As I now, unlike standard Lorenz-Mie theory, defining absorption and scattering cross sections for a particle in strongly inhomogeneous field is not obvious, so I don't know how to handle this problem.
In strong fields, nonlinear effects begin to appear. As for scattering, it is, for example, stimulated Raman scattering. Considering absorption in strong fields, it is necessary to take into account the multi-photon absorption. The cross section of all exemplified nonlinear processes depend on the intensity of the incident radiation.
More details on this issue is discussed in books on nonlinear optics, for example,