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I am currently studying Diode Lasers and Photonic Integrated Circuits, second edition, by Coldren, Corzine, and Mashanovitch. In chapter 1.2 ENERGY LEVELS AND BANDS IN SOLIDS, the authors say the following:

In gas and solid-state lasers, the energy levels of the active atomic species are only perturbed slightly by the surrounding gas or solid host atoms, and they remain effectively as sharp as the original levels in the isolated atom. For example, lasers operating at the $1.06 \ \text{$\mu$m}$ wavelength transition in Nd-doped YAG, use the $^4\text{F}_{3/2}$ level of the Nd atom for the upper laser state #2 and the $^4\text{I}_{11/2}$ level for the lower laser state #1.

I don't understand what is meant in this part:

For example, lasers operating at the $1.06 \ \text{$\mu$m}$ wavelength transition in Nd-doped YAG, use the $^4\text{F}_{3/2}$ level of the Nd atom for the upper laser state #2 and the $^4\text{I}_{11/2}$ level for the lower laser state #1.

In particular, I don't understand what $^4\text{F}_{3/2}$ and $^4\text{I}_{11/2}$ means. Is this supposed to have something to do with the energy levels of fluorine and iodine atoms?

I would greatly appreciate it if people would please take the time to clarify this.

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    $\begingroup$ These are referred to as Term Symbols. They indicate the spin, angular momentum, and symmetry of particular state. $\endgroup$
    – Tyberius
    Commented Jun 23, 2020 at 3:03
  • $\begingroup$ @Tyberius Thanks for the clarification. $\endgroup$ Commented Jun 23, 2020 at 3:16
  • $\begingroup$ Please also see Hund's rule on how to determine the ground state term-symbol. $\endgroup$
    – zimmervi
    Commented Mar 1, 2022 at 15:28

1 Answer 1

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These are known as term symbols. They describe the orbital angular momentum, spin and total angular momentum quantum numbers of a particular state.

The number in the upper left is $2S + 1$, or the spin multiplicity, where $S$ is the total spin angular momentum quantum number.

The letter denotes the total orbital angular momentum $L$, $\text{S}$ meaning $L=0$, $\text{P}$ meaning $L=1$ and so on. The same letters are used to denote the angular momentum quantum numbers of electron orbitals, just in lowercase.

The number in the lower right is the total angular momentum quantum number $J$.

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