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The way I see it, in both spontaneous and stimulated emission, one atom being de-excited would result in one photon being produced. So if we excite $10^{23}$ atoms, only $10^{23}$ photons would be produced when they de-excite. How can there be a net output of photons then? How is it that lasers can be sustained for a long time at high intensities?

Also, my notes state that when a system is in equilibrium, the rate at which atoms are excited is equal to the rate at which the atoms are de-excited. What is meant by equilibrium in this context?

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  • $\begingroup$ Perhaps I'm misreading your first paragraph but just to be clear: In stimulated emission one photon comes in and two photons of precisely the same frequency leave. In the process one atom is de-excited. This is where the photon gain comes from. $\endgroup$ – Chris Mueller Jan 12 '14 at 18:59
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The first point is that a laser is driven out of an equilibrium situation by what is called pumping. This means forcing a higher population of excited states than given by equilibrium Boltzmann distribution which depends basically only on temperature. In this case more atoms can de-excite than the ones being excited thus producing the laser radiation.

Keep in mind that this pumping is repeatedly done to give the system the energy necessary to perform a sustained stimulated emission. This is the source of the energy of the laser, which some part is used for the lasing and other part is lost in other forms like heat.

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  • $\begingroup$ So the only benefit to population inversion is coherence? Am I right in saying that over time, the rate of photon emission is still equal for both cases with and without metastable states? $\endgroup$ – user2246 Nov 26 '13 at 11:38
  • $\begingroup$ No, it's the main ingredient of the process. Without it, you wouldn't be able to achieve a chain reaction of stimulated emission to create the laser output. $\endgroup$ – Ignacio Vergara Kausel Nov 26 '13 at 11:43
  • $\begingroup$ But isn't the only benefit to the chain reaction coherence? Without metastable states, the multiple different energy transitions directly caused by the pumping will lead to multiple photons that are not coherent. But each photon will still lead to the excitation and de-excitation of an atom $10^8$ seconds later. A chain reaction might cause more rapid de-excitation but the de-excitation can't be faster than the excitation due to pumping, can it? If it is, the laser won't be sustainable. Am I right? $\endgroup$ – user2246 Nov 26 '13 at 11:55
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    $\begingroup$ Correct. a laser with higher emission coefficient than absorption coefficient is a laser that is outputting faster than it is being pumped, and will quickly fall below population inversion status and stop lasing. note that the peak output is much higher than in equilibrium lasing--so this is a much leveraged behaviour where ultrahigh intensity laser pulses are required. $\endgroup$ – gregsan Nov 26 '13 at 12:03

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