Consider a four level laser with an active volume V = 1 cm^3. The population den

Question

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 N_0. The photon number density is eta and the photon lifetime is T_p. Write the rate equations for N_2, N_1, N and eta in terms of N_0. the transition cross section sigma(v) and the times t_sp, T_1, T_2, T_21, and T_p. Determine the steady state values of N and eta.

Explanation / Answer

Given that the upper and lower laser levels are N2 and N1

N=N2-N1

Photon number density=n

Lifetime of photon=Tp

The steady state population difference N in absence of stimulated emission and absorpttion=No

Therefore No=Nn=(N2-N1)n

Number density n=No/(N2-N1)

Lifetime Tp=n/No

Transition cross section=volume *density=V*n

tsp=Tp/n

T1=N1/n

T2=N2/n

T21=(N2-N1)/n

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