General formulas for the beam properties of 1-D bidirectional leaky-wave antennas

In this paper, we analyze the beam properties of bidirectional 1-D leaky-wave antennas (1-D LWAs). Specifically, it is found that, even in the infinite-aperture case, the beam properties considerably change for certain combinations of the phase and the attenuation constants, and different radiation regimes are identified here. New analytic formulas are provided to exactly evaluate the beamwidth of an infinite 1-D bidirectional LWA operating in any radiating regime. However, when the antenna truncation is accounted for, the boundaries between the radiating regimes change as the radiation efficiency changes. Analytic formulas are, therefore, provided to accurately calculate such boundaries for any practical radiation efficiency. The interesting case of a finite-length bidirectional 1-D LWA radiating at broadside is then extensively discussed. With respect to previous beamwidth formulas found in the literature, the new formulas take into account the finiteness of the aperture, thus providing more useful and reliable results, especially in cases when the aperture truncation considerably affects the radiation efficiency. The numerical results corroborate the accuracy of the proposed expressions. These new formulas not only significantly improve the accuracy of the existing ones but also lay the groundwork for the analysis of the beamwidth properties of the important case of 2-D LWAs.