In this paper, we present optimized aperiodic structures for use as narrowband, highly directional thermal infrared emitters for both TE and TM polarizations. These aperiodic multilayer structures designed with alternating layers of silicon and silica on top of a semi-infinite tungsten substrate exhibit extremely high emittance peaked around the wavelength at which the structures are optimized. Structures were designed by a genetic optimization algorithm coupled to a transfer matrix code that computed thermal emittance. First, we investigate the properties of the genetic-algorithm-optimized aperiodic structures and compare them to a previously proposed resonant cavity design. Second, we investigate a structure optimized to operate at the Wien wavelength corresponding to a near-maximum operating temperature for the materials used in the aperiodic structure. Finally, we present a structure that exhibits narrowband and highly directional emittance for both TE and TM polarizations at the frequency of one of the molecular resonances of carbon monoxide (CO); hence, the design is suitable for the emitting portion of a detector of CO via absorption spectroscopy.