In this paper \gamma ^*--\gamma ^* scattering with large, but more or less equal virtualities of two photons is discussed using BFKL dynamics, emphasizing the large impact parameter behavior (b_t) of the dipole--dipole amplitude. It is shown that the non-perturbative contribution is essential to fulfill the unitarity constraints in the region of b_t > 1/2 m_\pi , where m_\pi is pion mass. The saturation and the unitarization of the dipole--dipole amplitude is considered in the framework of the Glauber--Mueller approach. The main result is that we can satisfy the unitarity constraints introducing the non-perturbative corrections only in initial conditions (Born amplitude).

PACS numbers: 12.38.Bx, 13.60.--r, 24.85.+p