Analysis of parametric effect in high temperature superconducting thin films

In this reference processes in a high temperature superconducting (HTSC) thin film circuit with nonlinear parametric resistance and inductance are theoretically examined. The fact that the active and reactive components of the impedance of HTSC film are modulated by the law of optical signal is accepted as a basic precondition for this discussion. By the analogy with the Josephson phenomenon we give certain phases for superconducting and normal states and accept that the alternating components of the photocurrent I-Phi and photovoltage U created by the radiation can be presented as a phase difference between superconducting and normal states respectively. Based on this, the equation for the equivalent circuit of the film presents a complicated differential heterogeneous equation of second rank. As a particular state the homogenous equation has been investigated and the Mathieu equation has been obtained. In a result the expression for the gain in power is obtained, which depends on the parameters of the optical signal and thin film. The possibility to control the gain in power by the selection of various values of the depth of modulation of the active and reactive components of the surface impedance, the intensity of radiation and other parameters of the HTSC film is shown.