Would absorbing photons make the EmDrive more efficient?

[IggyZ]

The EmDrive (fig. 1) is supposed to work by bouncing microwaves (photons) back and forward. Due to the shape of the thruster the photons will hit the left side at a higher speed than the right side.

This would create a large force on the left side of the thruster and a small force on the right side.

I wonder if it would be more deficient if the microwaves (photons) would be absorbed by a black surface (fig. 2). There would be no need to hit the right side and result in a smoother acceleration.

If so, what kind material would be first choice for the photon absorber and would cooling the photon absorber be difficult or even counter-productive for generating trust?