Module 8 : Laser- II
Lecture   : Rate equations for Lasers
 

where

$\displaystyle \beta = \frac{N_u}{N_m}=\frac{\tau_{u,m}}{\tau_{m,g}}\eqno (B)$

For population inversion to occur, the numerator of eqn. (A) must be positive, $ W_p\tau_{m,g}(1-\beta) >1$, i.e.,

$\displaystyle \boxed{W_p\tau_{m,g} >\frac{1}{1-\beta}}\eqno (C)$

From (B), $ \beta <1$as the lifetime for $ m\rightarrow g$transition is longer than that for $ u\rightarrow m$transition. Thus $ W_p\tau_{m,g} >1$is a sufficient condition for population inversion. A minimum pumping power determined by (C) is required to ensure population inversion. For $ \beta=0$,

$\displaystyle \frac{\Delta N}{N} = \frac{W_p\tau_{m,g}-1}{W_p\tau_{m,g}+1}$

As $ N_g$is ground level, its value is initially very large and at least $ N/2$atoms must be transferred to the upper level achieve population inversion. Hence a three level system is not very energy efficient.

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