As I said, there is a limited range of current for a diode - too much it is fried, too little and it
doesn't lase. This is something a datasheet for the diode would tell you.
Your constant current circuit isn't adjustable(*), so its not appropriate. Typically an adjustable
current source/sink would use an opamp and current-buffer and sense-resistor - the opamp
compares the voltage across the sense resistor to the control voltage and maintains it the same.
For instance the circuit on this page (ignore all the maths!): Nullor - Citizendium
(*) Except by varying the resistor, but that carries the entire load current, so its not practical.