Complex Permittivity Measurement Based on EMNZ Metamaterial Using Biased Magnetic Field for Liquid Crystals

Epsilon-near-zero (ENZ) metamaterials, characterized by low permittivity and infinite wavelength, have been proved to exhibit unprecedented impacts on a broad variety of microwave components. Particularly, metal-layer dopants can be employed to excite the epsilon-mu-near-zero (EMNZ) phenomenon. The higher Q value and consistency of the electric field direction of EMNZ metamaterials have created the greater potential to accurately determine the complex permittivity of anisotropic materials, such as liquid crystals (LCs). In this article, a simple permittivity measurement method based on EMNZ metamaterials for LC materials is proposed. Hollow metal waveguides operating close to the cutoff frequency are employed to simulate the ideal ENZ host. On this basis, a metal-layer cavity containing LC material under test (MUT) is employed as the dopant in the ENZ host to achieve the EMNZ effect. Due to the high sensitivity of EMNZ metamaterials, the transmission properties of LC-MUTs can be accurately characterized. More importantly, benefiting from the rotational symmetry of the employed structure, the rotation of the dopant structure with LC-MUTs by 90° can achieve alignment of LC molecules in both horizontal and vertical directions with only one biased magnetic field. Therefore, the calculation of complex permittivities for LC-MUTs can be efficiently executed using the perturbation method. Since the proposed method does not require alignment layers and complex biased circuits, it offers significant advantages in simplicity and efficiency compared to other methods. In summary, a prototype has been fabricated and tested to validate the approach. The complex permittivities of the LC-MUTs are accurately extracted at 4.6 GHz, confirming the effectiveness of the method.