Nonlinear response of superconducting (YBCO) fractal microstrip resonators: Distributed current ABCD-matrix model

In this work, we experimentally investigated the nonlinear microwave response of YBa2Cu3O7–x Hilbert fractal superconducting microstrip resonators with sharp and rounded corners. We developed a resonator model that incorporates a distributed current-dependent nonlinear propagation parameter, γ(I), and used the ABCD matrix method for numerical simulations. Our findings demonstrated that the nonlinear response of the resonators can be effectively modeled with a current-proportional propagation parameter, γ∼I. In addition, we observed a significant reduction in the nonlinear response when transitioning from sharp to rounded corners in the resonator design. This work provides valuable insights into improving the design of superconducting resonators by minimizing their nonlinearities, which is crucial for advancing applications in microwave and quantum technologies.