Stimulated emission. Energy of the photon inducing the emission.

In summary, stimulated emission requires a photon with the same energy as the difference between the lower and upper energy levels in an excited atom. However, the energy does not have to be an exact match and can still occur with a slightly lower or higher energy photon. The rest of the energy can come from or go into some form of collisional energy. The stimulated emission will be less probable with a photon that does not exactly match the energy levels. Einstein's coefficient for stimulated emission is only for a photon of the exact energy. Energy levels in atoms have a finite width due to the time-energy uncertainty principle, with a natural width of about 10^-4 angstroms. The Stark effect, which is caused by nearby atoms, can also contribute
  • #1
deccard
30
0
In order to produce stimulated emission we need a photon which has the same energy as the difference is the lower and upper energy levels in the excited atom. But how exactly the energy of the photon does have to correspond to the energy difference between the levels. Can stimulated emission still occur if the photon has little less or little more?

If so, where does the rest of the energy come from or where does the rest of the energy go?
Can we get the extra energy from or put the rest in some form of collisional energy?

If we have a photon that does not exactly match for the energy of the energy levels will the stimulated emission then be only less probable according to the stimulated emission cross section.

Einstein's coefficient for stimulated emission should in this case only be for a photon of the exact energy?
 
Physics news on Phys.org
  • #2
Energy levels in atoms aren't exactly discrete, they do have some finite width in energy due to the time-energy uncertainty principle. The natural width is pretty small, but photons with slightly different energy can be absorbed by an atom.

If we have a photon that does not exactly match for the energy of the energy levels will the stimulated emission then be only less probable according to the stimulated emission cross section.
Yes, that is true, the absorbtion cross section is a lorentzian function. It is peaked at the wavelength corresponding to the energy difference, then falls of on either side.
 
  • #3
AstroRoyale said:
Energy levels in atoms aren't exactly discrete, they do have some finite width in energy due to the time-energy uncertainty principle. The natural width is pretty small, but photons with slightly different energy can be absorbed by an atom.

So how large will the linewidth be due this uncertainty principle? I guess that it will be quite insignificant for example when compared to linewidth caused by Doppler-effect.

And what about this Stark effect line broadening? What is the process behind this broadening?
 
  • #4
Yes, the natural width due to the unceratinty relations is really small, much less than the effect of the thermal motions. For thermal broadening the width is,

[tex] \frac{2 \lambda}{c}\sqrt\frac{2kTln(2)}{m} [/tex]

So it depends on the mass and wavelength if the line, but say ~0.1 angstroms is in the ballpark

and for natural broadening the width is

[tex] \frac{\lambda^2}{\pi c t_0} [/tex]

where t_0 is the lifetime, about 10^(-8) seconds or so. So this gives a natural line width of ~10^-4 angstroms.

The stark effect is an effect of nearby atoms, the elcetric field of at ion or atom slghtly perturbs the energy levels of the atoms. In most cases it is pretty small, unless the density of particles is high. I can't remember the numebers off hand, but I'm pretty sure that it is more than natural and less than thermal in most cases.

doppler > collisional > natural (for most cases . . .)
 

What is stimulated emission?

Stimulated emission is a process in which an excited atom or molecule releases energy in the form of a photon when it is stimulated by an external energy source.

How does stimulated emission occur?

Stimulated emission occurs when an atom or molecule in an excited state is stimulated by a photon with the same energy level, causing it to release a second photon with the same energy and phase. This results in the amplification of light energy.

What is the energy of the photon that induces stimulated emission?

The energy of the inducing photon must match the energy difference between the excited and ground state of the atom or molecule in order to trigger stimulated emission.

What is the difference between stimulated emission and spontaneous emission?

Stimulated emission is triggered by an external energy source, while spontaneous emission occurs randomly without any external stimulation. Additionally, stimulated emission produces photons with the same energy and phase as the inducing photon, while spontaneous emission produces photons with random energies and phases.

What are some practical applications of stimulated emission?

Stimulated emission plays a crucial role in the functioning of lasers, where it is used to produce a coherent and intense beam of light. It is also used in fiber optic communication, medical imaging, and spectroscopy techniques.

Similar threads

Replies
18
Views
1K
  • Quantum Physics
Replies
4
Views
904
  • Quantum Physics
Replies
1
Views
691
Replies
6
Views
2K
Replies
2
Views
1K
Replies
1
Views
868
Replies
8
Views
781
  • Quantum Physics
Replies
20
Views
2K
  • Quantum Physics
Replies
15
Views
2K
Back
Top