Problem 4) Consider the following laser system. It consists of a conventional 4-level system (the laser action occurs between E2 and El as usual with spontaneous transition time τ2 between these states, and atoms in state El have spontaneous decay time τ| back to the ground state, Eo) 32 34 4 0 To obtain population inversion, atoms are pumped from state Eo to state E3. However, while some of the atoms decay to state E2 with spontaneous transition time 732 , some decay into a non-lasing state Es with spontaneous transition time 7,4. This leads to a second decay pathway from E4 back into the ground state with decay time T4 Note: You may not assume that any of the decay times are short enough to be considered instantaneous here. You may also not assume that the ground state is so populated as to be considered infinite population density. Assuming a pump rate Wp from the ground state to state E3, solve for the population inversion ÀN N2-N, n the steady state in terms of the time constants given, the pump rate and the total population NMt of atoms in all states. Problem 4) Consider the following laser system. It consists of a conventional 4-level system (the laser action occurs between E2 and El as usual with spontaneous transition time τ2 between these states, and atoms in state El have spontaneous decay time τ| back to the ground state, Eo) 32 34 4 0 To obtain population inversion, atoms are pumped from state Eo to state E3. However, while some of the atoms decay to state E2 with spontaneous transition time 732 , some decay into a non-lasing state Es with spontaneous transition time 7,4. This leads to a second decay pathway from E4 back into the ground state with decay time T4 Note: You may not assume that any of the decay times are short enough to be considered instantaneous here. You may also not assume that the ground state is so populated as to be considered infinite population density. Assuming a pump rate Wp from the ground state to state E3, solve for the population inversion ÀN N2-N, n the steady state in terms of the time constants given, the pump rate and the total population NMt of atoms in all states.