Answer Happy

1. Consider an amplifying medium composed of homogeneously broadened three-level atoms like shown in the fig. 1. Amplification is to occur on the 2-to-1 transition. Amplification is to occur on the level 2-to-1 transition. The medium is pumped by a laser of intensity Ip, which is resonant with the 3-to-1 transition. Level 3 decays spontaneously to level 1, which is the ground state of the system. The total number density of gain atoms is Nr=N1+Na+Nj. The various parameters are (30 points) kz, = 10/s, ką = 10/s, 0,=031 =3x10-cm?,0 = 10-8 cm? 2 = 400nm, 2 = 600nm N, =1.5x1026 / m) E, K32 E2 o op hv K31 K21 hv P E K30 K10 K20 E. Fig. 1 Level structure of a four-level gain medium. a. Sketch a level diagram appropriate for this case and indicate the various stimulated and decay processes with arrows on the level diagram. b. Write down the rate equations for the population densities of the levels. Include the presence of a field of irradiance I resonant with the 2-to-1 transition, the pump interaction, and the decay processes. c. Find and plot the steady-state small-signal population inversion Na-N1 as a function of pump irradiance. (recall that "small signal" is code for" set 1-0.") d. Find the pump irradiance Ip required to sustain a steady-state population inversion. e. Find the pump irradiance Ip required to sustain a small-signal gain coefficient of 0.01/cm. f. Find the pump irradiance Ip required to sustain a small-signal gain coefficient of 1/cm. a