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In this paper, we study the third-order nonlinear optical response due totransitions between excitonic levels in two-dimensional transition metaldichalcogeniedes. To accomplish this, we use methods not applied to thedescription of excitons in two-dimensional materials so far and combined with avariational approach to describe the $1s$ excitonic state. The aforementionedtransitions allow to probe dark states which are not revealed in absorptionexperiments. We present general formulas capable of describing any third-orderprocess. The specific case of two-photon absorption in WSe2 is studied. Thecase of the circular well is also studied as a benchmark of the theory.

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