A perturbed Toda lattice model for low loss nonlinear transmission lines

In communications, radar, and digital electronics one traditionally uses discrete components that have unavoidable discontinuities at device or package interfaces. These components are typically used by designing a resonant response in the band of interest. Such resonant responses are inadequate for high data rates and, consequently, distributed devices are a topic of great current interest in high frequency electronics. The semiconductor based distributed devices recently developed have demonstrated fast responses. However, the limiting factor in these devices is the loss introduced by the semiconductor elements that introduces the nonlinearity. Future generations of high speed electronics will require distributed devices with lower loss but equivalent nonlinearity. Our earlier work on electrically tunable coplanar waveguide (CPW) devices incorporating nonlinear dielectric thin films of strontium barium titanate has shown that compact microwave devices based on nonlinear dielectric thin films are fast, broad-band, easily-tunable, and low loss (loss tangent <10^-2). These components are at lower loss than semiconductor components at the microwave frequencies of technological interest, enabling extensive use of nonlinear wave, self-focusing and pulse-shaping concepts when modeling the transmission lines. We are investigating the application of our novel materials technology and modeling to various distributed high speed signal processing problems in such low loss nonlinear transmission lines. We have modeled the transmission lines with discrete elements using a perturbed Toda lattice. Our full numerical simulations have shown that the transmission line is able to shape an input pulse into a train of stable traveling solitons. We have developed a perturbation theory to capture the soliton dynamics. We emphasize that how to couple a signal into the transmission line is an important issue in modeling soliton generation and transmission along the line in a realistic experimental setting.