Article Open Access Published: 09 July 2020
Classification and characterization of electromagnetic materials
Yosef T. Aladadi & Majeed A. S. Alkanhal
Scientific Reports volume 10, Article number: 11406 (2020) Cite this article

[Abstract]
In this paper, we present an efficient method to classify complex electromagnetic materials. This method is based on the directional interaction of incident circularly polarized waves with the materials being tested. The presented method relies on an algorithm that classifies the test materials to one of the following categories: isotropic, chiral, bi-isotropic, symmetric anisotropic or general bianisotropic. The transmitted and reflected fields of right-handed and left-handed circularly polarized waves normally incident from three orthogonal orientations are utilized to determine the reflection/transmission coefficients and complex refractive indices. Both analytical and numerical solutions are used to compute fields of the circularly polarized waves from the arbitrary complex material slab. The complex materials are discriminated accordingly and then classified under an appropriate category. Additionally, new results for material characterization by extracting the scalar/tensorial parameters of bi-isotropic and gyrotropic materials are presented.

[Introduction]
Recent advances in the interaction of electromagnetic fields with complex composite media suggest the feasibility of creating novel materials with unusual electromagnetic properties and the possibility of constructing new electromagnetic devices using such materials. These improved materials can be engineered to possess several unique electromagnetic properties that make them suitable candidates for numerous applications in modern technology systems. Applications related to the fields of photonics1, optoelectronics2,3, radar cross-section reduction4,5,6,7, gigahertz devices8, antenna reconfiguration9, terahertz plasmonic filters10, and biosensors11 are the leading beneficiaries of such developments. These complex electromagnetic materials are often further classified to isotropic, bi-isotropic, anisotropic and bianisotropic based on their macroscopic electromagnetic properties12,13,14, which provide the description of certain materials through their constitutive relations.

Isotropic materials like unstressed glass and plastic, water and air, and fluids at rest, behave precisely in the same manner regardless of the direction of the wave propagation axis, because their permittivities and permeabilities are identical in all directions. In contrast, in anisotropic materials like wood, the electromagnetic properties are different in different directions. Materials with crystalline structure are biaxial anisotropic materials. For example, yttrium orthosilicate (YSO) is a dielectric material with biaxial anisotropy at optical frequencies. This well-known rare-earth host material has shown promising performance in quantum-engineered optical devices development15. Yttrium aluminum perovskite (YAP) crystal material, with orthorhombic symmetry, is designated as a symmetric anisotropic material16. Gyrotropic magnetized ferrites are asymmetric anisotropic materials that have been used in microwave engineering for years because of their non-reciprocal behavior that makes them very useful in the design of microwave devices like isolators, polarizers, and circulators17. Graphene in the static magnetic field is a gyrotropic and uniaxial anisotropic material in the absence of the external magnetic field18. More recently, materials with optical activity (chirality) have been considered for application in microwave and infrared regions. Chiral materials are a particular case of the more general bi-isotropic materials. A chiral composite can be constructed by embedding chiral objects such as wire helixes, Möbius strips, or irregular tetrahedrons in a nonchiral host isotropic medium19. A medium is bianisotropic when its constitutive relations are generalized 3?×?3 matrices or tensors. An artificial composite metamaterial composed of split ring resonators with rods20 can be modeled as bianisotropic material. Efficient methods for the classification and characterization of such materials based on determining their macroscopic electromagnetic properties are of growing importance but still in evolution12,13,14. The traditional characterization techniques used to measure the electromagnetic properties of scalar and tensorial permittivity and permeability of complex materials have received significant efforts in recent years1,3,21,22,23,24,25,26,27,28,29,30,31. These techniques are, essentially, based on measuring the scattering parameters from the investigated materials in free space22,28 using single or multiple normal32 and oblique33 linearly polarized wave incidence. The characterization procedures start from deducing the effective refractive index and effective wave impedance from the transmitted and reflected fields. However, these methods are liable to obtaining multiple branching ambiguity, which limits using them at high frequencies, especially for thick material slabs. In addition, the methods that use optimization schemes are usually accompanied by heavy computation costs and often yield multiple solutions. Efforts have been introduced to overcome these discontinuities based on the Kramers–Kronig (K–K) relation22,34, and phase correction techniques35,36,37. However, the K–K method is saturated at high frequencies, which limits its performance especially for thick structures. The phase correction techniques are sensitive to simple errors in phase data and they, also, are susceptible to slip to error solutions at zero refractive index values or if they were initialized at an arbitrary starting frequency36. The existing characterization methods attempt to find the practicable effective (equivalent) scalar and/or tensorial parameters that model the test material regardless of their essential classification or discrimination according to their inherent electromagnetic directional behavior.

This paper presents a novel method to classify complex electromagnetic materials based on their behavioral (directional) interaction with incident circularly polarized waves. The method is based on a classification algorithm of the unknown materials to one of the following categories: isotropic, chiral, bi-isotropic, symmetric anisotropic, or general bianisotropic. This method utilizes the scattering parameters of simple normal-incident (LCP/RCP) circularly polarized plane wave measurements from three different orthogonal axes and their corresponding refractive indices. The proposed scheme is a simple and direct classification process without demanding a complete intricate extraction process for the tensor elements that are usually accompanied by multiple solutions that need carful processing. Beside that, after classification, the characterization process (extraction of the tensor elements) becomes much easier when the investigated material model is predetarmined. Solutions from an analytical method based on the transmission matrix method (TMM) and numerical results from a full wave simulator are used to compute the transmitted and reflected fields of the circularly polarized waves from the arbitrary complex material slab. The different complex materials are discriminated accordingly and then classified under an appropriate category. Additionally, new accurate material characterization results are obtained by retrieving the scalar/tensorial parameters for bi-isotropic and asymmetric anisotropic materials.

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