Increase of intensity-dependent excitonic second- and third-harmonic generation induced by static electric fields demonstrated for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>K</mml:mi> </mml:math> exciton of a <mml:math xml

We compute and analyze the dependence of excitonic second- and third-harmonic generation (SHG/THG) as a function of the optical excitation intensity in the presence of static electric fields by solving the semiconductor Bloch equations. Our simulations are performed for excitation of the strongly bound intralayer exciton of an inversion-symmetric homobilayer of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>MoS</a:mi> <a:mn>2</a:mn> </a:msub> </a:math> with in-plane electric fields. We demonstrate that for resonant excitation at the <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mn>1</b:mn> <b:mi>s</b:mi> </b:math> K-exciton the SHG and the THG show complex dependencies on both the strength of the static field and the peak amplitude of the optical pulse. For sufficiently intense optical excitation, the THG increases and the SHG increases superlinearly with the amplitude of the static field as long as exciton ionization is not yet dominating. Microscopic simulations demonstrate that these dependencies arise from an interplay between several effects including static and transient Stark shifts, exciton ionization, off-resonant Rabi oscillations, and a modified interference between optical nonlinearities induced by the intraband acceleration. Our findings offer several new possibilities for controlling the strong-field dynamics of systems with strongly bound excitons.