Solutions_228A_midterm_W11

Solutions_228A_midterm_W11 - University of California Santa...

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University of California, Santa Barbara __Solutions___ Dept. of ECE ECE 228A Midterm Exam Winter 2011 This is a closed book exam. You are allowed to use both sides of a single 8.5”x10” sheet of paper for formula and constants. Calculators are only allowed for numerical computation only and not for storage of formulae. Clearly state all approximations and assumptions. You will only be graded for work shown. Good Luck! Problem 1 Problem 2 Problem 3 Total 30 pts 30 pts 40 pts 100 pts
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University of California, Santa Barbara __Solutions___ Dept. of ECE Problem 1 (30 points) For parts (a) and (b) assume λ 0 = 1.31 μ m, Δ = 2 x10 -3 , and n 1 =1.45. Perform your calculations to three decimal places. With the aid of the attached Figure: Part A, 10 pts Specify the maximum V and b that will allow 4 modes to propagate in a step index fiber. Calculate the effective mode index and the propagation constant β 11 for the HE 11 mode. Using the figure provided, the maximum V and b allowed for 4 modes to propagate can be found on the HE 11 curve: V 3.8, b 0.8 This allows HE 11 , HE 21 , TE 01 , and TM 01 modes to propagate Calculating the effective mode index for HE 11 : " = n 1 # n 2 n 1 $ n 2 = n 1 1 #" ( ) = 1.45 1 # 2 % 10 # 3 ( ) = 1.4471 ( ) ( ) 4471 . 1 45 . 1 8 . 0 4471 . 1 2 1 2 2 1 2 ! + = ! + = " ! ! = n n b n n n n n n b eff eff 4494 . 1 = eff n The propagation constant for HE 11 : " 11 = n eff 2 # $ 0 = 6.95 % 10 6 r/m Part B, 10 pts Specify the maximum value of V and b for single mode propagation. Calculate the fiber core radius, the effective mode index and propagation constant for the single mode case.
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This note was uploaded on 11/24/2011 for the course ECE 228a taught by Professor Bowers,j during the Fall '08 term at UCSB.

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Solutions_228A_midterm_W11 - University of California Santa...

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