In this thesis, we determine the formalism of the dynamic polarizability of diatomic molecules. This approach is then applied to investigate the effect of a DC field on the dynamic polarizability of a few rotational states of RbCs and NaK molecules at a wavelength of 1064 nm. We demonstrate the dependence of the dynamic polarizability on the DC field strength and find that at a certain DC field strength, two lowest rotational states of the molecules have identical dynamic polarizabilities. This magic field strength is verified to be independent of the light polarization. Besides this, we also investigate the angle dependence of the polarizabilities when the light is linearly polarized as a function of the relative angle with respect to the DC field. There exists a magic angle which is independent of the DC field strength. This state-insensitive polarizabilities finding can provide great advantages to the development of experiments where polar molecules trapped in optical lattices are ideal tools for quantum computing and simulations.