Unusual power dependence of two-tone intermodulation in high-Tc superconducting microwave resonators

We study the power dependence of two-tone intermodulation arising in high-Tc superconducting microwave resonators as a function of each tone separately. In the regime where the intermodulation power varies as the square of the input power for equally strong tones, we observe unexpected behavior of the power dependence on the individual tones. We show that this behavior can be understood in terms of a nonlinear inductance which varies linearly with the magnitude of the input current. These findings provide a consistent phenomenological picture of the unusual power dependence and should place constraints on a microscopic description of nonlinear behavior in high-Tc films where the intermodulation products vary like the square of the input power.