
#1
Apr2507, 04:19 PM

P: 11

1. The problem statement, all variables and given/known data
Simultaneous Laser Emission on Two Lines Consider the multilevel system show in the figure where amplification can occur at frequencies [tex]\omega_{12}[/tex] and [tex]\omega_{21}[/tex]. The arrow "triplets" are meant to indicate the 3 Einstein absorption and emission processes that take place between levels 2 and 3. Write down the population rate equations for levels 1, 2 and 3. The figure is attached. My problem is: I don't know if I have to introduce the pumping power inside the population rate equations. 2. Relevant equations Ni=number of particles in level i Between levels 1 and 2 we have: [tex]\downarrow \uparrow \downarrow[/tex] first down arrow: spontaneous trasition rate [tex]N_{2}A_{21}[/tex] up arrow: absorption rate [tex]N_{1}B_{12}W(\omega_{12})[/tex] second down arrow: stimulated emission rate [tex]N_{2}A_{21}W(\omega_{12}[/tex] 3. The attempt at a solution For level 3 I have: [tex]dN_{3}/dt =  N_{3}A_{31} + N_{1}B_{13}W(\omega_{13})  N_{3}B_{31}W(\omega_{13})[/tex] Level 2: [tex]dN_{2}/dt=  N_{2}A_{21} + N_{1}B_{12}W(\omega_{12})  N_{2}B_{21}W(\omega_{12})[/tex] Level 1: [tex]dN_{1}/dt =  dN_{3}/dt  dN_{2}/dt  N_{1}R{1}[/tex] Should I add P3 to level 3 and P2 to level 2? 


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