This is your laser then. http://www.o-like.com/b2b_cpinfo.asp?id=1008
Are you planning on plugging this into a AC-DC adapter? most batteries aren't 2A.
I forget what the concerns are of plugging a laser module into an adapter like that, but I don't think that the output on AC-DC adapters are very accurate. They spike a lot. My 4V adapter can go up to 7V.
No it wouldn't be a good idea, unless you can control the current and bring it down to 90mA, obviously 2A would blow it to the sky.
If it is DC, and you ran it through a driver which could control the current + the voltage then yes you would be fine, but otherwise the current would not be constant.
I agree with Larry. With such a wide input voltage range, these clearly have built in current regulation. Go ahead and use any 5V supply. The 2A rating refers to the maximum current that can be drawn from the power supply. It does not mean that the power supply puts out 2A. BTW a 2A rating likely means that it's a switching power supply and thus is likely very precisely regulated.
-Phil
In theory yes, provided the forward voltage of the diode is less than or equal to the voltage output of the adaptor. In reality, because it's taking AC, the DC output "ripples" and "spikes", and isn't a true DC supply. For instance, a "5V" wall adaptor would vary between 4v and 6v. In the 6V spikes, the current would surge, and kill the diode. This would also not work at temperature extremes, because the diode's forward voltage would drop, thus increasing the current and killing the diode.
In reality never. Applying a power supply with a voltage that is even slightly above the forward voltage of the laserdiode (ex: 3.7V supply to a 3.4V diode will easily fry it.) You MUST include some means of current limiting (if only -as Larry said- a resistor.) With that said, I'm 99% sure that those line modules have an integrated linear current regulator but it couldn't hurt to check. As long as it does, feel free to connect any wallwart within the specified voltage range which can provide -at least- the required current +10% and the built in current regulator will adjust the voltage to the diode to keep the current as set by the potentiometer. See their green line generator to see what the regulator board looks like and unscrew the case of the red one to make sure that there's one in there. Another reason to never connect a voltage regulated (any wallwart) power supply to a laserdiode -or any LED for that matter- is -as Charlie said- that the diodes' forward votages vary -destructively- with junction temperature. In other words, they draw more and more current until they inevitably blow up.
Just an update. The 5v 2A power supply worked fine with the 35mw 650nm laser. According to the power supply manufacturer it is a regulated stable current power supply.