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Download Final Exam Solution - Optical Modulation and Detection - Fall 2008 | ECE 240C and more Exams Electrical and Electronics Engineering in PDF only on Docsity!
— SOLUTIONS: Do Nor REMOVE —— University of California, San Diego Department of Electrical and Computer Engineering ECE 240A “Optics and Lasers” Fall 2008-Final Examination Time limit: 2 hours +16 wing Please answer the following three problems. Write your answers clearly and neatly, and please write down the formula before plugging numbers into it. PS. OPEN Book, NOTES, uwk, Problem 1: Gain saturation (10 points) You are given a homogeneously broadened gain cell of length d. Assume intensity at the input is lo and that the gain coefficient vis spatially constant. 1 /\I\/\/>|_ Gain coefficient y —> N\WVWV z=0 y= q (a) Find an algebraic expression for the intensity at the output, taking into account the effects of gain saturation. (6) (b) Assume I, =1 mW, Ip =0.1 mW, y= 10 cm”, and d = 1 cm. Calculate I(d). Calculate the ratio of (d) to lp exp(Yod). CL’) Problem 2:Thelaser (10 points) A laser consists of a cylindrical rod of a crystal (n = 1.83) with dimensions w=1 mm (radius of the cylinder) Vand d d=5 cm (length). The ends of the rod are cleaved and polished. Given ose = 3.2 x re 106 m?, Roads tee ove length) and tupper = 230 Ls (upper state lifetime). (The lower level * may be assumed to be fully depleted.) (a) Using the standard Fresnel formula, find the reflectivity of the ends. (Assume plane- wave and normal-incidence conditions.) (2) (b) Calculate the threshold inversion density (units of cm’). ca) (c) Calculate the minimum pump power required to achieve threshold, assuming unity efficiency, and that the upper level is directly pumped (units of Watts). C 4) 
