Experimental Demonstration of Exceptional Points of Degeneracy in Linear Time Periodic Systems and Exceptional Sensitivity

Abstract

We present the experimental demonstration of the occurrence of exceptional points of degeneracy (EPDs) in a single resonator by introducing a linear time-periodic variation of one of its components, in contrast to EPDs in parity time (PT)-symmetric systems that require two coupled resonators with precise values of gain and loss. In the proposed scheme, only the tuning of the modulation frequency is required that is easily achieved in electronic systems. The EPD is a point in a system parameters' space at which two or more eigenstates coalesce, and this leads to unique properties not occurring at other non-degenerate operating points. We show theoretically and experimentally the existence of a second order EPD in a time-varying single resonator. Furthermore, we measure the sensitivity of the proposed system to a small structural perturbation and show that the operation of the system at an EPD dramatically boosts its sensitivity performance to very small perturbations. Also, we show experimentally how this unique sensitivity induced by an EPD can be used to devise new exceptionally-sensitive sensors based on a single resonator by simply applying time modulation.

Ultra-Sensitive Radio Frequency Biosensor at an Exceptional Point of Degeneracy induced by Time Modulation

“…The sensitivity of the resonance frequency in a single, time-varying, LC resonator working at an EPD to perturbations has been demonstrated to be much higher than that of a single, time-invariant (i.e., standard), LC resonator. The practical implementation of this sensing technology seems straightforward since the time-modulated capacitance can be realized with a simple multiplier controlled by a modulated voltage pump [45] for example. The working principle for the proposed ultra-sensitive biosensor is general and can be easily implemented in existing systems to enhance sensitivity, paving the way to a new class of ultra-sensitive sensors.…”

“…To assess a fair comparison, we assume that the capacitance in the LTI-LC resonator is equal to the time average capacitance in the LTP-LC resonator, i.e., C 0 = (C 1 +C 2 )/2, and all the other parameters are the same as those of the LTP-LC case in Section II, i.e., L 0 = 15µH, R = 0.1Ω, C bio = 0.3 nF and G bio = 67 µS. at a second order EPD was observed experimentally in [45] in general terms, hence here we investigate the sensitivity to the variation of a MUT in a biosensing scenario. One may note that the value of α 1 in Eq.…”

“…[34], and the experimental demonstration of the occurrence of such EPD has been shown in Ref. [45]. In this paper we apply the EPD concept developed in these two papers to conceive a new class of biosensors.…”

“…It has been demonstrated that the perturbation of the eigenvalues of (3), hence the perturbation of the resonant frequencies, cannot be represented with a Taylor expansion of the degenerate resonant frequency around f e [47, chapter II.1.1]. The first order approximation of f p (δ) near the EPD is derived by a Puiseux series [47, chapter II.1.1] (also called "fractional power expansion") using the explicit recursive formulas given in [48,45] as…”

Demonstration of Exceptional Points of Degeneracy in Gyrator-Based Circuit for High-Sensitivity Applications

“…In other words, the EPD frequency coincides with double zeros, or double poles, of the frequency spectrum, depending on the way the circuit is described. In the past, EPD frequencies have been found by using loss and gain in a PT symmetry scheme [8], [9], [16], by including time-periodic modulation of a circuit element [34], [5], [17], and here by considering a gyrator and negative L and C.…”