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We examine the polarization signal of the cosmic microwave backgroundradiation associated with distant clusters.  The polarization is induced by the Thomson scattering of microwave photonswith ionized gas of clusters and contains information of quadrupole temperatureanisotropies observed at the clusters. The three-dimensional map of the signalare expressed in terms of the spin-weighted harmonics for its angulardependence. Its radial dependence is expanded perturbatively with respect tothe distances (equivalently redshifts) to the clusters.  The independent information that we can extract out from the map is clarifiedexplicitly.Comment: 14 pages, 4 figures, to appear in Phys.Rev.

Polarization signal of distant clusters and reconstruction of primordial potential fluctuations