Dark Schrödinger solitons and harmonic generation in left-handed nonlinear transmission line

Abstract

In this paper, we analyze the wave propagation in a practical left-handed nonlinear transmission line with series nonlinear capacitance composed of two back-to-back connected varactor diodes. Detailed circuit analysis of the transmission line shows that by properly choosing the circuit parameters, the equation governing the wave envelope evolution can be reduced to a one-dimensional nonlinear Schrödinger equation, which supports dark solitons propagation. By transient circuit simulation, the soliton evolution has been demonstrated both in time and frequency domain with input signal of either a continuous wave or a Gaussian modulated pulse. It is also shown that increasing the dissipation in the transmission line metamaterials is helpful to form steady dark solitons in short transmission lines. The establishing of the Schrödinger solitons also results in the third harmonic generation in the transmission line, which may find practical applications in communication systems.