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An innovative method has developed recently for biasing the varactors of a reconfigurable intelligent surface (RIS) by utilizing resonant standing waves on the “biasing transmission line (TL)” [E. Ayanoglu, F. Capolino, and A. L. Swindlehurst, “Wave-controlled metasurface-based reconfigurable intelligent surfaces,” IEEE Wireless Communications, vol. 29, no. 4, pp. 86-92,2022] located beneath the reflective surface. Using this approach, each RIS element does not require separate external biasing. For estimating the RIS reflection properties controlled by varactors, we analyze a planar array with phase gradient in one direction, of side length L, of reconfigurable elements. We employ the analytical model for predicting the reflection coefficients of the unit cells presented in [D. Hanna, M. Saavedra-Melo, F. Shan, and F. Capolino, “A versatile polynomial model for reflection by a reflective intelligent surface with varactors,” IEEE AP-S/URSI, 2022] and investigate how the standing wave biasing approach compares with the traditional way to generate field patterns of the reflected wave. 

A novel method for biasing the varactors of a reconfigurable intelligent surface (RIS) by using resonant standing waves on the biasing transmission line (TL) at a layer below the RF reflective surface to eliminate the need to bring external bias for each element of the RIS is described. We use an analytical model of the RIS to compare the field pattern of the reflected wave by (i) considering the ideal case, (ii) the case where reflection accounts for the varactor's model, and (iii) the case as in (ii) but where the biasing voltage distribution is constructed by using the wave control (i.e., standing waves). 

Exceptional points of degeneracy (EPD) can enhance the sensitivity of circuits by orders of magnitude. We show various configurations of coupled LC resonators via a gyrator that support EPDs of second and third-order. Each resonator includes a capacitor and inductor with a positive or negative value, and the corresponding EPD frequency could be real or imaginary. When a perturbation occurs in the second-order EPD gyrator-based circuit, we show that there are two real-valued frequencies shifted from the EPD one, following a square root law. This is contrary to what happens in a Parity-Time (PT) symmetric circuits where the two perturbed resonances are complex valued. We show how to get a stable EPD by coupling two unstable resonators, how to get an unstable EPD with an imaginary frequency, and how to get an EPD with a real frequency using an asymmetric gyrator. The relevant Puiseux fractional power series expansion shows the EPD occurrence and the circuit's sensitivity to perturbations. Our findings pave the way for new types of high-sensitive devices that can be used to sense physical, chemical, or biological changes. 

We study the rise of exceptional points of degeneracy (EPD) in various distinct circuit configurations such as gyrator-based coupled resonators, coupled resonators with PT-symmetry, and in a single resonator with a time-varying component. In particular, we analyze their high sensitivity to changes in resistance, capacitance, and inductance and show the high sensitivity of the resonance frequency to perturbations. We also investigate stability and instability conditions for these configurations; for example, the effect of losses in the gyrator-based circuit leads to instability, and it may break the symmetry in the PT-symmetry-based circuit, also resulting in instabilities. Instability in the PT-symmetry circuit is also generated by breaking PT-symmetry when one element (e.g., a capacitor) is perturbed due to sensing. We have turned this instability “inconvenience” to an advantage, and we investigate the effect of nonlinear gain in the PT-symmetry coupled-resonator circuit and how this leads to an oscillator with oscillation frequency very sensitive to perturbation. The circuits studied in this paper have the potential to lead the way for a more efficient generation of high-sensitivity sensors that can detect very small changes in chemical, biological, or physical quantities.