Let me see if I got this right, please:
You present a question: "...need proper fixed VOLTAGE..."
"...for a FIXED load...". NO, it's not a fixed load: it's a semiconductor.
After which a likely very experienced reply comes:
"...don't connect directly to a voltage..."
So, you then proceed to another possibility: A VOLTAGE, this time created by a zener, followed by an inevitable reply, explicitly warning: "laser diode is a current-controlled device.."
Generous with advice, that reply also mentions things (like necessary VOLTAGE) 'can vary a lot, with temperature..."
THEN you introduce another LDO regulator option and focus on... wait for it: VOLTAGE output to laser diode.
Granted, of course you have to ensure the headroom is sufficient, there.
To which, the predictable reply ends with:
'...to make a constant current sourc, e...'.
You then further 'experiment' with drive VOLTAGE, even mentioning current NOT constant, a little. (Whatever that means), 'happily' working, (and again, at whatever the device temperature was then...who cares?)
And yet, yet, again REPLY comes: to focus on 'current setting', for a temperature-dependant semi-conductor load.
Ok, I'm done.
Set your sights on 'device current'!!!
I made that mis-step a bunch of times, (tried voltage controls).