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Unformatted text preview: ECE 455: Optical Electronics Homework 5 Solutions 1 Threshold Gain (a) e Î³ th l g Â· R 2 Â· e Î³ th l g Â· R 1 = R 1 R 2 Â· e 2 Î³ th l g = 1 Î³ th = 1 2 l g ln ( R 1 R 2 ) = 1 2 Â· 30 cm ln (0 . 90 Â· . 99) = 0 . 0151 cm 1 (b) e Î³ th l g Â· R 2 Â· e Î³ th l g Â· R 1 = R 1 R 2 Â· e 2 Î³ th l g = 1 Î³ th = 1 2 l g ln ( R 1 R 2 ) = 1 2 Â· 75 cm ln (0 . 999 Â· . 99) = 7 . 367 Ã— 10 5 cm 1 (c) e Î³ th l g Â· e Î± th l 1 Â· R 2 Â· e Î± th l 1 Â· e Î³ th l g Â· R 1 = R 1 R 2 Â· e 2( Î³ th l g Î±l 1 ) = 1 Î³ th = Î±l 1 l g 1 2 l g ln ( R 1 R 2 ) = . 1 cm 1 Â· 5 cm 20 cm 1 2 Â· 20 cm ln (0 . 995 Â· . 95) = 2 . 64 Ã— 10 2 cm 1 (d) Start at one of the mirrors and follow the ray around the cavity. For example, start to the left of the mirror at the bottom right and follow the ray to the left. When you get to the 50% reflector, you then have 2 paths you need to keep track of, both of which take 50% of the incident intensity....
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This note was uploaded on 02/28/2012 for the course ECE 455 taught by Professor Eden,j during the Fall '08 term at University of Illinois, Urbana Champaign.
 Fall '08
 Eden,J

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