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I have seen the phrase 'modal gain' used in the context of photonics. Researching this phrase, I found this resource, which explains it as follows:

Modal Gain: which is the material gain adjusted to take into account the poor overlap that always exists between the optical mode and the electron envelope function in the quantum well.
(I.e: modal gain=material gain* confinement factor)

However, I don't find this explanation very illuminating. My understanding of photonics is at a novice level, so part of the problem is that this explanation is too advanced for me to understand. So, as a novice-level explanation, what is 'modal gain'? Furthermore, I am especially interested in what 'modal gain' means in the context of laser diodes. So what is 'modal gain' in the context of laser diodes?

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In a laser/maser the active environment (i.e., the atoms) is placed within a cavity, which assures that the light makes multiple passes through the active environment and thus becomes amplified (in laser diodes the role of the cavity/morrors is often played by the surfaces of the semiconductor crystal - while such cavities have low Q-factor, they are often sufficient for practical purposes.)

While this picture of photons bouncing between the mirrors is intuitively appealing, it is somewhat misleading: in practice the electromagnetic radiation in the cavity are standing waves, which have certain spatial structure - notably the maxima and the nodes. The part of the active environment around the maxima of the standing wave is strongly coupled to the radiation, whereas the atoms near the nodes are not coupled at all. A cavity may support multiple modes (of the order of hundreds or thousands in a laser diode), all of them having different spatial structure and differently coupled to the active environment. Thus, the gain is determined not only by the properties of the active environment, but also by the mode strucure and the specific lasing mode. It is not uncommon for a laser to support multiple modes (non-overlapping or having little overlap in space) in the same time - this is certainly the case of laser diodes.

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  • $\begingroup$ Thanks for the answer. What are these "nodes" that you mentioned? I'm familiar with 'modes' en.wikipedia.org/wiki/Longitudinal_mode in this context, but I don't understand what is meant by 'node'. $\endgroup$ Jul 7, 2021 at 11:33
  • $\begingroup$ Also, it isn't clear to me that you actually explain modal gain ("modal gain" isn't mentioned at all in your answer). $\endgroup$ Jul 7, 2021 at 11:39
  • $\begingroup$ @ThePointer Modes are the solutions of maxwell equations in the cavity, as shown in the wikipedia article that you linked above. As you see in the first figure in this article, in a simple Fabri-Perot resonator, the modes are simply standing waves, which have maxima and minima (nodes) that do not move. $\endgroup$
    – Roger V.
    Jul 7, 2021 at 11:42
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    $\begingroup$ These ecee.colorado.edu/~bart/book/book/chapter4/pdf/ch4_10.pdf lecture notes seem to elaborate on in further. $\endgroup$ Jul 7, 2021 at 12:30
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    $\begingroup$ @ThePointer These are good ones. Eq. (4.10.4) is what I meant: the gain calculated in (4.10.2) from the properties of the active media only, is multiplied by a factor due to the confinement factor due to mode shape (or more precisely the overlap between the mode and the active medium, if the latter does not fill all the cavity.) $\endgroup$
    – Roger V.
    Jul 7, 2021 at 12:41
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The material gain is independent of the cavity geometry. In practice, when placed in a laser cavity, only a portion of the gain region intersects the optical mode. This overlap is the modal gain. I'm not an expert on laser diodes, but you should read the book 'Diode Lasers and Photonic Integrated Circuits' (ISBN: 1118148177).

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