The Maxwell equations-based 3D-analytical solution for the terahertz (THz) 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 which crosses 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. It describes the THz wave half-cycle pulse at the arbitrary distance from a target surface including near-field zone rather than its standard far-field characterization. The analytical research has also been supplemented with the 3D simulations using the finite-difference time-domain method, which makes it possible for description of much wider spatial domain as compared to that from the particle-in-cell approach. The presented result sheds light fundamentally on the interference of the electron bunch field and the generated THz field of broadband transition radiation from laser-plasma interaction. The latter is studied for a long time in the experiments with solid density plasma and the theory developed may inspire to targeted measurements and investigations of unique super intense half-cycle THz radiation waves near the laser target.
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