 Solution

ID: past-exam-of-the-atomic-and-laser-physics-course-of-the-university-of-oxford/2022/4/b/solution

In a uniform steady amplifier, with no extra propagation losses, the local optical gain law gives

\frac{d I}{d z} = \frac{α _{0} I}{1 + I / I _{s}}, (\frac{1}{I} + \frac{1}{I _{s}}) d I = α_{0} d z .

Integrate between the two faces of length

L

to obtain

ln \frac{I _{out}}{I _{in}} + \frac{I _{out} - I _{in}}{I _{s}} = α_{0} L .

For

I ≪ I_{s}

, this reduces to exponential amplification. In deep saturation, the intensity increment approaches

α_{0} I_{s} L

: finite pumping limits the extracted power.

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