Minimizing the Q-switched pulsewidth. Figure 26.11 from the book (which is also provided below] shows the ratio to/to going down toward unity with increasing initial inversion ratio r. Therefore, for a fixed cavity coupling or cavity lifetime to the Q-switched pulsewidth to will go down toward to = To as the initial population inversion Mor the pumping energy to the laser is increased. Suppose instead you are given a fixed initial inversion value M just before the cavity Q is switched, but you can adjust the cavity coupling & and hence the cavity lifetime To in or the threshold inversion No that applies after the Q is switched. Show that in this situation the shortest possible Q-switched pulsewidth to is obtained by adjusting the initial inversion ratio to be r = 3 and that this minimum pulsewidth is given by to # 3.1 to Of To # 9.4 Imo, where is the Imo is exponential build-up time that energy in the cavity would have if the cavity were switched to have zero total losses just after switching. Note: You might need to use plotting software in the final step of the solution pulsawidth cavity Wifetime To/ TO 3 5 T Initial Inversion rabio r