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Habeebe
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Homework Statement
For a laser, assume single mode operation, only lifetime broadening due to A21 and A1. Write out the rate equations for the atomic densitions N1 and N2 and the flux [itex]\Phi[/itex].
Then there's a diagram where there's 2 stats. Pump rate is P, stimulated emission between 1 and 2 is allowed, and spontaneous emission from 1 to 2 and from 1 to the reservoir.
Homework Equations
The Attempt at a Solution
Below are the rate equations as I have them. My issue is that I don't know how to get the cross section (σ). I can't find it in the book. The example from class was the same as before, but spontaneous decay could happen from both states 2 and 1, and the pump went into both states also. For that case it was [itex]\sigma = \frac{\lambda^2}{\pi}\frac{A_{21}}{A_{21}+A_{2L}+A_{1L}}.[/itex]
Rate equations:
[itex]\dot{N_2}=P-\Phi\sigma(N_2-N_1)-A_{21}N_2[/itex]
[itex]\dot{N_1}=\Phi\sigma(N_2-N_1)+A_{21}N_2-A_1N_1[/itex]
[itex]\dot{\Phi}=\Phi \frac{c}{2d}[ln(R_1R_2+2l\sigma(N_2-N_1)][/itex]EDIT: I'm not sure if it's clear, but I need cross section in terms of wavelength/frequency and the A coefficients, as those are filled in later with actual numbers.
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