Lone-pair, electron-dominated, nonlinear optical responses in sulfur clusters and electric tunability properties

Sulfur clusters have abundant lone-pair electrons, tunable geometries, and electronic structures, thus providing a new concept for achieving a tradeoff between transparency and nonlinearity. In this study, the optical properties of the sulfur clusters were investigated through first-principles calculations. Sulfur clusters exhibit broad transmittance bands spanning from the visible to the far-infrared regions, moderate third-order nonlinear optical effects comparable to those of p-nitroaniline, and size-dependent third-order nonlinear anisotropy. Furthermore, this study demonstrated that the nonlinear optical responses of lone-pair electrons are sensitive to the nuclear binding strength. By tuning the nuclear binding strength using an external electric field, the third-order nonlinear optical responses of the sulfur clusters were improved considerably and yielded a moderate red shift in the transparent bands. This investigation of the optical behaviors of sulfur clusters provides profound physical insights into the development of nonlinear optical materials with lone-pair electrons.