  We propose a scheme for the resonant generation of counter-polarized single
photons in double asymmetric cavities with a small Kerr optical nonlinearity
(as that created by a semiconductor quantum well) compared to the mode
broadening. Due to the interplay between spatial intercavity tunneling and
polarization coupling, by weakly exciting with circularly polarized light one
of the cavities, we predict strong antibunching of counter-polarized light
emission from the non-pumped auxiliary cavity. This scheme due to quantum
interference is robust against surface scattering of pumping light, which can
be suppressed both by spatial and polarization filters.
