Originally Posted by Ziggurat in #17
Without stimulated emission, thermal radiation would result in the Wien distribution law
. By adding the hypothesis of stimulated emission, we get the Planck law of black body radiation. We conclude that the effect of stimulated emission is the difference between the Wien and the Planck distribution laws, and this difference
becomes substantial in the low frequency range.
Originally Posted by wogoga in #16
Originally Posted by Reality Check in #18
This is not the decisive point. The relevant condition for stimulated emission is the existence of "excited" states being able to provide the energy (and recoil), necessary for the emission of photons being coherent with the stimulating photons. In the case of blackbody radiation, the probability of this condition is the higher, the lower the frequency of the emitted photons. The reason is simple: The energy for emitted photons comes from kinetic energy of atoms/ molecules. The lower the needed photon energy, the more atoms/ molecules can provide it.
At the far end of the far-infrared (1 mm wavelength) of blackbody radiation of 5777 °K, the proportion between stimulated emission and spontaneous emission is 400*
. This means: One photon emerging spontaneously leads on average to around 400 coherent photons.
In the case of green light of 540 nm, only around 1 percent of the photons are due to stimulated emission. But this does not prevent such green photons from later becoming coherent with other photons of (almost) the same wavelength flying in (almost) the same direction.
* I hope my calculation (Planck's distribution formula at wavelength of 1 mm divided by corresponding value of Wien's distribution formula) is correct.