  Nonsequential two-photon ionization of inner-shell $np$ subshell of neutral
atoms by circularly polarized light is investigated. Detection of subsequent
fluorescence as a signature of the process is proposed and the dependence of
fluorescence degree of polarization on incident photon beam energy is studied.
It is generally expected that the degree of polarization remains approximately
constant, except when the beam energy is tuned to an intermediate $n's$
resonance. However, strong unexpected change in the polarization degree is
discovered for nonsequential two-photon ionization at specific incident beam
energy due to a zero contribution of the otherwise dominant ionization channel.
Polarization degree of the fluorescence depends less on the beam parameters and
its measurements at this specific beam energy, whose position is very sensitive
to the details of the employed theory, are highly desirable for evaluation of
theoretical calculations of nonlinear ionization at hitherto unreachable
accuracy.
