  We propose a multiscale approach for a nonlinear Helmholtz problem with
possible oscillations in the Kerr coefficient, the refractive index, and the
diffusion coefficient. The method does not rely on structural assumptions on
the coefficients and combines the multiscale technique known as Localized
Orthogonal Decomposition with an adaptive iterative approximation of the
nonlinearity. We rigorously analyze the method in terms of well-posedness and
convergence properties based on suitable assumptions on the initial data and
the discretization parameters. Numerical examples illustrate the theoretical
error estimates and underline the practicability of the approach.
