  Process of quantum tunneling of particles in various physical systems can be
effectively controlled even by a weak and slow varying in time electromagnetic
signal if to adapt specially its shape to a particular system. During an
under-barrier motion of a particle such signal provides a "coherent" assistance
of tunneling by the multi-quanta absorption resulting in a strong enhancement
of the tunneling probability. The semiclassical approach based on trajectories
in the complex time is developed for tunneling in a non-stationary field.
Enhancement of tunneling occurs when a singularity of the signal coincides in
position at the complex time plane with a singularity of the classical
Newtonian trajectory of the particle. The developed theory is also applicable
to the over-barrier reflection of particles and to reflection of classical
waves (electromagnetic, hydrodynamic, etc.) from a spatially-smooth medium.
