There's a good chance the laser idea might not work well...at all.
The materials in it all have different coefficients of thermal expansion. Throwing it in liquid nitrogen will probably just shatter several parts of the diode and it's casing. Especially the glass window glued to a metal can, I doubt that part survives, as well as many of the other places where different materials are in contact.
Not saying low temperatures won't have an effect on how a laser works, but that sudden drop in temperature and with how the diode is mounted in the can, I don't see it ending well.
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LN can also make metals very brittle; especially certain types of metals, which can undergo a huge change in toughness at low temperatures. Many steels will have this property, but not all. If you're not sure for a type of steel, just google the designation for that metal and "dbtt" or "ductile brittle transition temperature". So some ordincary pieces of steel, which are quite tough at room temperature, will shatter with just a hit from a hammer at LN temperature (this may or may not be safe for you and your circumstances; take LOTS of precautions, little shards of flying steel are not something you want hitting you in the eye).
You can also make liquid oxygen [smiley=evil.gif]. Quite flammable, and something you don't want to try at home, as well. Some things, when soaked in liquid oxygen, can detonate spontaneously or unpredictably. You probably won't be able to get much oxygen anyway, but it can still be dangerous stuff. Oh yeah, and it's blue, which I think many people don't expect (I didn't).
Sorry, I just keep suggesting all these "don't do this" ideas. But at least you'll have them later when you're in safer environments, like real labs where it's ok.