Problem 2. Show that if a Fabry-Perot etalon has an intensity gain per pass of G, its peak (1-R)2G transmission is given as (1-RG)2 Problem 3. Starting with the definition F=m+1 for the finesse of a Fabry-Perot etalon Av1/2 and using semi-quantitative arguments, show why in the case where the root-mean square surface deviation from the perfect flatness is approximately A/N, the finesse cannot exceed FN/(2n), where N is some constant, n is the refractive index of the etalon's medium and the medium outside the etalon is air. [Hint: Consider the spreading of the transmission peak due to a small num- ber of etalons of nearly equal length transmitting in parallel.] Note that A1/2 is the frequency width of the transmission resonance around each resonance frequency Vm such that I/I, 0.5 at v = Vm ± Aas will be discussed in class, also known as full-width half-maximum or FWHM linewidth.

Fig: 1