Why is the downward transition of electrons in a three level pumping scheme of laser non radiative? Laser produces coherant monochromatic waves by stimulated emission of radiation. In the three level pumping scheme of laser the downward transition of electrons from E3 to E2 is spontaneous and from E2 to E1 is stimulated emission. However electrons after being pumped to E3 undergo downward transition to measurable level E2 through nonradiative transitions. How can these transitions not radiate photons? How does this not violate the law of conservation of energy? Moreover the atoms are trapped at the level as spontaneous transition from level E 2 to E1 is forbidden. How is it forbidden?
 A: These E3 to E2 transitions can be vibrational and rotational modes of the active medium.
Energy conservation is maintained by phonons (in solids, lattice vibrations) or thermal radiation (in gas).
E.g. of a 4 level system. Collisions of Helium and Neon. See HeNe Laser. 

Pumping of Helium to the excited state. Collision of the small atom to the neon is an energy transfer. Since energy levels are quantized, a part of the energy will be infrared radiation.
Forbidden transitions violate conservation laws. E.g. quantum numbers or momentum conservation.
A: Although Stefan Bischof's answer is correct, I would like to add a few things.
Your main question is, how can an excited electron relax in a non-radiative way, without emitting photons.
The answer to the question is phonons. In non-radiative relaxation, the energy is dissipated in the form of phonons, that is, lattice vibrations of a solid (or liquid).
Phonons are collective excitations in a periodic, elastic arrengament of atoms or molecules in a condensed matter. A phonon is a QM description of an elementary vibrational motion in which a lattice of atoms or molecules uniformly oscillates at a single frequency.
So the answer to your question, is that the electrons relax by releasing phonons, that is, vibrational motions in the lattice, and this is a form of energy and heat dissipation.
