  Emission of terahertz waves in free electron lasers (FELs) with both planar
(linear) and helical undulators has been explored. The analysis employs
Lienard-Wiechert fields to characterize FEL radiation within the THz region.
Specifically, the study delves into the analytical examination of radiation
pattern of THz waves, which provides insight into the angular distribution of
radiation energy. The variations of radiation pattern for various parameters
such as different harmonics, Lorentz factor, magnetic parameter, and total
number of periods of planar and helical undulators were investigated. The
Fourier transform of free electron laser electric field is showcased across
four distinct sets of FEL parameters. The interplay between electron beam and
undulators parameters sheds light on how these factors influence the
directionality of THz waves. Simulation results indicate that planar undulators
often produce radiation with noticeable side lobes, especially at higher
harmonics, while helical undulators typically exhibit reduced side lobes,
resulting in a more focused main radiation peak. However, the radiation pattern
of THz waves tends to concentrate predominantly in the forward direction and
the polarization of the emitted radiation is determined by the properties of
the undulator and electron beam, rather than the specific undulator geometry.
The study underscores that an optimal selection of undulator and beam
parameters can effectively maximize the angular distribution of emitted
radiation.
