To test the lasers that I already own, I made a high resolution spectrograph that would be able to resolve the extremely small differences in wavelengths emitted by the laser. Below are some pictures and a video.
I'll start off with a picture of my violet laser, at a very low current. At this current the laser isn't yet lasing. What you see is just the spontaneous emission leaking out of the cavity modes.

When the current is increased, the laser starts to lase. The pattern of modes that lase is quite irregular and depends strongly on the current flowing through the laser. In the next picture the current was set at a value that resulted in operation that resembled 'single mode' the most:
As you can see, one mode is lasing brightly, but there are some parasitic modes on the right. At even higher current, things get worse:
Now you see lasing in a lot of modes at the same time. Clearly not the kind of operation you want for holography.The next picture is my green laser module. Its mode pattern is highly irregular. At first sight, it looks like there are just three modes lasing. But if you look closer, you'll see that the mode spacing is way smaller than the distance between those three modes. So between the three modes that are lasing, there are many modes that aren't lasing. In the video (see below) you can see this more clearly.
The cause for this is probably the fact that this is a DPSS laser. It consists of a diode pump laser that lasers at around 808 nm. This laser pumps another laser that normally lases at around 1064 nm. But the mirrors in this second laser are designed to keep most of this light inside the cavity instead of letting a portion escape like in a normal laser. Instead there's a crystal inside the laser cavity that doubles the frequency of a tiny portion of the light that passes through it. This light *does* escape the cavity and shows up as 532 nm. I assume that because of the many interacting cavities inside this laser, its mode structure is so irregular.Last but not least, my red laser. You can see a couple of modes, but clearly one is way brighter than the others. This is the sole mode that's lasing in this laser. It's so bright that it gets diffracted a bit by the diaphragm blades. This shows up as the six rays that extend from the spot. The band on the left is probably an artifact.

As you can see, my red laser is very suitable for holography, it emits almost all of its light in one mode. The green and violet lasers aren't well suited for making holograms. One can make holograms with them, but only of things that can be put very close to the plate like coins.
I also made some videos of the mode changes (see below). In the first video you can see a phenomenon known as mode hopping. One moment the laser is lasing at one wavelength, and the other it flips to another one. In the video I'm tuning the current up and down to induce the effect.
As you can see in the other video of the green laser, it switches between two completely different mode structures. Again, probably due to it being a DPSS laser.
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