Coupled Plasmon - Phonon Behavior is caused when semiconductors /electronic materials containing free carriers having plasmon frequencies that are comparable to phonon frequencies leading to coupling between them (e.g., Coupled Plasmon-Lo phonons in III-V semiconductors such as GaAs).  In other words, the coexistence of phonons and plasmons leads to a coupling between the two participants.  The Plasmion frequency is linearly proportional to teh square root of the free career concentration (n), and the higher the value of n is, then the greater the degree of the reflectivity of  samples.

If I might add an additional comment. Plasmon-phonon coupling can be viewed as a resonant transfer of energy and momentum from plasmon to the phonon mode, when plasmon energy and momentum matches that of the phonon mode. More precisely one should think in terms of the hybrid mode which has both the characteristics of the plasmon (collective electron oscillations) and phonon (lattice vibrations).

A peculiar thing happens in graphene when one looks at the coupling between plasmons and optical phonons since longitudinal plasmons couple only to the transverse optical phonons and vice verse:

http://journals.aps.org/prb/abstract/10.1103/PhysRevB.83.161409

What are the typical frequencies we are speaking about? To what energies of plasmons(phonons) this will correspond? 

If I know the plasmon frequency, can I estimate the energy of phonon it is going to excite?

How efficient is this coupling? I.e. pumping 1 W to plasmons, how much will end up in corresponding phonon mode?

This coupling will be most efficient on resonance, when plasmon has the same energy and momentum as the phonon mode. Typical phonon energies are 0.1 eV so this coupling requires plasmons of the similar energies. To have 0.1 eV plasmons in graphene requires Fermi energy (doping) of at least 0.1 eV (for lower doping plasmons will experience strong Landau damping).

One should really think in terms of a hybrid plasmon-phonon mode. So if you pump 1W of power into this mode, approximately 0.5W will be stored in plasmon and 0.5W in phonon mode (on resonance).

Typical phonon energies are 0.1 eV so this coupling requires plasmons of the similar energies.

This I do not quite get: are we consider the same energies or the same frequencies in order to get coupling? If energies - it will be hardly doable, as bulk plasmons are of the order of eVs, while phonons are 10s of meVs.

Also it is not quite clear that the energy distribution should be uniform: if you distribute the energy equally, the momentum will be disballanced due to substantially different masses. What will govern the process: energy or momentum?

This is just my naive view...

Indeed, typical metals have Fermi energies of the order of few eV which gives also plasmon energies of few eV and there is no hope to see plasmon-phonon coupling. Great thing about graphene is that one can tune the Fermi level (and plasmon energy) over broad range (0-1eV) and therefore observe plasmon-phonon coupling.

I didn't understand the question of energy distribution.

One would expect the uniform distribution over the degrees of freedom, once these degrees are equivalent, like x,y,z components of velocity for gas molecules. But phonons and plasmons should have substantially different mass, why the energy should distribute equivalently?

This also refers to  the coupling: having the same energy does not mean they oscillate at the same frequency. So why the energy should be the same, not the frequency?