  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 $k\cdot p$ 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.
