# A Forbidden Transitions in the He-Ne Laser?

1. May 11, 2016

### kq6up

This is a quick question. This entry in the Laser Encyclopedia states that transitions differing in the angular momentum quantum number "l" by 1 are allowed. Here is the link:
https://www.rp-photonics.com/forbidden_transitions.html
However, diagrams that show energy transitions labeled "laser" transitions (my understanding this are "forbidden") are going from 3s to 3p and 2s to 2p. These should be fast transitions based on what I know about selection rules. What am I missing here? Here is the link to one of the images:

Thanks,
KQ6UP

2. May 11, 2016

### blue_leaf77

The selection rule for the quantum number $l$ in electric dipole approximation is $\Delta l = \pm 1$.

3. May 11, 2016

### kq6up

So then the 3s, 3p and 2s, 2p should be fast transitions not metastable transitions, correct?

KQ6UP

4. May 11, 2016

### blue_leaf77

They are more precisely the stimulated transition. If the lifetime between those states are too short (which what you possibly mean by "fast transition"), then the pumping rate might not be high enough to keep the population inversion. In fact, the favored states to be used as the upper laser level are those having long lifetime to give more times for the electrons to accumulate in that state before undergoing de-excitation giving up the laser photons.

5. May 11, 2016

### kq6up

True, then the states that carry the excited atoms in an inversion should have only slow (not selected) transitions. However, S->P as the diagram shows match the $\Delta l$ condition. This seems like a contradiction, so either I am missing something (more likely), or the diagram I posted the link to is wrong.

Thanks,
KQ6UP

6. May 11, 2016

### blue_leaf77

Allowed transition does not always mean fast lifetime, the lifetime of a particular state depends on various things including the energy differences with the nearby states. The term "allowed" here means dipole allowed transition, in which one photon dominates during the transition.

7. May 11, 2016

### kq6up

So sometimes the "allowed" state is also the state from which you are stimulating the transition, correct? I was thinking it was always a "disallowed" state to keep the half life of that state long enough to cause an inversion. My understanding is that it could leak out by the lower probability quadrapole term. This is the very thing that is confusing me. However, if a dipole transition is slow enough I guess that can work too. I guess the non-radiative transfer from the Helium is the important part of the pumping of the inversion in this case correct?

Thanks,
KQ6UP

8. May 11, 2016

### blue_leaf77

Indeed there is always a leakage through higher order dipole terms but as you have known, their probability is very small and very little photons are emitted via these paths.
In He-Ne laser, the essential transition is the excitation by electron collision (Anregung durch Elektronenstoesse in that picture) in the He atoms. This transition is difficult to realize through optical method because the dipole transition between ground states and 21S and 23S are forbidden. Therefore, an electron staying in levels 21S and 23S will stay for a longer time without too much depletion due to de-excitation back to the ground levels via higher pole terms, and hence will have higher probability to collide with Ne atoms.

9. May 12, 2016

### kq6up

Got it. So the metastable state here is the species that gets pumped, not the Neon, correct? That makes more sense now. Is there a single species laser that is an example of a four state system. I am trying to choose a clear example for my Laser/Maser paper. Clear cut examples are better, but maybe this is the most well understood system. My paper is longish already, so I wanted the simplest 4 level example to explain.

Thanks,
KQ6UP

10. May 12, 2016

### blue_leaf77

Yes, the metastable levels are those two excited levels of He atoms.
If you shift to another point of view, you can actually model He-Ne laser as a 4-level system, for example .
Other examples, according to my literature, includes excimer laser and Nd:YAG laser.

11. May 12, 2016

### kq6up

Ok, so I think I have this correct now after watching the video. The He is metastable because off forbidden transitions, and the Ne is not metastable because of forbidden transitions, just that it achieves an inversion in homeostasis (if that word is applicable here) because the middle level to ground depopulates faster than the highest level to the middle level. Therefore, a a photon with $\nu=(E_h-E_m)/h$ frequency is more likely to stimulate an emission than excite a transition of $E_m->E_h$ level (where $E_m$ is the mid level energy, and $E_h$ is the high level energy). Do I have this 100%?

Thanks,
KQ6UP

12. May 12, 2016

### blue_leaf77

Yes, that's in fact the key point in the working of a laser through population inversion. Such situation must apply in all types of lasers, not only restricted to He-Ne laser.

13. May 12, 2016

### kq6up

Last edited: May 12, 2016