Now we consider stimulated transitions. The incident energy Usig(t) equals the number of photons times the photon energy, Usig(t) = n hn . When it is transferred through the lasing medium, stimulated absorption and emission occurs. If population inversion exists, N2-N1>0, the incident signal will be amplified, the equation describing the increase of Usig is:

Where K is a proportional parameter. The solution of the above equation is:

So the signal will increase exponentially when there is population inversion. The exponential increase continues until the population inversion reaches a certain balance, then the signal saturates, reaches the steady state. Power saturation is discussed in detail in books on lasers, we won’t go into depth here. Our purpose is to extract the laser power for doing useful work. We need the extracted power to be powerful enough. Since the gain of a single pass through the lasing medium is not big enough, people designed resonators to get high power gains. For example, we let the laser light transfer back and forth through two parallel plane mirrors, each pass through the lasing medium, the laser light is amplified, then we can extract from the oscillating light a certain fraction of the energy, which serves as the laser output.

Another thing we must consider now is the energy losses. First, the reflecting mirrors are not 100% reflective, so the mirrors absorb part of the oscillating power. Second is the coupling loss, i.e., we extract part of the oscillating power as laser output. At steady state, the laser oscillation system has a gain of 1, that is the energy gain is just equal to the energy loss, a dynamical equilibrium is sustained, a constant laser output is generated, which is what we desired. From here we can compute the oscillation threshold condition.

This comes to an end of our brief discussion on how laser works. Next we will discuss laser cavities and resonators.