  We show that doping of hole charge carriers leads to formation of electric
dipolar clusters in cuprates. They are created by many-body interactions
between the dopant ion outside and holes inside the CuO planes. Because of the
two-fold degeneracy holes in the CuO plane cluster into four-particles
resonance valence bond plaquettes bound with dopant ions. Such dipoles may
order into charge-density waves (CDW) or stripes or form a disordered state
depending on doping and temperature. The lowest energy of the ordered system
corresponds to a local anti-ferroelectric ordering. The mobility of individual
disordered dipoles is very low at low temperatures and they prefer first to
bind into dipole-dipole pairs. Electromagnetic radiation interacts strongly
with electric dipoles and when the sample is subjected to it the mobility
changes significantly. This leads to a fractal growth of dipolar clusters. The
existence of electric dipoles and CDW induce two phase transitions with
increasing temperature, melting of the ordered state and disappearance of the
dipolar state. Ferroelectricity at low doping is a natural consequence of such
dipole moments. We develop a theory based on two-level systems and
dipole-dipole interaction to explain the behavior of the polarization as a
function of temperature and electric field.
