Electro-optic Kerr effect induced by nonlinear transport in monolayer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>WTe</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math>

The nonlinear Hall effect (NLHE) can induce optical anisotropy by modifying a material's dielectric tensor, presenting opportunities for novel characterization and device applications. While the magneto-optical Kerr effect (MOKE) probes the linear Hall effect (LHE) in magnetic materials, an analogous optical probe for NLHE in nonmagnetic, time-reversal symmetric systems remains highly desirable. Here, we theoretically propose and investigate an NLHE-induced electro-optic Kerr effect (EOKE) as such a probe. Focusing on monolayer (ML) ${\mathrm{WTe}}_{2}$, a prototypical NLHE material, our analysis considers contributions from Berry curvature dipole (BCD), Drude, injection, and shift mechanisms. We demonstrate that the EOKE signal in ${\mathrm{WTe}}_{2}$ is predominantly governed by the BCD. Furthermore, the Kerr angle exhibits temporal oscillations at different optical frequencies, suggesting EOKE as a promising route for the time-resolved detection of NLHE and the dynamic investigation of material topology.