Search for: All records

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. 

We investigate the modal characteristics of coupled-mode guiding structures in which the supported eigenmodes coalesce; the condition we refer to as an exceptional point of degeneracy (EPD). EPD is a point in a system parameter space at which the system eigenmodes coalesce in both their eigenvalues and eigenvectors, where the number of coalescing eigenmodes at the EPD defines the order of the degeneracy. First, we investigate the prospects of gain/loss balance and how it is related to realizing an EPD. Under geometrical symmetry in coupled resonators or coupled waveguides such scheme is often attributed to PT-symmetry; however, we generalize the concept of PT-symmetry to coupled waveguides exhibiting EPDs that do not necessarily have perfect geometrical symmetry. Secondly, we explore the conditions that lead to the existence of EPDs in periodically coupled waveguides that may be lossless and gainless. In general, we investigate properties associated to the emergence of EPDs in various cases: i) uniform, and ii) periodic, lossy or lossless, coupled-mode structures. Generally, the EPD condition is very sensitive to perturbations; however, it was shown recently with experimental and theoretical studies that EPDs' unconventionai properties exist even in the presence of loss and fabrication errors. Extraordinary properties of such systems at EPDs, such as the giant scaling of the quality factor and the high sensitivity to perturbation, provide opportunities for various applications in traveling wave tubes, pulse compressors and generators, oscillators, switches, modulators, lasers, and extremely sensitive sensors.