Large linear and nonlinear electro-optic coefficients in two-dimensional ferroelectrics

Analytical derivations and first-principles calculations are performed to investigate the electro-optic (EO) response of the two-dimensional ferroelectric SnS in its monolayer form. In addition to derive the formula for EO coefficients for two-dimensional systems, large linear and nonlinear electro-optic coefficients are discovered, along with a strongly nonlinear electro-optic response as a function of electric field. The origin of these electro-optic responses is further found and involves a few specific phonon modes, in general, and the evolution of their frequencies and atomic characteristics under electric fields, in particular. Large linear and nonlinear electro-optic coefficients can be found in other two-dimensional ferroelectrics, paving the way for potential optical device applications.