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We demonstrate a high efficient carbon nanotube (CNT) based infrared (IR) detector combined with a nano antenna. A nanoscale antenna is used as a metallic field enhancement structure for boosting the electric field intensity at the position of the sensing element. Here, we report the theoretical analysis and experimental characterization of a nano antenna for CNT based IR sensors. We propose a comprehensive mathematical model which accounts for the quantum-confinement effects on the conductivity and dielectric function of the nano antenna, to theoretically predict the field enhancement effect at the CNT sensing region. Numerical simulations and experimental results reveal the electric field and photocurrent of the CNT sensors are increased after adding the nano antenna. By measuring the photocurrent response of the sensor before and after the antenna, the efficiency and characteristics of the nanoantenna was verified experimentally. The experimental result indicates that the nano antenna increases the photocurrent by more than 10-fold. This matches with the theoretical prediction and implies that the electric field in the vicinity of the detector is enhanced by the nanoantenna.