Shock Wave Generation and Cut off Condition in Nonlinear
Series Connected Discrete Josephson Transmission Line

Hamid Reza Mohebbi and A. Hamed Majedi, Member, IEEE

Abstract— The nonlinear wave propagation in a series-connected Discrete Josephson Junction Transmission Line (DJTL) is investigated. This structure consists of a superconductive Coplanar Waveguide (CPW), that is periodically loaded by either single or lumped arrays of Josephson junctions (JJs). Each junction is represented by the basic circuit model which leads to a nonlinear inductor element. Having a significant number of junctions per wavelength, the discrete transmission line (TL) can be considered as a uniform nonlinear transmission line. The nonlinear wave equations are solved numerically by Finite Difference Time Domain (FDTD) method. Features and characteristics such as cut-off propagation, dispersive behavior and shock wave formation, which are expected from wave propagation through the nonlinear DJTL, are discussed.

Index Terms— Applied superconductivity, Microwave superconductivity, Discrete Josephson transmission line, Finite Difference Time Domain Method, Nonlinear microwave propagation, Josephson junction devices, Nonlinear transmission lines, Shock waves, Dispersion.

Manuscript received 19 August 2008. This work was supported in part by the Ontario Graduate Scholarship (OGS), QuantumWorks, and Institute for Quantum Computing (IQC) at the University of Waterloo. The authors are with the Department of Electrical and Computer Engineering and Institute for Quantum Computing (IQC), University of Waterloo, Waterloo, ON, N2L 3G1 Canada (e-mail: hmohebbi@maxwell.uwaterloo.ca; ahmajedi@maxwell.uwaterloo.ca).

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