光电子学与光子学原理与实践第四章答案.pdf

Preliminary Solutions to Problems and Questions Chapter 4 Note: Printing errors and corrections are indicated in dark red. Only Question 4.15 is affected. 4.1 Pumping of three laser systems Consider the 3-level system in Figure 4.2(a). Assuming that the transitions from E to E are very fast, and the spontaneous decay time from E to E is  , show that the 3 2 2 1 sp minimum pumping power needed (the power that must be absorbed by the laser medium) for population inversion (N N ) is 2 1 P (minimum) = Volume × (N /2)h / . p 0 13 sp Consider a ruby crystal that has 1×1020 Cr3+ ions cm-3, and is 50 mm long and 7 mm in diameter. The spontaneous decay time is 3 ms. Apply this equation to the above ruby laser and find the minimum power that must be absorbed if the excitation is to the band of energies in the blue around ~ 3 eV) in Figure 4.3(a) Solution Consider the 3-level system Figure 4.2 (a) To achieve population inversion we need to get half the ions 3+ at E to level E so that N = N = N /2 since N is the total concentration of Cr ions all initially at E . 1 2 2 1 0 0 1 We will need [(N /2)h × volume] amount of energy to pump to the E -band. The ions decay quickly 0 13 3 from E to E . We must provide this pump energy before the ions decay from E to E , that is before  . 3 2