Question 3 - Propagating Through a Lossy Cavity (20 Marks) Here we'll consider a Fabry-Perot resonator consisting two identical mirrors (R, = R) separated by a distance d, which contains some relatively low-loss gaseous material between the mirrors. The refractive index of the gos is n = 1.03 and it's passive loss coefficient a, = 0.03 m' This cavity is illuminated by a I as pulse from an external 532 am laser source. The output beam of the cavity is observed to be a regular sequence of 1 as pulses spaced apart by 5 ns. The energy of the output pulses decreases exponentially with a time constant of 35 ns. a) Using the relationships between loss term V* and loss coefficient a,: V* = Exp[-a, , and gain term G and gain coefficient a: G = Exp[-a , show that the equation for resonator lifetime 7 = [Lecture 1, Slide 23 now including G), is equivalent to 7= bj Using either expression for r, determine the dependence on the losses and gains for the cavity full-width-at-half- maximum, Finesse and Q-factor. c) Using the observations from the introduction above, calculate the cavity length, the mirror reflectivity, the cavity finesse, photon lifetime, and Q-factor