Revealing the THz wave-laser velocity effect during air filamentation via the travelling-wave-antenna model

During femtosecond laser filamentation in air, the velocity ratio (K) between the terahertz (THz) phase velocity and the laser group velocity plays a crucial role in THz wave generation. However, K is typically assumed to be unity, and its impact has long been overlooked due to the attention paid to the more easily controlled filament length. Here, we investigate the obscured contribution of K to the THz radiation characteristics by using the improved travelling-wave antenna (TWA) model. It has been found that, under both single- and two-color laser pumping schemes, K significantly determines the far-field spatial distribution of forward or backward THz radiation, as well as the change from Bessel-type to single-ring-type THz emission patterns. These results establish the TWA model as a reliable theoretical tool for studying the mechanisms of THz beam shaping via the designed K. Moreover, for cases of K not being controlled, its value can also be inferred by the proposed TWA model, which could be an effective method to confirm whether the laser ionization front is superluminal or subluminal compared with the generated THz waves.