Exceptional points in transistor-metamaterial-inspired transmission lines

Motivated by our recent findings in [Phys. Rev. Lett. 128, 013902, 2022], which introduced a new class of electromagnetic bulk materials whose response is similar to conventional semiconductor transistors, here we propose a one-dimensional (1D) version of such materials based on transmission lines coupled with FET isolators. We demonstrate that the response of this 1D system is nonreciprocal and non-Hermitian, analogous to the idealized transistor-metamaterial, and is also characterized by a broken time-reversal symmetry. We analyze the wave propagation in the system and find that the interaction between the eigenmodes can either lead to gain or loss, depending on the propagation distance. Furthermore, it is also shown that the system may be operated at an exceptional point, wherein the response becomes singular, and the power gain is maximized. Finally, we demonstrate that the exceptional point coincides with the point of operation of typical microwave amplifiers, such as the distributed amplifier.