Asymmetric parametric amplification in nonlinear left-handed transmission lines

Abstract

We study parametric amplification in nonlinear left-handed transmission lines, which serve as model systems for nonlinear negative index metamaterials. We experimentally demonstrate amplification of a weak pump signal in three regimes: with the signal in the left-handed band, with the signal in the stop band, and with the signal at a defect frequency. In particular, we demonstrate the amplification of the incident wave by up to 15dB in the left-handed regime.Left-handed transmission lines are compact systems showing regimes of backward-wave propagation similar to negative-index metamaterials. They have been applied to a number of engineering applications, including the study of leaky wave antennas, compact resonators, and dual-band couplers (see, e.g., Ref.[1] and references therein). In a number of these applications nonlinear elements have been introduced to create tunable structures [2,3] and, in addition, they have been used as a platform for the study of nonlinear wave propagation in the systems supporting the propagation of backward waves [4,5,6].Parametric gain is a nonlinear process whereby a highenergy pump wave exchanges energy with a weaker signal wave through modulation of the material or circuit parameters, thus amplifying it. This effect is commonly used in optical systems, and it has been proposed as a way to mitigate the losses in negative-index metamaterials. In particular, in Ref. [7] parametric gain was exhibited in the left-handed region for a short structure consisting of seven periods with an external DC bias, and parametric generation of backward waves in similar transmission lines was studied both experimentally and theoretically in Ref. [8].Recently, we have demonstrated a bistable regime of left-handed propagation in an asymmetric nonlinear lefthanded transmission line due to the existence of multiple dynamic states [9]. In this Letter, we demonstrate that such structures may exhibit substantial parametric gain in three different regimes of the signal wave: with the signal in the left-handed band, with the signal in the stop band, and with the signal at a defect frequency.In particular, we demonstrate the amplification of the incident wave by up to 15dB in the left-handed regime.Our nonlinear transmission line consists of 20 periods of elementary cells, each cell containing a series varactor diode (SMV1405), shunt inductor (18nH chip type), and a 10 mm section of 50Ω microstrip transmission line, as shown in Fig. 1. The resultant transmission response is presented by a solid curve in Fig. 2. The dispersion relation is of great importance to all parametric processes, * Electronic address: david.a.powell@anu.edu.au and it can be calculated analytically as [1]:where κ is the Bloch wavenumber (in radians per period), L L and C L are the shunt inductance and series capacitance introduced to create the left-handed line;

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].…”

Theoretical thermodynamics connections between Dual (Left-Handed) and Direct (Right Handed) systems: Entropy, temperature, pressure and heat capacity

“…Related studies have been realized by comparing its electromagnetic characteristic. In fact, broadly, spatially extended electrical setups allow us to study Right-Handed (RH) and LeftHanded (LH) systems [5][6][7][8][9][10][11][12] including nonlinear ones [13,14]. Moreover, intensive researches related to excitations on electrical networks and their connections to broad physical problems have been well settled.…”

“…The case when γ¼1 has been studied widely in wave-guides-transport [2,[5][6][7][8][9][10][11][12]19] with practical consequences. Nevertheless in this work we consider the generalization for arbitrary γ and, more important, associated thermodynamics properties.…”

Resonances in Left-Handed Waves Developed in Nonlinear Electrical Lattices

“…The line has noteworthy dispersive property that the propagating wave exhibits LH (RH) properties when its carrier frequency is greater (less) than the line's characteristic frequencies. Furthermore, several activities have clarified the wave dynamics in CRLH lines with nonlinearity introduced by voltage-controlled devices [5][6][7][8][9][10][11][12][13]. In our case, the shunt capacitor each cell of a CRLH line contains is replaced with the Schottky varactor [10,14].…”