  This paper is concerned with the inverse problem to recover the scalar,
complex-valued refractive index of a medium from measurements of scattered
time-harmonic electromagnetic waves at a fixed frequency. The main results are
two variational source conditions for near and far field data, which imply
logarithmic rates of convergence of regularization methods, in particular
Tikhonov regularization, as the noise level tends to $0$. Moreover, these
variational source conditions imply conditional stability estimates which
improve and complement known stability estimates in the literature.
