  General Relativity describes the trajectories of light-rays through curved
spacetime near a massive object. In addition to gravitational lensing, we
include an absorbing dielectric medium given by a complex refractive index
known as the Drude model. When absorption is included the eikonal becomes
complex, with the imaginary part related to the absorption along a ray between
emission and observation points. We extend results from the literature to
include dispersion in the index of refraction. The complex Hamiltonian splits
into a real part that describes the equations of motion and a constraint
equation that governs the momentum loss in the system. We work in coordinates
which are fully real, with a real metric in physical spacetime. We assume the
dust and plasma distributions of the Drude matter to coincide and vary as a
power-law $1/r^h$. We find that transmission requires $h>1$, otherwise
exponential absorption occurs along ray paths. We use ray-tracing through
strongly absorbing matter near the surface of the compact star, as well as
specializing to a point-lens in the weak-field limit with weakly absorbing
matter to generate potentially observable light curves for distant observers.
In the appropriate limits, our theory reproduces results from the literature.
