This study introduces a new technique for achieving dual-band functionality in a printed dipole antenna with integrated balun feeding without additional elements. By employing an optimization algorithm, the fundamental parameters of the antenna are extracted, resulting in an antenna design that operates effectively in two distinct frequency bands of 2.4–2.5 and 5–6 GHz for WLAN/ISM and biomedical applications. By implementing the proposed design in a two-element array structure, the antenna successfully achieved a fan-beam radiation pattern in both frequencies. The array antenna exhibits fan-beam radiation patterns and peak gains of 6.90 dB and 7.84 dB, respectively, in two frequency bands: 2.06–2.52 GHz and 5.09–5.93 GHz. According to the proposed design, the array antenna has measured half-power beamwidths (HPBWs) of 38.34° and 25.14° in the two frequencies specified. The overall dimensions of the antenna are 1.100λ × 0.563λ × 0.004λ. This research design offers advantages such as smaller dimensions, higher gain, and a more straightforward structure compared to dual-band array antennas with fan beam radiation patterns.