Rate Equations in a Four-Level Laser. Consider a four-level laser with an active volume V = 1 cm ^3 . The population densities of the upper and lower laser levels are N 2 and N 1 and N = N 2 - N 1 . The pumping rate is such that the steady-state population difference N in the absence of the stimulated emission and absorption is No. The photon-number density is n and the photon lifetime is Tp . Write the rate equations for N 2 , N 1 , N, and n in terms of No, the transition cross section s(v), and the times tsp , T1, T2, T21, and Tp . Determine the steady-state values of N and n.