Lecture 8: Laser amplifiers

Four-level systems
Levels |3> and |2> need to satisfy the same conditions as in a three-level
system.
The population in level |1> relaxes very quickly back to the ground level,
ideally 1 ≈ 10 remains relatively unpopulated in
comparison with level |2> when the system is pumped.
Under these conditions,
N 1 ≈ 0; R 2 ≈ W p (N t –N 2 )
where the effective pumping rate W p is proportional to the pump power.
In the steady state when W p is held constant, by taking dN 2 /dt = 0,
(ignoring dN 1 /dt because N 1 ≈ 0)
N 2 e –N 1 a ≈ N 2 e =(W p 2 e )N t [1 + W p 2 + (I 2 /h) e ] -1
=> No minimum pumping requirement for an ideal four-level system because
level |1> is initially empty. A practical four-level system is much more
efficient than a three-level system.
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