  The Maxwell equations based 3D analytical solution for the terahertz
half-cycle electromagnetic wave transition radiation pulse has been found. This
solution describes generation and propagation of transition radiation into free
space from laser-produced relativistic electron bunch crossing a target-vacuum
interface as a result of ultrashort laser pulse interaction with a thin
high-conductivity target. The analytical solution found complements the theory
of laser initiated transition radiation by describing the generated THz wave
shape at the arbitrary distance from the generating target surface domain
including near-field zone rather than the standard far-field characterization.
The analytical research has also been supplemented with the 3D simulations
using the finite-diference time-domain (FDTD) method, which makes it possible
for description of much wider spatial domain as compared to that from the
particle-in-cell (PIC) approach. The results reported fundamentally shed light
on the interfere of an electron bunch field and THz field of broadband
transition radiation from laser-plasma interaction studied for a long time in
the experiments with solid density plasma and may in future inspire them to
targeted measurements and investigations of unique super intense half-cycle THz
radiation waves near the laser target.
