Understanding Nd:YAG Laser Energy Levels

[paultsui]

Hey guys,

A simplified diagram for the energy levels involved in Nd:YAG laser can be found here:
http://upload.wikimedia.org/wikipedia/commons/6/69/YAG2.svg

Two (short) questions:

1. Selection Rules
The lasing transition happens between $^{4}F_{3/2}$ and $^{4}I_{11/2}$. In the process J (of the electrons) changes from 3/2 to 11/2. Since a photon only carries J=1, how does the process not violate conservation of angular momentum? (Is it something to do with the emission of phonons? If phonons are also required to be emitted in the lasing process, would this affects down the lasing effect?)

2. Transition Intensity
Besides $^{4}I_{11/2}$, there are also many other close levels such as $^{4}I_{13/2}, ^{4}I_{15/2}$ etc. Why is the coupling between $^{4}F_{3/2}$ and $^{4}I_{11/2}$ the strongest? Is there a rule of thumb for determining which transition is the strongest?

 

[Cthugha]

1. Selection Rules
The lasing transition happens between $^{4}F_{3/2}$ and $^{4}I_{11/2}$. In the process J (of the electrons) changes from 3/2 to 11/2. Since a photon only carries J=1, how does the process not violate conservation of angular momentum? (Is it something to do with the emission of phonons? If phonons are also required to be emitted in the lasing process, would this affects down the lasing effect?)

The transition would be forbidden for isolated ions. However, you have a situation where you have replaced some of the ions in the material by other ions. This creates local perturbations and the crystal field will split the energy levels into several sublevels, thus making the desired transition weakly allowed. This is actually a good thing as you want the lasing level lifetime to be long compared to the level from which it is refilled and a long lifetime also means that spontaneous emission is not too strong.