A) draw energy level diagrams for three and four level discrete energy laser systems and explain how population inversion is obtained. which system is likely to have the lower lasing threshold and why? [5 9r b) derive the two rate equations for the upper and lower energy levels of a four level system. assume that the only physical mechanisms of interest are stimulated emission, spontaneous emission, stimulated absorption and optical pumping. [4] 10-9 9 c) sketch the relationship between (i) population inversion and (i) optical output power with pumping rate. [4] d) consider a he-ne laser operating at a wavelength of 632.8nm with a mirror separation of 0.40m and mirror reflectivities of 95% and 100%. assuming the loss coefficient is 0.05m, calculate the threshold gain coefficient of the laser. 12] d) the threshold gain of a laser is 1.1m1. given that the mirror reflectivity is 0.8 and the device length is 0.5m, determine the scattering loss.