Generalized Theory of PT-Symmetric Radio-Frequency Systems with Divergent Exceptional Points

The emergence of exceptional point (EP) and its divergent form, so-called divergent exceptional point (DEP), in parity-time (PT)-symmetric trimer opens a new pathway for making radio-frequency (RF) telemetric sensor systems with unprecedented sensitivity. Here, we put forward a rigorous and formally exact analysis for PT-symmetric electronic multimers, shedding light on the lower bound of the inductive coupling coefficient required to achieve DEPs. One clear observation is that there exists a subtle compromise among the degree of diverging bifurcation, critical inductive coupling strength, and spectral noises arising from modal interferences. We conclude that an electronic PT-symmetric trimer, although not sufficient to work at the lowest inductive coupling strength, may be the simplest structure that enables the emergence of DEPs. Our findings may provide the theoretical underpinnings and open avenues for various RF telemetry and wireless sensing systems.