Optimum Gain Conditions for 1-D Unidirectional Leaky-Wave Antennas

The optimization of the radiating performance for finite-length 1-D unidirectional leaky-wave antennas (LWAs) is first treated in the general case, i.e., assuming that the phase and attenuation constants can be varied freely. In this general case, an approximate analytical formula is derived to calculate the gain from the beamwidth, improving the accuracy of previous existing formulas. When a particular class of 1-D LWAs is considered, design equations are required to relate the geometrical parameters to the relevant LWA wavenumber. Leaky rectangular waveguides and other LWAs based on partially reflecting sheets (PRS) are two important classes of LWAs for which approximate expressions are available. Design procedures for optimizing the gain are given here for general 1-D LWAs, including leaky rectangular waveguides and other PRS-based LWAs.