  The optical properties of PT-symmetric periodic stack of the layers with
balanced loss and gain are examined. We demonstrate that tunnelling phenomenon
in periodic structures is connected with excitation of surface waves at the
boundaries separating gain and loss regions within each unit cell and
tunnelling conditions for periodic stack can be reduced to the conditions for
one period. Alternatively, it is shown that coherent perfect absorber laser
states are mediated by excitation of surface modes localised at all internal
boundaries of the structure. The effects of the structure parameters and angle
and direction of incidence on the resonant phenomena and spontaneous symmetry
breaking transition are determined. It is shown that structure periodicity
significantly increases the number of resonant phenomena, especially in stacks
with high real and imaginary parts of dielectric permittivity of the layers.
Gaussian beam dynamics in this type of structure is examined. The beam
splitting in PT-symmetric periodic structure is observed.
