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MIT6_013S09_pset12

# MIT6_013S09_pset12 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.013 – Electromagnetics and Applications Problem Set 12 (six problems) Suggested Reading: Text: Sections: 12.3-12.4, 13.1-13.2.1, 13.2.3-13.2.4, 13.3, 9.4 Problem 12.1 A certain clad optical fiber can be approximated by a dielectric slab waveguide of thickness D 1 and permittivity ε 1 = 4 that is centered in a dielectric of D 1 thickness D 2 and permittivity ε 2 = 3.9, as illustrated. Assume the angle of incidence within the inner fiber is θ i = 85 o , which is beyond the critical angle θ c . (a) What is the critical angle θ c ? (b) In terms of the free-space wavelength λ o , what is the 1/e decay length α -1 in the cladding ( ε 2 ), where E(x) = y ˆ E o e - α x ? Normally D 2 is made many times thicker than α -1 to ensure no external attenuation occurs. A four-level laser has equally spaced atomic energy levels E 4 > E 3 > (c) Roughly guess what D 1 reasoning. is in terms of λ o for the TE 1 mode. Briefly explain your Problem 12.2 4 3 E 2 > E 1 , as illustrated. Assume the spontaneous transition rates A 41 , 2 A 42 , A 31 , and A 32 0, while the others are larger. 1 (a) When the 1-4 transition is pumped, in which energy level do most atoms eventually find themselves in the absence of lasing? Briefly explain your reasoning. (b) For this case, approximately what is the maximum possible energy efficiency of this laser (P out /P pump ) for the 3-2 laser transition?

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MIT6_013S09_pset12 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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