  The optical Kerr effect of material with negative refraction is estimated for
the first time. This is done via three-dimensional finite-difference
time-domain (FDTD) simulations of disordered bidisperse metasurfaces consisting
of high index (GaP) spheres at the wavelength of 532~nm. The metasurfaces
comprise spherical particles randomly arranged on plane having two sizes close
to the magnetic and electric dipole Mie resonances. The real part of the
effective nonlinear refractive index of the metasurfaces is computed in the
vicinity of the Mie resonances where the metasurface possesses the negative
index of refraction. The optical Kerr nonlinearity has a peak under the
condition for the negative refraction. Intensity-dependent refractive index of
the bidisperse metasurfaces is studied through concentration transition to the
negative refraction state. It is shown that the nonlinear Kerr coefficient of
the monolayer metasurface has maximum when the effective linear refractive
index is close to zero.
