Magnetic field modulation effects on the microwave transmission through superconducting thin films of Y-Ba-Cu-O

We have measured the magnitude and phase of the microwave transmission through thin films of Y-Ba-Cu-O on MgO substrate in the presence of a dc magnetic field $H_0$ and an oscillating magnetic field. The oscillating field modulates the microwave transmission in the superconducting state with the generation of many high-order even harmonics for $H_0$=0. For $H_0$≠0 there is a symmetry-breaking and additional odd-harmonic generation. This strong nonlinear behavior may be explained by a model which assumes an array of Josephson junctions and vortex motion in the presence of a magnetic field. An estimate of the Josephson-junction area is obtained from the field dependence of the amplitude of the second harmonic.