Effect of electric potentials on electromagnetic waves

May 2016
What happens to an electromagnetic wave when it is radiated on an object with an electric potential? Namely, what does that electric potential do to the electromagnetic wave?

Context: there is a stream of electromagnetic waves being radiated on the object. The object has varying electric potentials, with many underlying frequencies of electric potentials within the object, and Fourier transforms can be applied to determine all the underlying frequencies, etc, in the "waves" of electric potentials.

However, the stream of electromagnetic waves need to carry information relating to the amplitude of that electric potential at each point in time.

So, what happens to the electromagnetic wave? Does interferometry of some sort need to be applied to read the changes? Or does the wave itself get impacted by the electric potential within the object in a way that can be received, perhaps as a larger amplitude itself?

My guess is that the electric potential affects the amplitude (and more relevantly energy levels that can be read from) of waves at the particular frequency being radiated on the object.

Any peer-review references would be appreciated, but any inputs are welcome!