Third Harmonic Microwave Generation by Superconductors

Third harmonic microwave power at 35 GHz generated by a superconductor irradiated by microwave power at 11 -2/3 GHz was detected as a function of temperature (T), 11-2/3 GHz power (P(,1)) and applied static magnetic field (H(,DC)). The superconductor was variously film or bulk samples of Pb, Pb(,0.9)Bi(,0.1), bulk samples of La(,0.92)Gd(,0.08)Sn(,3), and a sputtered film of Er(,0.43)Ho(,0.57)Rh(,4)B(,4). The measurements were made using a two phase detection system that allowed for the measurement of the magnitude of the generated third harmonic magnetic field (VBAR)H(,3)(VBAR). The detection system could detect third harmonic power at the level (TURN) 10('-18) Watts. Central to the detector methods was a double resonant microwave cavity which coupled the incident power into the sample and the generated power out to the detector. Film samples of Pb were the most extensively studied. The temperature dependence of the signal ((PROPORTIONAL) (VBAR)H(,3)(VBAR)) was a peak just below T(,c) when P(,1) was sufficiently small. As P(,1) was raised the peak broadened to form a plateau where the signal came on at T(,c) and stayed large at low temperature. At fixed temperature the signal versus P(,1) showed a succession of peaks with decreasing amplitude. The signal was a periodic function of H(,DC). The period ranged from 2.2 mG to 0.4 G for a particular sample measured at different times. Other samples showed modulation with periods less than or about 0.5 G. The data from other samples was mostly confined to the temperature dependence of the signal. These data also showed a peak at low P(,1) and a plateau at high P(,1). The sputtered film of (ErHo)(,1)Rh(,4)B(,4) showed sensitivity to changes in the local magnetic field of order 10 mG. The theory of Entin-Wohlman based on modulation of the order parameter as expressed by a time dependent Ginzberg-Landau equation was applied to the data on temperature dependence. The theory was found not to fit the data. A model based on a RF SQUID circuit is developed. The model exhibits periodic modulation of the third harmonic flux by applied DC flux, oscillatory dependence on the applied AC flux, and peak or plateau dependence on temperature depending on the level of AC flux. The model qualitatively explains much of the data.