  The analytical structure of a static transverse component of polarization
tensor in complex momentum plane is numerically studied, which is
holographically determined by a Einstein-Maxwell theory in asymptotically
$D=3+1$ dimensional Anti-de Sitter spacetime. This strongly-coupled transverse
polarization shows a pair of conjugate simple poles on the imaginary-axis at
low temperature, which is different with the longitudinal component of the
corresponding polarization and the counterpart in its weakly-coupled version.
