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In an infrared photodetector, noise current (dark current) is generated throughout the volume of the detector. Reducing the volume will reduce dark current, but the corresponding smaller area will also reduce the received signal. By using a separate antenna to receive light, one can reduce the detector area without reducing the signal, thereby increasing its signal to noise ratio (SNR). Here, we present a dielectric resonator antenna (DRA) coupled infrared photodetector. Its performance is compared to a conventional resonant cavity enhanced slab detector. The Noise Equivalent Power (NEP) is used as a figure of merit for the comparison. Formulas for the NEP are derived for both cases. A pBp photodiode detector is assumed in the comparison. The active region of the photodiode is an InAs/GaSb Type II Superlattice (T2SL). A Genetic Algorithm is used to optimize the dimensions of the detector and the DRA to achieve the smallest NEP. The result is a photodetector that converts over 85% of the incident light into carriers with a volume reduced by 95%. This optimal geometry leads to a NEP reduced by 6.02dB over that of the conventional resonant cavity enhanced slab detector.