Frequency Selective Surfaces (FSSs) and, more generally, metasurfaces, are commonly used in a variety of applications in order to restrict, absorb, or redirect the electromagnetic (EM) fields’ propagation. Recent advances in 5G, Internet-of-Things, increased use of wearable connected devices, and the reduction in fabrication costs made FSSs and metasurfaces very attractive to the designers of new-generation electronics. However, significant challenges for accurate simulation of FSS-equipped devices still exist (A. Menshov, F. Sheikh Hosseini Lori, and J. Aronsson in EMC-SIPI, Jul. 2019).

FSSs and metasurfaces are layered structures that consist of carefully tuned metallic unit elements (with features smaller than the operating wavelength) deployed on a dielectric substrate. Unlike more general metasurfaces, FSSs assume the periodicity of the pattern in the arrangement of unit elements. Traditionally, the numerical EM simulation of FSS structures is performed via modal analysis and Floquet ports (P. Harms, R. Mittra, and W. Ko, IEEE TAP, vol. 42, no. 9, 1317–1324, Sep. 1994) that accurately analyze one unit cell and use periodicity to characterize the whole structure.

Such analysis results in the reduced accuracy since significant edge- and finite-size effects are not captured. Moreover, these types of methods are hard to be generalized for metasurfaces with complicated arrangements of unit elements, especially when metasurfaces are deployed on substrates with non-constant curvature and infinite quasi-periodic approximation does not apply. At the same time, the initial design of the unit elements and choice of the substrate often has to take curvature into account (H. Zahra et al. in USNC-URSI Rad. Sci. Meet., Jul. 2019).

To combat these limitations, the entire finite-size metasurface can be meshed and used for a full-wave EM simulation. Such simulation can also allow modeling the frequency selective metasurface interaction with other device components more accurately. For practical examples, such discretization usually results in several millions of unknowns and poses a challenge for EM simulation software due to the sheer number of degrees of freedom in a resultant linear system and moderately large electrical size of the metasurface structure.

In this paper, we demonstrate a rigorous simulation for frequency-selective surfaces and metasurfaces deployed on a different curved NURBS (non-uniform rational B-spline) surfaces. We compare the solution obtained via CEMWorks’ Wave3D solver with the one obtained using Floquet ports in different settings and demonstrate the performance of the metasurface on a practical example.