  In this work we analytically investigate the longitudinal optical
conductivity of the C$_{2v}$ symmetric topological insulator. The conductivity
expressions at $ T = 0 $ are derived using the Kubo formula and expressed as a
function of the ratio of the Dresselhaus and Rashba parameters that
characterize the low-energy Hamiltonian. We find that the longitudinal
inter-band conductivity vanishes when Dresselhaus and Rashba parameters are
equal in strength, also called the persistent spin helix state. The
calculations are extended to obtain the frequency-dependent real and imaginary
components of the optical conductivity for the topological Kondo insulator
SmB$_{6}$ which exhibits C$_{2v}$ symmetric and anisotropic Dirac cones hosting
topological states at the $ \bar{X} $ point on the surface Brillouin zone.
