Wave propagation in nonlinear left-handed transmission line media

Abstract

Using a one-dimensional system, we demonstrate a wide variety of wave propagation phenomena possible in nonlinear left-handed media. These include effective second-harmonic generation where the fundamental wave and the second-harmonic wave are badly mismatched. We also observe parametric instabilities accompanying intensive harmonic generation. © 2005 American Institute of Physics. ͓DOI: 10.1063/1.2056581͔Negative-refractive-index metamaterials, also known as left-handed ͑LH͒ media, first postulated by Veselago, 1 are now being demonstrated in resonant rf and microwave circuits. [2][3][4][5] The majority of studies and applications of oneand two-dimensional LH media to date are in the linear regime of wave propagation. 6 However, materials that combine nonlinearity with anomalous dispersion exhibited by LH media have also recently attracted much attention. Nonlinear properties of left-handed metamaterials, as well as some approaches to make metamaterials nonlinear, have been discussed in several publications. 5,[7][8][9][10][11][12][13][14][15][16][17] We have presented a theoretical investigation of the basic nonlinear wave propagation phenomena in LH medium, 17 which is based on the dual of the conventional nonlinear transmission line ͑NLTL͒, a left-handed ͑LH͒ NLTL exhibiting anomalous dispersion. The transmission line approach we used proved to be a realistic description of the LH media. It provides insight into the physical phenomena of LH media and is an efficient design tool for LH applications. 4 We found that nonlinear wave form evolution in a LH NLTL can be understood in terms of competition between harmonic generation and parametric instabilities.Confirming our general predictions, 17 we present here the first experimental results for harmonic generation and parametric generation in 1D left-handed NLTL media operating in the microwave regime. Understanding of the nonlinear phenomena in LH NLTL media is very important for both the development of new types of devices and improvement of the performance of recent tunable devices based on LH NLTLs like phase shifters, 5 tunable leaky-wave antennas 4,18 and notch filters. 16 We fabricated one-dimensional nonlinear LH media, four-and six-section LH NLTLs having identical sections ͓Fig. 1͑a͒ shows a 4-section LH NLTL͔. Circuits were realized on Rogers RT/Druid 3010 board with r = 10.2 and thickness h = 1.27 mm. A row of 0.5 mmϫ 0.5 mm copper pads separated by 0.2 mm gaps was formed on the surface of the Rogers board by standard lithography. M/A-COM hyperabrupt junction GaAs flip-chip varactor diodes ͑MA46H120͒ were attached between these pads using conductive silver epoxy. The C j0 of the diodes, from the manufacturer's data sheet, is 1.1 pF, and they show a capacitance ratio C͑0 V͒ / C͑10 V͒ = 7.5. The nonlinear capacitance in each section is formed by two back-to-back diodes with dc bias applied between them. Shunt inductances were implemented with 0.12-mm-diam copper wires connecting the pads to the ground plane on the back side of the board. The via hole...

Tunable transmission and harmonic generation in nonlinear metamaterials

“…Some of these features have already been experimentally observed in nonlinear left-handed transmission lines which are model systems allowing for combining nonlinearity and anomalous dispersion [17,18,19]. Moreover, first results on harmonic generation in infrared were reported in Ref.…”

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].…”

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…”

“…In the results below, we have fixed the parameters related to the soliton's amplitude as η = 1 and ε = 0.02, which correspond to an initial value of the voltage equal to V 0 = 0.5 V (similar, and even smaller, values have also been used in experiments [29][30][31][32][33][34]). Furthermore, we have fixed the initial soliton position to X 0 (0) = 1/2, and we have varied the frequency f and the soliton wave number K (recall that the latter sets the initial soliton momentum).…”