Spatial and frequency dependencies of local photoresponse of hts strip-line resonator in the regime of two-tone microwave intermodulation excitation

High-T_c superconducting (HTS) films have been widely applied in passive microwave electronics including high-Q resonators for mobile telephony. One of the crucial problems in applying such HTS devices remains their nonlinear (NL) response with respect to pumping power. This manifests itself as global intermodulation product distortion (IMD) when two or more high-frequency (HF) signals are NL mixed in the resonant frequency band. A predominately local origin of NL sources through global NL media motivates the development of spatially resolved methods to identify the dominant mechanisms of NL response. We have previously shown that by using different imaging contrast modes of low-temperature (LT) laser scanning microscopy (LSM) one can solve this problem with great success. Additionally, a new paradigm of HF frequency-dependent singularity of LSM images was developed to spatial describe (i) local changes in surface resistance δR_s(x, y) and (ii) HF current density distribution J_HF(x, y) as a function of resonator (x, y) surface coordinates by using a method of spatially-resolved complex impedance partition. Here, we propose a new phenomenological approach to spatially-resolved research of NL microwave properties of operating thin-film superconducting resonators. The approach is based on frequency and spatial uniqueness of LSM images that can be extracted from a set of 2-D patterns representing x-y distribution of the LSM photoresponse, PR_f(x, y), at fixed third-order IMD frequencies 2f₁-f₂ and 2f₂-f1 as a result of two-tone resonator microwave excitation at equidistant frequencies f₁ and f₂ relative to the fundamental resonance, f₀. We show that similar to what is described in manipulation of LSM images at 2f₁-f₂ and 2f₂-f1 can be used to present NL components of IMD LSM PR(x, y) in terms of its independent spatial varia- - tions of (i) inductive PR_IMD,x(x, y) and (ii) resistive PR_IMD,R(x, y) contributions. In particular the realistic spatial coherence between such IMD components and J_HF(x, y) flow, so crucial for determining the NL properties of the device, have not been investigated.