Second harmonic generation in nanoscale films of transition metal dichalcogenide: Accounting for multipath interference

The transfer matrix method has been widely used to calculate wave propagation through the layered structures consisting entirely of either linear or nonlinear optical materials. In the present work, we develop the transfer matrix method for structures consisting of alternating layers of linear and nonlinear optical materials. The result is presented in a form that allows one to directly substitute the values of material constants, refractive index and absorption coefficient, into the expressions describing the second harmonic generation (SHG) field. The model is applied to the calculation of second harmonic (SH) field generated in nano-thin layers of transition metal dichalcogenides exfoliated on top of silicon oxide/silicon Fabry-Perot cavity. These structures are intensively studied both in view of their unique properties and perspective applications. A good agreement between experimental and numerical results can be achieved by small modification of optical constants, which may arise in an experiment due to a strong electric field of an incident focused pump laser beam. By considering the SHG effect, this paper completes the series of works describing the role of Fabry-Perot cavity in different optical effects (optical reflection, photoluminescence and Raman scattering) in 2D semiconductors that is extremely important for characterization of these unique materials.