Assume a regular power (10-30mW) laser diode in a communication setting, IOW in the 1550nm band. Peltier-cooled with proper temp regulation. Now you want to de-tune it by about 0.5nm. In order to play it safe the control circuit would not try to force the loop by going to the abs max current but instead it would just switch it from, say, 150mA to 250mA or maybe a tad above target to speed up the run-in.
How long would it typically take for the diode to get to within 90% of it's wavelength at 250mA? How much the other way around? I asked a laser diode mfg engineer and he said they do not have data about that because it isn't needed for the usual applications.