Lecture 8: Laser amplifiers

Rate equations
The net rate of change of population density in a given energy
level is described by a rate equation.
Here we only write the rate equations for the upper laser level
|2> and the lower laser level |1>.
In the presence of a monochromatic, coherent optical wave of
intensity I at a frequency ,
dN 2 /dt = R 2 –N 2 / 2 – (I/h) (N 2 e –N 1 a )
dN 1 /dt = R 1 –N 1 / 1 + N 2 / 21 + (I/h) (N 2 e –N 1 a )
where R 2 and R 1 are the total rates of pumping into energy
levels |2> and |1>, and 2 and 1 are the fluorescence lifetimes
(total lifetimes) of levels |2> and |1>. The rate of population
decay, including radiative and nonradiative spontaneous
relaxation from |2> to |1> is 1/ 21 .
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