  We study the optical properties of the solar gravitational lens (SGL) under
the combined influence of the static spherically symmetric gravitational field
of the Sun---modeled within the first post-Newtonian approximation of the
general theory of relativity---and of the solar corona---modeled as a generic,
steady-state, spherically symmetric free electron plasma. For this, we consider
the propagation of monochromatic electromagnetic (EM) waves near the Sun and
develop a Mie theory that accounts for the refractive properties of the
gravitational field of the Sun and that of the free electron plasma in the
extended solar system. We establish a compact, closed-form solution to the
boundary value problem, which extends previously known results into the new
regime where gravity and plasma are both present. Relying on the wave-optical
approach, we consider three different regions of practical importance for the
SGL, including the shadow region directly behind the Sun, the region of
geometrical optics and the interference region. We demonstrate that the
presence of the solar plasma affects all characteristics of an incident
unpolarized light, including the direction of the EM wave propagation, its
amplitude and its phase. We show that the presence of the solar plasma leads to
a reduction of the light amplification of the SGL and to a broadening of its
point spread function. We also show that the wavelength-dependent plasma effect
is important at radio frequencies, where it drastically reduces both the
amplification factor of the SGL and also its angular resolution. However, for
optical and shorter wavelengths, the plasma's contribution to the EM wave is
negligibly small, leaving the plasma-free optical properties of the SGL
practically unaffected.
