )] and reflection phase coefficient [1 þ Δϕ m,n ( f )] of meta-atoms, where 100 is the number of samples and 18 represents the input to a fully connected layer. In fully connected layers, the neurons of the layer are connected to every neuron of its preceding layer. By combining the fully connected layers and activation layers appropriately, the ΔA m,n ( f ) and Δϕ m,n ( f ) can be learned from those neurons. Finally, the scattering patterns of metasurfaces can be computed with tensor format in analytical layer by combining the actual EM responses of meta-atoms and their corresponding position information through Equation (1). As there are no additional parameters involved in the math computations on tensor segments, this step is nontrainable. Generally, the proposed fully connected layers are only responsible for training reflection responses of "Unit 0" and "Unit 1" at 18 different states. The approximate analytical calculation based on Equation (1) is the last step to generate scattering pattern of metasurface array. After training is finished, the learnable parameters ω l1 to ω l6 corresponding to the fully connected layer l 1 to l 6 can be directly extracted from the model. For arbitrary one-hot vector x with shape of 1 Â 18, its corresponding 1 Â 41-dimensional amplitude weight ΔA and phase weight Δϕ can then be calculated as Hence, the 18 unique arrangements of elements' actual amplitude weights and phase weights can be sequentially calculated from Equation (2) and (3). Likewise, once a metasurface of arbitrary size P Â Q is converted to the corresponding integer coding matrix, its ΔA and Δϕ vectors for each meta-atom can be found by Equation (2) and (3), respectively, given the trained weights ω l1 till ω l6 extracted from the DNN trained with 10 Â 10 metasurface data. This facilitates us to substitute ΔA and Δϕ vectors (obtained by DNN) to Equation (1) and calculate the radiation pattern of an arbitrary size metasurface accounting mutual coupling. More detailed information of weights plots at various neighbors can be seen in the Supporting Information 2. It should be noted that this article proposes a general framework applied to all EM problems related to array synthesis and optimization. Here, we use a scattering metasurface with RCS reduction as an example for illustration. Detailed network structure and computational graph of this model can be found in the Supporting Information 3.

Characterizing Model Performance
To validate our approach, we start with benchmarking studies on small-sized samples. Two different types of metasurface structures, "V" shape-based metasurface and square ring shape-based metasurface are studied in this article, respectively. For the metasurface with "V"-shaped meta-atoms, the spacing between adjacent elements is 15 mm and the RCS with 41 points ranged from 6 GHz to 14 GHz in a step of 0.2 GHz is evaluated. To verify the generality of our approach, we also extend the framework for the design of metasurface consisting of metaatoms of "square ring" with 31 points ranged from 5 to 20 GHz in a step of 0.5 GHz. [40] The period of meta-atoms of "square ring" is 6.6 mm in this design. The well-predicted performance on the test set indicates both weights of reflection amplitude and phase are well trained in this model, and the www.advancedsciencenews.com www.adpr-journal.com detailed loss plot of "V" shape atoms are presented in Supporting Information 4. In terms of amplitude weights or phase weights, we can obtain nine different coupling states for each "unit" after training. To clearly show the variation of weights at different iterations, the averaged reflection amplitude weights and phase weights are calculated and presented in Figure 2. Additionally, this figure also displays predicted RCS of a test sample. After the first iteration, there is a large difference between the predicted and target RCS. While after ten iterations, as we can see in Figure 2, the predicted and target RCS gradually get close to each other, but the average reflection amplitude weights curve still has large fluctuations. For 50 and 800 iterations, only marginally difference exists in terms of RCS results and average reflection amplitude and phase weights. The mean square error (MSE) for 1, 10, 50, and 800 iterations is 10.71, 1.25, 0.28, and 0.21, respectively. Meanwhile, except for 7 and 9.2 GHz frequency points, it can be seen from Figure 2 that the variation of average phase weights in most of frequency points is smaller than 0.1. While the average amplitude weights change rapidly in 9.2, 10, 12.4, and 13.2 GHz, it indicates the rapid variation of amplitude values at these frequency points.

Model Scaling to Large Disordered Metasurfaces
The good agreement between predicted and simulated results demonstrates that the fully connected layers in the proposed model can successfully generate the reflection amplitude and phase of two different "units" under the influence of mutual coupling. The amplitude weights ΔA and phase weights Δϕ for "Unit 0" and "Unit 1" with different numbers of neighboring elements can be directly calculated based on the weights (ω l1 to ω l6 ) in the fully connected layers. Substituting the learned reflection parameters into the analytical formula Equation (1), the calculation of the far-field scattering pattern of metasurfaces in arbitrary grid dimensions with uniform distribution is straightforward, and it does not incur too much of additional computation effort. Figure 3 presents the analytically calculated RCS from predicted reflection weights and simulated RCS of metasurfaces at various scales with randomly selected coding sequences, and the calculation of RCS for every sample is less than 1 s. As the size of the metasurfaces enlarges, the overall RCS of the metasurfaces also increases, while the resonant frequency points of metasurfaces decided by the structure of metaatoms are not changed. In order to compare the performance of predicted results on different scales, the cosine similarity is used to measure the similarity between the predicted results and simulated results. The cosine similarity is 0.999, 0.997, 0.997, and 0.996 for the test samples 15 Â 15, 20 Â 20, 30 Â 30, and 40 Â 40, shown in Figure 3, respectively. It is apparent that the predicted results from learned reflection weights show good agreement with the simulated results. For the "V" shape-based structure, we randomly select one test sample for each ratio between two "units" ranging from 0.1 to 0.9 in steps of 0.1 at various scales. The average cosine similarity for 15 Â 15, Figure 2. Scatter plots of variation of reflection amplitude, phase weights, and RCS results of a test sample after 1, 10, 50, and 800 iterations. The amplitude weights ΔA( f ) and phase weights Δϕ( f ) trained in the DL module are shown in the first row and second row, respectively. The different coupling states (different 3 Â 3 environments) are represented by different colored "circle" and "star" symbols, while the black line and red line represent the average curve for "Unit 0" and "Unit 1," respectively. The corresponding variation of predicted RCS results for metasurface can be seen in the third row. To verify the universality of the proposed model, we also apply it to the design of large-scale metasurfaces with meta-atoms of "square ring" with a wideband phase difference of π. Similar to the previous "V" shape structure process, we can retrain DL model based on the square ring structure dataset with 10 Â 10 dimension to obtain the actual reflection amplitude and phase weights of square ring-based meta-atoms. According to the extracted reflection amplitude weights ΔA( f ) and phase weights Δϕ( f ), the larger scale square ring-based metasurface can be calculated in a relatively short period of time. Like previous "V" shape-based metasurface, as the scale of metasurfaces enlarges, the average RCS of square ring-based metasurfaces increases as well. Moreover, influenced by the wideband phase difference of π of square ring-based meta-atoms, different order of meta-atoms shows more diverse RCS results. As shown in Figure 4

Optimizing Design Based on Learned Reflective Parameters
One of the benefits to develop analytical formula to accelerate large-scale metasurface designs is that we can now apply conventional optimization tools, i.e., the GA, instead of using full-wave simulations to achieve optimal solutions, according to arbitrary objective functions such as reflection beam manipulation and scattering reduction, etc. By incorporating analytical solution and appropriate objective functions, the GA can achieve beam pattern steering at expected direction, and the detailed information for the process of GA is shown in Supporting Information 6. To verify the correctness of optimization process, two V shapebased nonperiodic samples are optimized to generate dual-beam pattern steering at (45°, 45°) and (45°, 225°) and four-beam pattern steering at (30°, 45°), (30°, 135°), (30°, 225°), and (30°, 315°), respectively, at the normal incidence. The simulation results are shown in Figure 5a,b. At the operating frequency 12.4 GHz, the simulated results agree well with the expected scattering direction from the optimization target in GA.
While applying GA to optimize RCS reduction of metasurfaces with two different types of meta-atoms, we show, in Figure 6b, that significant RCS reduction for the metasurface   www.advancedsciencenews.com www.adpr-journal.com of the experimental results coincides well with the simulated result. The scattering patterns of two samples at operating frequency points are illustrated in Figure 6d,e. In addition, the comparison between the optimized design and chessboard structure is shown in the Supporting Information 7. In contrast to the chessboard structure metasurface, where mutual coupling has a strong negative impact on performance, the optimized design still exhibits expected results with mutual coupling effects. Additionally, this phenomenon also demonstrates the performance of disordered metasurface can be improved through the appropriate use of coupling effects.

Conclusion
In this article, we develop a semianalytical approach based on the DL model to account for the influence of mutual coupling on target meta-atoms and apply it to optimize large-scale disordered metasurfaces for beam control and RCS reduction. The novelty of our approach is that a quantitative analysis of the mutual coupling effects between different units is investigated using the DNN technique in a quite small dataset. For the binary nonidentical metasurface with 10 Â 10 scale, there are a total of nearly 2 100 possible permutations. Here, we only collect 500 samples  as the dataset to train the EM-driven deep interactive learningbased model, which is far from meeting the amount of data needed for a strict network training strategy. Moreover, instead of regarding the neural network as the "black box" to characterize the models solely by its inputs and outputs during the training step, the reflection responses of meta-atoms given by the weights values in the cascaded dense layers describe certain physical mechanism of EM scattering. The weights extracted from fully trained networks can straightforwardly substitute the amplitude and phase weights in the proposed analytical function to calculate the pattern function and RCS of metasurface in a very short period without the restriction of meta-atoms arrangement and dimensions. The approach is validated by optimizing two large disordered metasurfaces with different types of meta-atoms, which demonstrate its versatility and flexibility. We believe that the proposed approach can be applied to any metasurface design including metalens with enormously largely disordered structures and closely packed meta-atoms.

Experimental Section
Data Gathering: In order to train the proposed model, a large number of metasurface pattern matrices and the corresponding RCS are required to establish the dataset. As our model validated two distinct types of metasurface structure, we separately generate two datasets here. Generally, we collect 500 pairs of metasurface pattern matrices and their corresponding RCS in each dataset. The y-polarized plane wave illuminates the surface along þz axis in both datasets, and all x, y, and z directions assume an open space condition. For V shape-based metasurface, the metasurface pattern matrices consist of 10 Â 10 binary coding matrix, and the dimension of RCS is 1 Â 41, where 41 represents the frequency of interest. It is worth noting that the proportions between "Unit 0" and "Unit 1" in the metasurface range from 0.1 to 0.9 to make sure we can cover as much of the sample distribution as possible. For square ring-based metasurface, the metasurface pattern matrices are identical to those for V shape-based metasurface, while the shape of RCS is 1 Â 31. To form our datasets, we generate 350 samples as a training set, 150 samples as a testing set, and the rest 50 samples as a validation set. The detailed information of metasurface structure is shown in the Supporting Information 8.
Neural Network Training: In the training process, we train the network structure of our model using the simulation dataset with a minibatch size of 1 on the deep learning frameworks TensorFlow and Keras. Specifically, we employ the Adam optimizer for stochastic gradient descent for training our model. All the hyperparameters are deploy default parameters except for the learning rate. In the first 200 epochs, the learning rate is 0.01, and then decreases to 0.002 in the next 200 epochs. In the last 400 epochs, the learning rate is set to 0.0002. The detailed model structure information is shown in the Supporting Information 3. Later, based on learned reflective parameters, the optimization of RCS reduction and beam optimization are processed in MATLAB with GA. We trained the GA for 800 iterations, which takes %14 h on an i7-8750 H CPU.
Structure of Metasurfaces: In this article, we simulate two different types of structures: one is V shape-based metasurface and the other is ring shape-based structure (see Supporting Information 9 for detailed structure and corresponding reflection responses of meta-atoms).
Experimental Setup: The experimental setup is shown in Figure 6a; two broadband horn antennas connected to a vector network analyzer (VNA) are used as transmitter and receiver antennas, respectively. The transmitter antenna is fixed to the top of the sample to generate quasiplane wave, and the receiver antenna can move along the arch to obtain reflective signals of sample on the azimuth plane.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.