Millimeter wave microstrip antennas with left-handed materials substrates are studied with method of moments. Discrete complex image method is extended to the computation of Green's function in microstrip circuits with left-handed materials substrates. It is shown that this kind of antennas will achieve similar radiation patterns to the ones of conventional millimeter wave microstrip antennas in some cases, and can obtain radiation patterns characteristic of narrow main lobes with low elevation angles in other cases. Potential applications for directive antennas with these unusual radiation patterns of this kind of antennas are proposed.
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