Question

4.) When our laser source interacts with a liquid sample, 1% of the incoming light scatters from the sample (elastic + inelastic scattering). If we built a Raman spectroscopy setup with a collection efficiency of 20%, what should be the power of the input laser considering our detector can detect as low as 1 nW. (Hint: you need to consider what percentage of the total scattering is inelastic scattering)

Answer 1

The percentage of Photons undergoing inelastic scattering and giving stokes signal is approximately 0.000001% of the total scattered Photons (Rayleigh scattered (predominant) + stokes scattered + anti-stokes scattered).

This means, for a 1nW collected light, the power scattered will be:

P_s = (1 x 10^-9)/0.00000001 = 0.1 W

This is the total scattered power.

Now, only 1% of the total Photons scatter. So, total power received for the experiment is:

P = P_s/0.01= 10 W

This power is only due to the 20% of the collected light. Therefore, input power must be atleast:

P_in = P/0.2 = 50 W.

This should be the input laser power.