How Lasers Work — Question 9

Question 9

The pump and laser wavelengths bound the optical conversion efficiency

An ideal laser absorbs pump photons of wavelength $\lambda_p=808\,\mathrm{nm}$ and emits laser photons of wavelength $\lambda_L=1064\,\mathrm{nm}$. Assume at most one laser photon per absorbed pump photon, no stored-energy change, and no other energy source.

1. Derive the maximum optical energy-conversion efficiency.

2. For 5.00 W absorbed pump power, find the maximum laser power and minimum non-laser power under this one-photon model.

Question 9 - Solution

The pump and laser wavelengths bound the optical conversion efficiency

(a) Method and calculation

$$\eta_{\max}=\frac{E_L}{E_p}=\frac{hc/\lambda_L}{hc/\lambda_p}.$$$$\boxed{\eta_{\max}=\lambda_p/\lambda_L=808/1064=.7594}.$$

(b) Interpretation and further calculation

$$\boxed{P_{L,\max}=5.00(.7594)=3.797\,\mathrm W}.$$$$\boxed{P_{\mathrm{nonlaser,min}}=P_p-P_{L,\max}=1.203\,\mathrm W}.$$

Physical check

The remaining energy must leave through heat or other radiation in steady operation. Real output is further reduced by imperfect pumping, nonradiative decay, and cavity losses.