  A new phenomenological approach to spatially-resolved research of nonlinear
(NL) microwave properties of operating thin-film superconducting resonators is
proposed. The approach is based on frequency and spatial singularity of Laser
Scanning Microscopy (LSM) images that can be extracted from a set of 2-D
patterns representing x-y distribution of the LSM photoresponse, PR(x, y), at
fixed third-order intermodulation (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. It was shown by us earlier
that the total LSM PR(x, y) originates from two independent (resistive, PRR(x,
y), and inductive, PRX(x, y)) contributions which can be extracted directly
from the LSM images acquired at f1 and f2 by using a method of
spatially-resolved complex impedance partition [1]. Here, we show that
practically the same 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 variations of (i) inductive IMD_IND(x, y) and (ii) resistive IMD_RES(x,
y) contributions reflecting the origin of the local sources of microwave NL.
[1] A.P. Zhuravel, S.M. Anlage, and A.V. Ustinov, Appl. Phys. Lett., vol. 88,
p. 212503, 2006.
