Prelasing

Laser action, occurring during the pump phase in an amplifier, results from the residual feedback of the various interfaces in the optical path. The condition for stable operation can be derived by considering the gain in an amplifier rod of length  pumped to an inversion level characterized by a gain coefficient g per unit length. Let the end faces of the rod exhibit residual reflectivities of R₁ and R₂. Then spontaneous emission emanating from any given location in the rod, traveling normal to the rod end faces, will exhibit a loop gain after one round trip in the rod of approximately R₁R₂ exp(2g ). If this loop gain is greater than unity, oscillations will build up until the usable stored energy is depleted. The requirement for an amplifier is thus
R₁R₂ exp(2g ) < 1, ......(1)
which sets an upper limit on rod length.