Lecture 8: Laser amplifiers

Spectral lineshape
The spectral characteristic of a resonant transition is therefore
never infinitely sharp.
Any allowed resonant transition between two energy levels
has a finite relaxation time constant because at least the
upper level has a finite lifetime due to spontaneous emission.
From Quantum Mechanics, the finite spectral width of a
resonant transition is dictated by the uncertainty principle of
quantum mechanics.
Intuitively, any response that has a finite relaxation time in
the time domain must have a finite spectral width in the
frequency domain. (recall the impulse response discussed in
Lecture 2)
We will see that the rate of the induced transitions between
two energy levels in a given system is directly proportional to
the spontaneous emission rate from the upper to the lower
level.
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