Is it possible to transfer light between two elements at a distance closer than the wavelength of the light? Let's say we have a nanoscale laser or led(5nm width/length/height) emitting photons(red, 650nm wavelength) in a direction parallel to its plane, then at 20nm distance in the direction of the emission there is a photodiode(light detector, 5nm width/length/height).
The question: will the photodiode absorb the light(photons) emitted by the laser? Or will the electromagnetic wave wrap around it, and no light will be detected?
Second question: If it will be absorbed, and 20nm is less than air free mean path(68nm at ambient pressure), will all the energy in the electromagnetic wave be transferred to the photodiode, in simpler terms, will all the photons hit the target?
Thanks
 A: 
Is it possible to transfer light between two elements at a distance closer than the wavelength of the light?

As the mathematics of maxwell's equations work the same way whether in nanometer wavelengths or in kilometers let us reason with what happens for kilometer wavelengths, i.e radio waves.
Obviously the answer is yes, the light is transferred coherently so that information can be carried along with no problems.
To answer your example is more difficult because at nanometers one has to deal with the particle nature of light , i.e. photons and their quantum mechanical interactions. How a beam of classical electromagnetic waves emerges from zillions of individual photons is mathematically known, and it is instructive to look how this happens in a simple laser experiment, one photon at a time. In this experiment one sees how the boundary conditions on how the photon scatters are important. So in the case of your example what percentage and how the  photons will impinge on your detector will depend on the specifics of the detector, and as @scrx2 says in his/her answer, the numbers depend on quantum electrodynamics calculatioms.
A: In FRET you have transfer of energy from one emitter/donor (an excited fluorophore, analog to your nm-laser) to one acceptor (the detector) in close proximity (nm). This  near field exchange (i.e. closer than the wavelength) is very sensitive to distance between the two molecules. It is mediated by strange virtual photons, which do not exist, are instantaneously absorbed, cannot be detected, violate energy conservation, but still are useful to picture what happens. The details are in  quantum electrodynamic theory (beyond my knowledge).
A: There is no reason why the light should not be absorbed. Of course you may see interference effects.
Over such short distances light can even tunnel across a region where it cannot propagate.
A: Classical EM theory cannot answer your question. Classical answers can be extrapolated to such short distances, but there is no particular reason to think they would be correct. If the experiment had been done and results did not fit predictions, classical theory would have been revised or abandoned, but it didn't happen.
I believe the same reasoning applies to quantum electrodynamics. It would be possible to make predictions. Such predictions should take into account the effect of non-radiation electric and magnetic charge, which would be much larger than usual.
Can we expect those predictions to be accurate? Maybe not. Are there effects we usually would not notice, that would matter this time? Maybe.
