Topological insulator films are promising materials for optoelectronics due to a strong optical absorption and a thickness dependent band gap of the topological surface states. They are superior candidates for photodetector applications in the THz-infrared spectrum, with a potential performance higher than graphene. Using a first-principles $kcdot p$ Hamiltonian, incorporating all symmetry-allowed terms to second order in the wave vector $k$, first order in the strain $epsilon$ and of order $epsilon k$, we demonstrate significantly improved optoelectronic performance due to strain. For Bi$_2$Se$_3$ films of variable thickness, the surface state band gap, and thereby the optical absorption, can be effectively tuned by application of uniaxial strain, $epsilon_{zz}$, leading to a divergent band edge absorbance for $epsilon_{zz}gtrsim 6%$. Shear strain breaks the crystal symmetry and leads to an absorbance varying significantly with polarization direction. Remarkably, the directional average of the absorbance always increases with strain, independent of material parameters.
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