This paper describes a methodology of obtaining only third harmonic along with the fundamental using shaped superconductors. It also indicates how one can design a nonlinear superconducting resistor with the required current versus resistance variation.
This paper presents a comprehensive study of microwave nonlinearities in superconductors, with an emphasis on intermodulation distortion and third-harmonic generation. It contains the analysis of various resonant and nonresonant test devices and its validation using numerical simulations based on harmonic balance (HB). The HB simulations made on test devices show that the closed-form equations for intermodulation and third-harmonic generation are only valid at low power levels. The paper also contains examples of application of HB to illustrate that this technique is useful to simulate superconductive devices other than simple test devices, and that the validity of the simulations is not restricted to low drive power levels. Most of the analyses and simulations of this paper are based on electrical parameters that describe the nonlinearities in the superconducting material. These parameters are compatible with many existing models of microwave nonlinearities in superconductors. We discuss the particulars on how to relate these electrical parameters with one of the existing models that postulates that the nonlinear effects are due to a dependence of the penetration depth on the current density in the superconductor.
Local oscillator sources have become a major technological deficit approaching the terahertz frequencies. For applications, where a narrow linewidth is necessary, such as coherent remote sensing, the best solution to signal generation is frequency multiplication, where phase locking can be easily achieved using the fundamental source. We present an alternative to existing frequency multiplier technologies for cryogenic applications. The device is a superconducting waveguide that has kinetic inductance dependent on the rf current through the device. The nonlinear kinetic inductance is anomalous to a nonlinear optical medium, where the Kerr effect causes 3- or 4-wave mixing, as demonstrated in microwave parametric amplifiers utilizing the same nonlinear effect. In 4-wave mixing, three photons at the fundamental frequency are mixed to generate a single photon at the third harmonic. Dispersion engineering is used to achieve wideband phase matching and phase out harmonics higher than the third. The device length is designed to be the point where most photons are up-converted to the third harmonic. Simulations of these devices lead to expected efficiencies as high as 90%. We report results from a NbTiN frequency multiplier from 34.2 to 104 GHz with efficiency better than 50%.