Electromagnetic metamaterials are being developed and employed in a variety of applications such as sensing, imaging and optics, and signature reduction and cloaking. One application of particular interest to the military is the need for electromagnetic protection to defend battlefield electronics against high-power microwave (HPM) directed-energy weapons (DEWs) currently under development worldwide.

HPM DEWs are a popular branch of DEW research, as microwaves propagate in the atmosphere more readily than high-energy lasers or particle beams. HPM DEWs also offer a viable non-kinetic option when collateral damage is to be avoided or a kinetic option is unavailable. However, prior research has demonstrated that properly constructed electromagnetic metamaterials are able to prevent microwave transmission by redirecting the incident wave into either absorption or reflection. Such metamaterial shields are typically designed as composite structures consisting of patterned, conductive elements integrated with dielectric materials and arrayed in a manner that generates a desired, predictable spectral response. An example of a metamaterial structure can be seen in the accompanying figure. Depending on the application, such metamaterials can become structurally complex, which makes them very difficult to model and simulate, particularly across a large frequency domain.

The purpose of this research is to present a method for retrieving equivalent medium parameters from a metamaterial structure, and then use those parameters in a homogenized finite element model in order to streamline simulation and design of macroscopic-scale objects made of metamaterials. The method proposed uses scattering data from either a simulation of a precise metamaterial structure or an experimental measurement of an actual metamaterial sample. With that data, it develops characteristic reflection and transmission spectra for the metamaterial. The characteristic coefficients are used in a system of equations to calculate the frequency-dependent properties for an equivalent homogeneous material, that would respond to the electromagnetic incident radiation equivalently to the sampled metamaterials. The derived properties can then be applied to a homogeneous layer in a finite element model.

The result is a simplified computer model, which closely mimics the performance of the original, structurally complex, metamaterial sample, but that can be readily modified in scale and geometry without additional computational burden. A designer would thus be able to rapidly conduct simulated scale-model testing of a metamaterial assembly without the need for multiple physical models.

Numerous systems of equations have been developed that consider electromagnetic metamaterials as homogeneous structures parameterized with frequency-dependent material properties such as permittivity and permeability. Such systems typically branch into multiple correct solutions, resulting in ambiguity when attempting to select the correct set of homogenized parameters. Methods for resolving branch ambiguity usually require a material with a known permittivity and permeability at a known frequency, parameters collected from multiple thicknesses of the material, or parameters collected across multiple frequencies. In the case of this method, the initial material properties of the metamaterial were unknown, multiple thicknesses of the material were unavailable, and the simplest metamaterial analyzed was only resonant at a single frequency.

The proposed method instead addresses branch ambiguity as the ratio between the effective medium transmission path and effective wavelength in the medium. Although previously proposed systems deal in effective permittivity and permeability for a metamaterial, the finite element models employed for this research also required electrical conductivity in order to successfully predict the scattering parameters, attenuation within the simulated medium and joule heating in response to absorbed radiation. The proposed method presents an expression for estimating effective conductivity from the impedance and the geometry of the metamaterial unit cell. Finally, prior research rarely extrapolated the performance of the retrieved parameters outside the unit cell analyzed. The proposed method retrieves parameters valid for a homogenized scale model as well as a periodic unit cell.

This work was done by Chester H. Hewitt III for the Naval Postgraduate School. For more information, download the Technical Support Package (free white paper) here under the Optics, Photonics, and Lasers category. NPS-0013


This Brief includes a Technical Support Package (TSP).
Analysis of Broadband Metamaterial Shielding for Counter-Directed Energy Weapons

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This article first appeared in the October, 2020 issue of Aerospace & Defense Technology Magazine.

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