We consider a boundary value problem for the harmonic functions in an unbounded perforated strip Π∖ω¯¯¯ , ω being the “Dirichlet hole”, namely a bounded Lipschitz domain of R , where a Dirichlet condition is prescribed. The other boundary conditions are periodicity conditions on the lateral boundary of Π = (0, H) × (−∞, ∞). We study properties of the coefficients of the so-called polarization matrix, while we highlight the dependence of these coefficients on the dimensions of the hole by means of two examples.