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Typically a stimulated photon will be one of a pair with its stimulating photon.

If the leading photon is absorbed by a particle in the ground state, will it then be re-emited by the stimulated emission caused by the second photon?

If it causes a stimulated emission from an excited particle, will there then be a train of three photons, or will the new pair leave the excited particle excited?

I am interested in the case where there is not a population inversion, but presumably the same rules would apply to lasers.

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Check out the Einstein equations (wikipedia page, also the pages on stimulated and spontaneous emission). The probability of emission is the same as the probability of absorption. The probabilities of either type of emission are independent of the population inversion.

Photons which entered the system are indistinguishable from the ones generated either thru stimulated or random emission (aside possibly from phase & polarization). Similarly, there's no way to tell an excited particle state caused by photon absorption from the same state caused by any other mechanism.

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  • $\begingroup$ I don't seem to have explained my question very well:-( Einstein only considered the interaction of one photon with a molecule. My question is "How does a molecule react to the two photons produced by a stimulated emission?" $\endgroup$ – Abbe Mac Jul 25 '14 at 17:37
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In stimulated emission, energy is added to the existing radiation field. It does not create a new field at a later time. The field contains one additional quantum of excitation. That's a single state of the field with a higher "occupation number".

In other words, you don't end up with two photons, one after the other.

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  • $\begingroup$ Okay, but what happens when this field interacts with an excited molecule, and with an unexcited molecule? In either case, since it has twice the energy, it cannot react with the molecule. $\endgroup$ – Abbe Mac Jul 25 '14 at 17:26
  • $\begingroup$ Ah! It has twice the intensity, which means more photons per second. But each photon still has the same energy. The interactions go (usually) one photon at a time. Only one quantum is added (or removed) from the field. The occupation number of the state is increased by one or decreased by one. All of those photons have the same energy. $\endgroup$ – garyp Jul 25 '14 at 17:52
  • $\begingroup$ What you are describing is the absorption of radiation in an isotropic field, but stimulated emissions produce coherent radiation which is not isotropic. $\endgroup$ – Abbe Mac Jul 26 '14 at 12:41
  • $\begingroup$ No, my comment applies to stimulated emission in any situation. Can you tell me what I've said that sounds like I'm specializing to an isotropic field? Then I'll clarify my answer. $\endgroup$ – garyp Jul 26 '14 at 13:16
  • $\begingroup$ You wrote "Only one quantum is added (or removed) from the FIELD." You seem to be arguing that each photon can be considered individually, which would make sense in an isotropic field. But here we have two photons with identical phase and direction, i.e. linked by coherence. My question is how does this affect their ability to be absorbed and to stimulate emission. $\endgroup$ – Abbe Mac Jul 26 '14 at 13:48
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The energy is not conserved in the situation you describe: you start with two photons and a particle in the ground state, and you end up with three photons and a particle in the ground state.

If the first photon excites the particle and the second causes stimulated emission, you end up with two identical photons. In fact, you will not be able to distinguish if this excitation-emission happened at all, or if photons didn't interact with the particle.

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  • $\begingroup$ The energy is conserved because the molecule (particle) has internal energy which is converted into the energy of the gained photon. Do you have any evidence that the first photon exciting the molecule and the second stimulating an emission is not what happens? $\endgroup$ – Abbe Mac Jul 26 '14 at 13:52
  • $\begingroup$ You specified that the molecule is in the ground state. When the first photon excites the molecule, it is gone, you only have the second photon left. If the second photon stimulates the emission, then you again have two indistinguishable photons. $\endgroup$ – gigacyan Jul 27 '14 at 16:06
  • $\begingroup$ OK, if the molecule is in the ground state there will be no net absorption. What happens if the molecule is excited? References please. $\endgroup$ – Abbe Mac Jul 28 '14 at 15:42

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