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Tunable devices and materials have always been extremely important for a variety of applications in the optical as well as the µ-wave and mm-wave bands. With the arrival of 5G communications networks and the ubiquitous use of wireless gadgets and applications ranging from smartphones to the implementation of the Internet of Things (IoT), the need for compact, versatile, and lightweight devices is imperative. Liquid Crystals (LCs) are anisotropic and tunable, and these properties make them an attractive proposition for use in portable devices and communication hubs. In this paper, three such LC-based devices operating in the 5GHz I 30GHz (5G) bands are presented: A frequency-agile patch antenna, a variable phase shifter, and a beam­ steerable leaky wave antenna. In all cases, tunability is achieved via the application of a low-strength external bias electric field. This affects the dielectric properties of the crystal by re-orienting its molecules, the macroscopic orientation of which is denoted by a unit vector called the director. The dielectric properties of the LC-cell are characterized by its relative permittivity tensor, which is a function of the directors' orientation. The latter is determined at every point of the cell by solving a coupled system of partial differential equations (PDEs) numerically. The obtained relative permittivity tensor is input into a high-frequency full­ wave electromagnetic simulator based on the finite-element method (FEM). Finally, the simulation results are analyzed and the performance and capabilities of the applications are discussed.

In this Letter, an investigation is performed on the utilization of nematic liquid crystal (NLC) cells in the design of leaky-wave antennas (LWAs) for millimeter-wave (mm-wave) radiation in order to dynamically control its beam scanning capability at a single frequency. A NLC compound is sandwiched between two single-sided copper-plated substrates allowing a traveling wave to be guided through a substrate-integrated waveguide. The tuning capabilities of the structure, based on the use of K15 or GT7-29001 as the middle layer, were evaluated for different biasing conditions demonstrating the associated dynamic scanning of the main beam. A quasi-periodic LWA was designed to operate in the 5G mm-wave band, thus supporting a fast-wave propagation with tunable phase constant and dynamic beam steering at a single frequency. The simulated results clearly illustrate a dynamic beam scanning range of 45° through the use of an external bias voltage ranging between 0 and 40 V. These results are quite promising creating a fertile ground for the utilization of NLCs in the design and fabrication of LWAs for 5G wireless communication networks.

A robust two-dimensional (2D) formulation for the electrical characterization of nematic liquid crystals (N-LCs) under low-frequency (LF) AC biasing conditions is proposed. The finite-difference (FD) method is first implemented to solve Poisson's equation in the domain of interest in order to obtain the governing LF electric field, which affects the local dielectric properties of the anisotropic material. Then, the nonlinear Euler–Lagrange partial differential equation (PDE), governing the orientation of the directors, is solved using one of three FD schemes with relaxation proposed in this paper. Once the N-LC layer is characterized, the average refractive index as a function of the x -coordinate is calculated assuming a normally incident monochromatic laser beam. The results are compared with published data in the literature obtained using a finite element method (FEM). Solution of the PDE governing the orientation of the directors in a non-uniform 2D electric field is obtained using either strong anchoring or soft anchoring. An investigation of the effects of boundary conditions on the average refractive index is presented.

A nematic liquid crystal (N-LC) cell is used as a substrate to a microstrip patch antenna in order to control its resonant frequency through the use of a DC or low-frequency AC bias voltage. The dielectric tensor properties of the liquid crystal (LC) are dependent on the orientation of the LC molecules, called the directors. The directors' tilt angle is controlled by the amplitude of an externally applied electric field. A finite-difference (FD) scheme with relaxation is formulated in order to solve the highly nonlinear partial differential equation (PDE) that models the directors' tilt angle in the LC. The problem of solving for the directors' field is coupled to an electrostatic boundary value problem (BVP) in a nonhomogeneous anisotropic medium. The orientation of the directors determines the constitutive parameters of the material. The HFSS is then utilized to obtain the radiation characteristics of the antenna under various bias conditions. Comparisons with measurements are provided in order to validate the proposed numerical approach and illustrate the potential use of LC's as tunable materials in microwave and millimeter-wave frequencies.

A frequency-agile microstrip patch antenna printed on a biased nematic liquid crystal (N-LC) substrate is accurately modelled. The dielectric properties of the N-LC are controlled through the strength of the bias voltage. The model is based on the solution of Poisson's equation coupled to a nonlinear partial differential equation (PDE) describing the orientation of the directors in a non-homogeneous electric field. The coupled problem was solved using an iterative finite difference (FD) scheme. The obtained numerical results are compared and verified against measurements already published in the literature.

A Nematic Liquid Crystal (N-LC) compound may be injected into a cavity beneath a printed patch antenna to act as a tunable material whose dielectric properties are controlled by an externally applied electric field. The strength and direction of the applied low-frequency field affects the orientation of the LC molecules known as directors. The orientation of the directors determines the dielectric tensor entries of the LC compound which, in general, is anisotropic and lossy. The directors' tilt angle is governed by a Partial Differential Equation (PDE) which is obtained through minimization of the Oseen-Frank free-energy functional and solved using a Finite-Difference (FD) scheme. The profile of the directors' tilt angle underneath the patch follows a flattened sinusoidal shape along the normal-to-the-patch direction. In previous work by the authors, this non-uniform dielectric profile was averaged out, thus treating the LC substrate as a homogeneous but lossy material. In this paper, we are investigating the accuracy of this model as compared to a more realistic representation of the sinusoidal dielectric profile using multiple homogeneous layers. In addition, we are proposing ways to improve the existing design of the tunable LC patch antenna in order to obtain enhanced radiation characteristics such as gain and radiation efficiency.

TM, electromagnetic scattering from a perfectly conducting wedge with a cylindrical tip is formulated using a mode-matching technique. The eigenmode expansion is then written in a convenient form, where the total field is expressed as a superposition of a wedge-diffraction term based on the uniform theory of diffraction, a geometrical optics term, and a Correction Field term due to the presence of the cylindrical tip. The obtained diffraction coefficient can be easily incorporated into existing ray-tracing, high-frequency codes for the prediction of scattered fields from electrically large structures. The underlined formulation and obtained expressions are verified by comparing numerical results with the finite element method.

A design for a tunable, frequency-agile antenna is proposed. The structure consists of a microstrip patch and a nematic liquid crystal (N-LC) cell which serves as substrate. The N-LC cell is subject to an applied DC or low-frequency AC electric field. The strength of the bias field alters the tilt-angle of the directors, and thus, affects the relative dielectric tensor of the anisotropic material. The non-linear partial differential equation (PDE) governing the behavior of the directors' field is coupled to Poisson's equation for the electric potential in a non-homogeneous anisotropic medium. The coupled problem is solved iteratively using a finite difference (FD) numerical scheme. It is shown that the resonant frequency of the antenna can be altered using relatively low applied voltages. The obtained results are compared with measurements illustrating the potential use of LCs as tunable materials in microwave and millimeter-wave frequencies.

In the current work we examine the application of Nematic Liquid Crystals (N-LCs) to frequency-agile antennas. A patch antenna design with a liquid crystal base is proposed. N-LCs are anisotropic and their electrical properties are determined by the macroscopic orientation of their molecules (director tilt-angle). However, these depend on the applied electric field, which means that the electric properties of the N-LC base can be effectively controlled. The above described problem is governed by a coupled system of PDEs. It is solved iteratively using a finite-difference scheme with relaxation. Once the director field is obtained, the dielectric properties of the material are determined for each value of the bias voltage. The proposed antenna is then simulated using HFSS. The return loss and resonant frequency are computed for each of value of the applied voltage. It is shown that the antennas under consideration can be tuned using relatively low applied voltages. This demonstrates the potential of liquid crystal based antennas in frequency-agile antenna design.

In the current work we propose an efficient and accurate numerical approach to the problem of electrical characterization of Nematic Liquid Crystal (N-LC) microstructures under the influence of low-frequency AC electric fields. N-LCs are anisotropic and their electrical properties are determined by the directors' tilt angles which in turn depend on the applied electric field. Therefore, the problem is governed by a coupled system of two-dimensional PDEs: A Poisson equation with variable coefficients for the electric potential and a highly nonlinear second-order equation for the tilt angle of the directors. Both equations are solved using finite-difference schemes with relaxation and the results are found to be in good agreement with the literature. Various 2-D geometries are considered and it is shown that a low DC voltage is sufficient to tune the average refractive index of the N-LC structures under consideration.

Cholesteric Liquid Crystals (Ch-LC) are anisotropic and inhomogeneous materials with intriguing and useful properties in the visible region of the electromagnetic spectrum. In this paper, we use eigenmode analysis to obtain the supported field expressions in a thin, homogeneous sub-layer of the Ch-LC cell; the liquid crystal is made of multiple sub-layers. The cell is sandwiched between layers of dielectric and is excited by an elliptically polarized plane wave at an oblique incidence. The governing field expressions in the dielectric layers are also obtained using eigenmode analysis. A mode-matching technique (MMT) is then employed to enforce the continuity of the tangential electric and magnetic fields at the interface of two neighboring layers, thus, resulting in a matrix system representative of the problem at hand. Solution of the linear system of equations yields the reflection and transmission coefficients on the two principal planes as well as the expansion coefficients for the modal fields inside the Ch-LC and the dielectric layers. The underlined formulation is verified by comparing results to the open literature.

In the current work, the nonlinear problem of electromagnetic wave propagation in a Nematic Liquid Crystal (NLC) cell is solved numerically. The LC is sandwiched between two glass layers of finite thickness and a linearly polarized beam is obliquely incident to the cell. The dielectric properties of N-LCs depend on the tilt angle of the directors. When the excitation beam enters the cell, and providing the incident intensity is above the Freedericksz threshold, the directors reorient themselves changing the LC's relative permittivity tensor. In turn, this affects beam propagation throughout the crystal. The electromagnetic field is modeled by the time-harmonic Maxwell equations whereas the director field is governed by a nonlinear ordinary differential equation (ODE). Our solution method is iterative, consistently taking into account this interaction between the excitation beam and the director field. The Maxwell equations are solved employing the Mode-Matching Technique (MMT). The solution of the nonlinear differential equation for the director field is obtained with the aid of a finite difference (FD) scheme.

The reflection and transmission spectra from right-handed cholesteric liquid crystals are computed in the visible region for a linearly, circularly, or elliptically polarized incident plane wave at oblique incidence. The liquid crystal cell is sandwiched between dielectric layers of certain thickness and refractive index. The underlined formulation is based on a modal analysis of the governing field expressions in the dielectric and liquid-crystal regions. A representative matrix system is obtained after enforcing the continuity of the tangential electric and magnetic fields at the material interfaces. Solution of the governing matrix system results in the reflectance and transmittance for a given wavelength. Numerical results for both normal and oblique incidence were obtained and compared with data published in the literature. The underlined formulation is effective, accurate, robust, versatile, and computationally efficient.