Layer of material that transmits light in one direction and absorbs it in the other direction I am looking for a material (or layer of materials) which transmits light coming from one side and absorbs light coming from the other side. The absorption should be as good as possible and the transmission should happen with minimal losses. Furthermore the layer of material should be very thin if possible and it is enough if it works at 1064 nm wavelength!
Another requirement is that the light which is incoming has the same polarization before and after transmission.

I have already checked the possibility of a one-way mirror or I tried to play with the Faraday effect, but I could not find a way to fulfill the above named criteria.
Many thanks in advance!
 A: Unfortunately, a one-way window in the sense your talking about would contradict the second law of thermodynamics:
Say you have two chambers with a one-way window between them, the direction selective transmission would then cause spontaneous energy transfer in the direction of allowed transmission. If the two chambers were initially at the same temperature, then the directional energy transfer would case the temperature in one of the chambers to rise while the temperature of the other chamber decreases. This is is stark contradiction to the second law of thermodynamics.
The one-way mirrors found in e.g. interrogation rooms relies on a high reflectivity/low transmitivity of the window and then having one room brightly lit and the other rather dark. Someone in the dark room could quite easily see into the bright room since there is little light reflected back at them from their own room and much light coming from the brightly lit room; at the same time someone in the light room would hardly see anything from the dark room since the little light which is transmitted from the dark room is washes out by the reflection from the light room, even though the transmitivity is equal in both directions.
Edit:
A little further research into this question has led me to optical isolators which are essentially one-way windows for light. So it seems like there are indeed instances of one-way windows, and to be even more specific to the question it seems as if a polarization-independent optical isolator would do the trick for you.
So aren't they violating the second law of thermodynamics? Could we use them to gain free energy?
The answer to that is unfortunately still no. As @Jan SE points out in his/her comment, the fact that the non-transmitted light is absorbed, means that the isolator itself will get warm and then radiate heat in both directions, thus avoiding the indefinite energy flow in one direction.
