Topological insulators in the ${\text{Bi}}_{2}{\text{Se}}_{3}$ family have an energy gap in the bulk and a gapless surface state consisting of a single Dirac cone. Low-frequency optical absorption due to the surface state is universally determined by the fine-structure constant. When the thickness of these three-dimensional topological insulators is reduced, they become quasi-two-dimensional insulators with enhanced absorbance. The two-dimensional insulators can be topologically trivial or nontrivial depending on the thickness, and we predict that the optical absorption is larger for topological nontrivial case compared with the trivial case. Since the three-dimensional topological insulator surface state is intrinsically gapless, we propose its potential application in wide bandwidth, high-performance photodetection covering a broad spectrum ranging from terahertz to infrared. The performance of photodetection can be dramatically enhanced when the thickness is reduced to several quintuple layers with a widely tunable band gap depending on the thickness.