Hansen-Woodyard Condition for 2-D Leaky-Wave Antennas

A Hansen–Woodyard condition is developed for a 2-D radial leaky-wave antenna. The optimum phase constant that gives maximum endfire directivity is calculated for two cases; one considers the array factor only and the other includes the element pattern. A comparison between 1-D and 2-D Hansen–Woodyard conditions for leaky-wave antennas is made. The optimum radiation efficiency that maximizes the endfire gain of a 2-D leaky-wave antenna is also found.