Xunwang Dang

Quasi-Periodic Array Modeling Using Reduced Basis Method

Many electromagnetic devices such as reflectarray antennas, metasurfaces, etc., can be modeled as quasi-periodic arrays. In these devices, similar array elements with a few varying geometrical parameters are positioned in a periodic lattice. Compared to modeling of periodic arrays, efficient modeling of quasi-periodic arrays can be very challenging due to the loss of periodicity in the array. In this work, we applied the reduced basis method to integral equation solvers for quasi-periodic array modeling. In this scheme, a new basis set based on the varying parameters is constructed through an offline process. Because of the similarities among elements, the number of basis functions for each element can be much less than direct modeling from geometrical mesh. Numerical examples show that both the computational and memory efficiency are improved compared to direct modeling using method of moments.

2D quasi-periodic array modeling using reduced basis method

Many electromagnetic devices such as reflectarray antennas, metasurfaces, etc., can be modeled as quasi-periodic arrays. In these devices, similar array elements with a few varying geometrical parameters are positioned in a periodic lattice. Compared to modeling of periodic arrays, efficient modeling of quasi-periodic arrays can be very challenging due to the loss of periodicity in the array. In this work, we applied the reduced basis method to integral equation solvers for quasi-periodic array modeling. In this scheme, a new basis set based on the varying parameters is constructed through an offline process. Because of the similarities among elements, the number of basis functions for each element can be much less than direct modeling from geometrical mesh. Numerical examples show that both the computational and memory efficiency are improved compared to direct modeling using method of moments.

A fast algorithm for quasi-periodic array modeling using reduced basis method

Planar quasi-periodic arrays are widely used in many electromagnetic devices such as metasurfaces, reflectarray antennas, nano particle arrays, and etc. They constitute similar elements located on periodic grids. Simulation of wave interaction with such arrays are very challenging as they are large multi-scale problems. In this work, we introduce a fast algorithm for quasi-periodic array modeling. This algorithm numerically recovers periodicity using linear current projection and reduced basis method. The reduced basis method can also take advantage of the similarities among elements and reduce the number of unknowns to solve. These two schemes together allow us to recall the power of fast Fourier transform as we solve periodic arrays. The computational complexity of this algorithm is O(NlogN) where N is the number of elements in the array. Numerical example shows the potential to solve large scale quasi-periodic arrays.

Modeling and analysis of quasi-periodic arrays

Planar quasi-periodic arrays are widely used in many electromagnetic devices such as metasurfaces, reflectarray antennas, nano particle arrays, etc. They comprise similar elements located on periodic grids. In this work, we compare the reflection phase of elements in the array between the designed value and the practical one. This difference is mainly because real quasi-periodic arrays break the periodicity assumption used in computing the designed element phase. To study this error, we develop a formulation based on Floquet theory to compute the reflection phase of a unit-cell in a practical array. We observe that the error can be significant for elements with high-Q resonances and can deteriorate the performance of reflectarray antennas or metasurfaces. As a remedy, we develop a workflow for element phase correction based on full-wave simulation of the entire array. An improvement in performance is observed for arrays with high-Q resonances.

Quasi-periodic array modeling using reduced basis from elemental array

Many electromagnetic devices can be modeled as quasi-periodic arrays such as reflectarray antennas, metasurfaces, and etc. These devices have similar array elements positioned on periodic grids. Compared with modeling of periodic arrays, efficient modeling of quasi-periodic arrays can be very challenging due to the loss of periodicity in the array. In this work we applied the reduced basis method to model quasi-periodic arrays based on the fact that a reduced basis set can be constructed from array elements due to their similarities. A new reduced basis set is constructed by considering the coupling between elements as well. Numerical examples also show a significant speed up in simulating 2D quasi-periodic arrays compared with direct modeling using integral equation solvers.

Application of the reduced basis method to ID quasi-periodic array modeling

The reduced basis method is a model-order reduction technique that converts the original system equations into smaller ones using a reduced basis set. This basis set is usually derived from a set of solutions of the system equation with different values of control parameters. If the system model changes affinely with the parameter values, a reduced-order model can be derived. In this abstract, we apply the reduced basis method to method of moments for quasi-periodic array modeling. With this method, a new basis set for a single element is constructed through an offline process. Because of the similarities among elements, the number of basis functions for each element can be much less than directing modeling from geometrical mesh. Numerical example shows that both the computational and memory efficiency is improved compared with direct modeling using method of moments.

Numerical study on the field projection error in the equivalence principle algorithm

The equivalence principle algorithm is a domain decomposition scheme based on integral equation formulation. One of the key building blocks in this algorithm is the equivalence principle operator that computes the scattered equivalent current on a virtual closed surfaces. In this abstract, we studied the numerical error of the inside-out procedure in the equivalence principle operator. This procedure projects smooth electromagnetic fields in three dimensions onto two-dimensional equivalence currents that may contain geometrical discontinuities. We observe that the field projection error is related with the geometry of the equivalence surfaces as well as the choice of expansion functions for electric and magnetic currents. A careful choice of these parameters could help to further improve the accuracy of the equivalence principle algorithm.