Rami Arieli: "The
Laser Adventure" Chapter 2.10 page 1
We saw in the rate equation that:
Since the same amount of energy (hn)
is involved in every transition up or down, than the rate at which energy
is absorbed in a unit volume of atoms is given by the transition rate times
the unit of energy:
dUadt = Kn(t)[N1(t)-N2(t)]*hn
Two processes decrease the population number of the excited level: Spontaneous
emission and stimulated emission.
One process increases the population number of the excited state - absorption.
Ua = energy density in stimulated transitions.
Compare this equation to the rate equation. What is the difference?
The incoming energy
Usignal(t) = n(t)*hn
The absorbed energy is taken out of the incoming signal, so the rate
of loss of energy from the incoming signal is:
dUsignal(t)/dt = -K*n(t)*[N1(t)-N2(t)]*hn
= -K*[N1(t)-N2(t)]* Usignal(t)
The same equation can be written for the photon
dn(t)/dt = -K* [N1(t)-N2(t)]*n(t)