  We investigate the optical response induced by a d.c. current flowing in a
nonmagnetic material that lacks inversion symmetry. In this class of materials,
the flowing current experiences a nonlinear Hall effect and induces a
nonequilibrium orbital magnetization, even in the absence of spin-orbit
coupling. As a result, an orbital-driven Kerr effect arises that can be used to
probe not only the orbital magnetization but also the nonlinear Hall effect. In
addition, in the long wavelength limit, the nonlinear Hall effect leads to a
rectification current that can be used to detect terahertz radiation. We apply
the theory to selected model systems, such as WTe$_2$ bilayer and metallic
superlattices. The nonequilibrium orbital Kerr efficiencies obtained in these
systems are comparable to the largest values reported experimentally in GaAs
and MoS$_2$, exceeding the values reported in metals and suggesting a large
terahertz current responsivity.
