Solutions_Homework2

# Solutions_Homework2 - | Delta are used in calculating the...

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GEORGIA TECH LORRAINE GEORGIA INSTITUTE OF TECHNOLOGY School of Electrical and Computer Engineering ECE 6543 Fiber Optic Network Spring Semester 2009 Problem 1 1. From course, we know that the cutoﬀ wavelength is: λ cutoff = 2 πa 2 . 405 q n 2 1 - n 2 2 From the numerical values, we ﬁnd that the core refractive index is n 1 =1.45454. Therefore for the ﬁber to be single-moded for λ > 1 . 2 μm , we have 1 . 45 < n 1 < 1 . 45454. 2. We have: V = 2 πa λ q n 2 1 - n 2 2 From the numerical values, we ﬁnd that the core refractive index is n 1 =1.4552, using b ( V ) = (1 . 1428 - 0 . 9960 /V ) 2 . We obtain b(2.0) = 0.41576 and the eﬀective refractive index is 1.45218, therefore the prop- agation constant, β = 2 πn eff =5.887 μm - 1 . Problem 2 The speciﬁed nominal value of a must satisfy λ cutoff < 2 π (1 . 05 a ) 2 . 405 n 1 2 × 1 . 1 × 0 . 005 From the numerical values, we ﬁnd that the largest value that can be speciﬁed is a = 2.78 μ m// Note that we have used the property that λ cutoff increases with increase in a or | Delta so that the largest possible values of a and

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Unformatted text preview: | Delta are used in calculating the cutoﬀ wavelength. Problem 3 From the assumptions, we can derive the pulse spread and the group velocity dispersion • Δ τ = 1 . 732 ps • β 2 = 0 . 1732 ps 2 /km 1. The pulse output width is equal to 3.6 ps 2. The pulse output width is equal to 2.2 ps 1 Problem 4 From the course, the pulse broadening relation is T z T = s ± 1 + κβ 2 z T 2 ² 2 + ± β 2 z T 2 ² 2 This equation rewrites: T z T = v u u t ± 1-κz L D ² 2 + ± z L 2 D ² 2 1. From the diﬀerentiation of the above equation, we yield to z min = κ 1 + κ 2 L D For κ = 4, we obtain z min = 0 . 154 L D 2. The pulse width equals that of an unchirped pulse if bigg (1-κz L D ² 2 + ± z L 2 D ² 2 = 1 + ± z L 2 D ² 2 For κ = 4, we obtain z min = 0 . 5 L D 2...
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## This note was uploaded on 09/01/2010 for the course ECE 6543 taught by Professor Boussert during the Spring '09 term at Georgia Tech.

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Solutions_Homework2 - | Delta are used in calculating the...

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