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.

Tunable Single-Negative Metamaterials Based on Microstrip Transmission Line With Varactor Diodes Loading

“…In recent years, tunable metamaterials have attracted intensive attentions due to their particular applications in optical switching, nonlinear modulation, and so on [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59]. The common mechanism is to introduce certain controllable materials or lumped elements into the metamaterial units.…”

“…People also find in the transmission line metamaterials, varactor diodes can give rise to the tunability as they are very sensitive to a low direct current voltage, for instance, leaky-wave antenna with tunable radiation angle and beamwidth, tuneable directional coupler, and so on [51][52][53][54][55]. Specifically, transmission line metamaterials with varactor diodes can even serve as model systems for investigating several nonlinear phenomena in negative-index metamaterials, like asymmetric parametric amplification, abnormal pulse formation, dark schrodinger solitons and harmonic generation [56][57][58][59].…”

Exact Travelling Envelope Solitons and Kink-soliton Solutions for the Josephson Nonlinear Left-handed Transmission Line

“…We see clearly that the form of the solution depends on certain parameters, and this agrees with ref. [15,16,17]. The existence of soliton envelopes, kink solitons in the JNLHTL is confirmed.…”

Quasidiscrete microwave solitons in a split-ring-resonator-based left-handed coplanar waveguide

“…III) we use a value for the initial voltage equal to V 0 = 0.5 V (in physical units). For such a value of the voltage (similar, and even smaller, values have also been used in relevant experimental works [29][30][31][32][33][34]), it can be found that…”

“…[31] and the relevant work of Ref. [32]); moreover, analytical approximations, based on a continuum nonlinear Schrödinger (NLS) equation, allowed the description of bright [32,33] or dark [32,34] envelope solitons observed in the experiments.…”