# Minimum Power Required to Maintain a Population Inversion

According to many sources, the minimum power required to maintain a population N in the upper level of a two level laser system is $$P_{min}=fA_{21}Nh\nu$$ where $f$ accounts for the lack of 100% efficiency, $A_{21}$ is the Einstein A coefficient and $\nu$ is the frequency of the transition. This is just the energy required to counteract the spontaneous decay in the system.

However I don't really understand why this is a minimum energy? A possibility is that if some external radiation field is applied we should also get an imbalance in the rates of spontaneous emission and absorption and so is this the extra contribution that we are missing in the above calculation (if not, why not)? Thanks in advance!

• Are you suggesting that the additional field will raise or lower the minimum power due to the effect of stimulated emission? – garyp Jan 6 '16 at 14:03
• @garyp well you want more stimulated emission than absorption in a laser so the required power would be larger than the minimum power (the minimum power wouldn't change though because it by definition is the minimum) – Watw Jan 6 '16 at 14:08
• Can you provide a source for your first statement? I didn't think a two level system could have a population inversion... – Floris Jan 6 '16 at 14:51
• It seems your expression is valid for maintaining the population inversion between the two levels of a four-level laser between which laser action occurs. – Floris Jan 6 '16 at 14:53