  We present an analysis of the circular polarization of gravitational-waves
(GWs) using results from three-dimensional (3D), general relativistic (GR)
core-collapse simulations of a non-rotating $15 M_{\odot}$ star. For the signal
detection, we perform a coherent network analysis taking into account the four
interferometers of LIGO Hanford, LIGO Livingston, VIRGO, and KAGRA. We focus on
the Stokes $V$ parameter, which directly characterizes the asymmetry of the GW
circular polarization. We find that the amplitude of the GW polarization
becomes bigger for our 3D-GR model that exhibits strong activity of the
standing accretion shock instability (SASI). Our results suggest that the
SASI-induced accretion flows to the proto-neutron star (PNS) lead to a
characteristic, low-frequency modulation (100 $\sim$ 200 Hz) in both the
waveform and the GW circular polarization. During the vigorous SASI phase, we
observe that the GW polarization switches from the right- to left-handed mode,
which is clearly visible in the spectrogram. By estimating the signal-to-noise
ratio of the GW polarization, we demonstrate that the detection horizon of the
circular polarization extends by more than a factor of several times farther
comparing to that of the GW amplitude. Our results suggest that the GW circular
polarization, if detected, could provide a new probe into the pre-explosion
hydrodynamics such as the SASI activity and the $g$-mode oscillation of the
PNS.
