How does stimulated emmision work?

[Superposed_Cat]

Hi all, I was wondering mathematically how stimulated emission works, could someone please explain it more concisely than wikipaedia? Thanks for any help...:shy:

 

[mathman]

Mathematically? Stimulated emission is a physical process where a photon stimulates something which is in a higher energy state to drop to a lower energy state where the energy difference is the same as the energy of the photon. The result is a coherent interference between the incoming photon and the the stimulated photon.

The above description is general in that it applies to masers (microwave - molecular transitions) as well as lasers (atomic transitions).

 

[Superposed_Cat]

There has to be some mathematical relation/equation/formulism surely?

 

[Superposed_Cat]

I heard that einstein discovered stimulated emission, he didn't do that heuristically.

 

[king vitamin]

Einstein used the principle of detailed balance. Essentially, when the atoms are in thermal equilibrium with radiation at a given temperature, they should reach a steady state equilibrium. At this state, the rate of photons emitted by a transition from a higher to lower energy level, $m \rightarrow n$ must be equal to the rate of photons absorbed, exciting the lower level to the higher level $n \rightarrow m$. So you need to balance the two rates.

What Einstein found was that the only way for this to work is to include not only spontaneous emission, but also stimulated emission, otherwise there is no way for the thermodynamics to be consistent. You ask for mathematical models, but these are quite easy to find online and I didn't feel the need to write them out here. Here are two nice sources, which assume familiarity with statistical mechanics and blackbody radiation:

http://en.wikipedia.org/wiki/Einstein_coefficients (see "detailed balancing")

http://farside.ph.utexas.edu/teaching/qmech/Quantum/node119.html