Dear Balaji, please see the Fig .2 (a) & (b). Water not absorb 808 nm, very low absorption. And with increasing Nd3+ concentration we can see heat generation is increasing due to concentration quenching.
The CW laser intensity for experiments( ex vivo) is 1.5 W/cm2 (not power 1.5 W). No optical damage was observed in our experiments (1 - 4 W/cm2).
You can find the little more details on this paper. There are similar works cited on this paper comparing 980 to 808 or 800 nm. Water absorption cross-section is low at 808 nm compared to 980. Most of these works reported based on the very simple experiment, NPs were mixed in water and monitored the temperature before and after the exposure of your excitation source. If your medium is other than water, same setup can be repeated.
Importantly, your power of laser does not matter on this kind experiment. Power density matters. Beam size can be tuned depending on the sample or exposure we want. You can generate less than solar power density with 1.5 W of laser making very large beam size. I hope this will answer your question.