Analog computer studies of frequency multiplication and mixing with the Josephson junction

Using a point-contact Josephson junction (JJ), direct frequency measurement of far-IR laser lines can be performed by mixing the Nth harmonic of a microwave frequency ν2with the laser frequency ν1to produce a beat signal νIFsuch that νIF= ν1- Nν2. Analog computer simulation of the JJ has revealed an efficient mode of frequency multiplication and mixing. This is a condition wherein the self oscillation, νJ, is phase locked to a frequency νJ= ± ℓν2± kν1± m νIFwhere ℓ, k, and m are integers. The analog studies show that this phase locking can occur at very low as well as at high levels of the external drives. The result of the phase lock is an efficient transfer of energy into the νIFoutput signal. At least one experimental result has verified the occurrence of phase locking to difference frequencies. It is also well known that the optimum bias points in mixing lie between the ν2steps. The interpretation of these results and the direct role played by νJin mixing experiments has not, however, been generally recognized.