  The discovery of gravitational waves, which are ripples of space-time itself,
opened a new window to test general relativity, because it predicts that there
are only plus and cross polarizations for gravitational waves. For alternative
theories of gravity, there may be up to six polarizations. The measurement of
the polarization is one of the major scientific goals for future gravitational
wave detectors. To evaluate the capability of the detector, we need to use the
frequency dependent response functions averaged over the source direction and
polarization angle. We derive the full analytical formulas of the averaged
response functions for all six possible polarizations and present their
asymptotic behaviors based on these analytical formulas. Compared with the
numerical simulation, the full analytical formulas are more efficient and valid
for any equal-arm interferometric gravitational wave detector without optical
cavities in the arms and for a time-delay-interferometry Michelson combination.
