I have a question about the upper laser level (the metastable level) in a 3-level laser system. I will call the ground level of the 3-level laser system by "g" and the metastable level by "m".
The metastable level m has a long life time, meaning that it decays only slowly via spontaneous emission. I understand that this is because of the angular momentum selection rules which forbid transitions between the metastable level m and the ground level g through radiation. If a transition is possible between two energy levels, the emitted photon carries away an amount of angular momentum, "which for the photon must be at least 1, since it is a vector particle" (quote from Wikipedia/selection_rules). So I assume that in a forbidden transition (like the one from m to g), the difference in angular momentum between the states m and g does not match the amount of angular momentum that can be carried away by a photon.
Metastable states are necessary in laser systems in order to achieve population inversion between levels m and g. If we pump the 3-level system, the electrons will get excited and eventually accumulate in the state m and will not decay to the state g via spontaneous emission (because m is metastable). However, by an incoming photon of the right frequency v, stimulated emission will happen, taking an electron from m to g, while releasing a second photon with frequency v. This process then cascades through the system, de-exciting the electrons from m to g, and producing the desired coherent optical amplification effect.
My question is: If the metastable state forbids the spontaneous emission because of the selection rules of angular momentum, then why is a de-excitation via stimulated emission possible? Wouldn't this imply that the second (emitted) photon would have to carry an angular momentum forbidden by the selection rules?
I would be glad for an explanation. Or, if there is a logical mistake in my reasoning, I would be glad to find out where.
Thanks a lot in advance, A.F.