Defect induced asymmetric soliton transmission in the nonlinear circuit

Electrical diode, the first device to rectify the current flux, has significantly revolutionized fundamental science and advanced technology in various aspects of our routine life. Motivated by the one-way rectification effect, considerable effort has been dedicated to the study of the unidirectional transmission in other physical systems for the potential applications, such as the acoustic diode, thermal diode, etc. The nonlinear LC circuit, which has unique advantages in the measurement of energy with which the voltage and current can be achieved by digital oscilloscope conveniently, provides a simple and effective way of studying the nonlinear wave propagation in a dispersive medium. In this paper, we design a defective LC nonlinear circuit deliberately to realize asymmetric transmission of energy, and the energy carrier is nonlinear wave which is so-called soliton, instead of the linear wave in the pass band. The defect-induced localized wave is a kind of intrinsic bound-state wave mode that is evanescent away from the defect site but vibrates around the site with an intrinsic frequency f(r). In the LC circuit, when the defect is close to the driver, with the frequency of driven signal in the forbidden band of system approaching to the intrinsic resonance frequency f(r) of the defect, the resonance induced by the defect enables the circuit to turn on, which is relevant to but somewhat different from what was uncovered by Leon et al. about the intrinsic instability of evanescent waves stirred up directly by a boundary drive. On the other hand, the system acts like an insulator, for the defect is far away from the drive. The defect changes the homogeneity of the line, which allows the soliton to be released in one direction by the local resonance, with the driver being at a lower amplitude. As a result, the introducing of defects significantly improves conversion efficiency from the driver energy into the soliton. To further understand this phenomenon in the defective LC nonlinear circuit, we numerically investigate the relationship among transmission energy, defect coefficient and driver amplitude. Finally, the combined defects are also considered to further adjust the LC nonlinear circuit.