Nonlinear optics of graphene and other 2D materials in layered structures

We present a theoretical framework for nonlinear optics of graphene and other 2D materials in layered structures. We derive a key equation to find the effective electric field and the sheet current density in the 2D material for given incident light beams. Our approach takes into account the effect of the surrounding environment and characterizes its contribution as a structure factor. We apply our approach to two experimental setups, and discuss the structure factors for several nonlinear optical processes including second harmonic generation, third harmonic generation, and parametric frequency conversion. Our systematic study gives a strict extraction method for the nonlinear coefficients, and provides new insights in how layered structures influence the nonlinear signal observed from 2D materials.