Calculation of the nonlinear response functions of intraexciton transitions in two-dimensional transition metal dichalcogenides

In this paper we study the third-order nonlinear optical response due to transitions between excitonic levels in two-dimensional transition metal dichalcogenides. To accomplish this we use methods not applied to the description of excitons in two-dimensional materials so far and combined with a variational approach to describe the 1s excitonic state. The aforementioned transitions allow us to probe dark states which are not revealed in absorption experiments. We present general formulas capable of describing any third-order process. The specific case of two-photon absorption in WSe2 is studied. The case of the circular well is also studied as a benchmark of the theory.