Question

3. a. Starting with the rate equations for a three-level laser (see notes pl12), derive the equation for the steady-state inversion. Note: do not neglect absorption and stimulated emission b. Show that the equation for the steady-state inversion when absorption and stimulated emission are ignored can be modified using the substitutions: to recover the same result as part (b)

Answer 1

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within 2 hours of answer time, it is impossible for me to answer both of the questions. I request you to repost the questions with a request to solve part b.

If we assume that transition take place only between these three levels then we may write, N = N_1 + N_2 + N_3 equation (1a) N implies total # of atoms/volm we may write rate equn describing the rate of change of N_1, N_2 & N_3. For example for N_3, dN_3/dt = W_p (N_1 - N_3) - T_32 N_3 equation (1) W_p = rate of pumping per atom from level 1 to level 3. T_32 N_3 implies Spontaneous transition from level 3 to 2. T_32 = A_32 + S_32 A_32 & S_32 correspond radiative & non radiative transition rates between levels 3 & 2. \r\n In the equn (1) we have neglected T_31 N_3 which corresponds to spontaneous transitions between levels 3 & 1 since most atoms raised to level 3 make transitions to level 2 rather then to level 1. In same way we can write, dN_2/dt = W_1 (N_1 - N_2) + N_3 T_32 -