  We address the propagation of light beams in longitudinally modulated
PT-symmetric lattices, built as arrays of couplers with periodically varying
separation between their channels, and show a number of possibilities for
efficient diffraction control available in such non-conservative structures.
The dynamics of light in such lattices crucially depends on the ratio of the
switching length for the straight segments of each coupler and the longitudinal
lattice period. Depending on the longitudinal period, one can achieve either
beam rectification, when the input light propagates at a fixed angle across the
structure without diffractive broadening, or dynamic localization, when the
initial intensity distribution is periodically restored after each longitudinal
period. Importantly, the transition between these two different propagation
regimes can be achieved by tuning only gain and losses acting in the system,
provided that the PT-symmetry remains unbroken. The impact of Kerr nonlinearity
is also discussed.
