Homework_Chapter_02

Homework_Chapter_02 - EEE 165 CSUS Instructor: Russ Tatro...

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EEE 165 CSUS Instructor: Russ Tatro Chapter 2 Dielectric Waveguides and Optical Fibers S.O. Kasap, Optoelectronics and Photonics, Principles and Practices , 2001 Solutions to Chapter 2 Homework. Problems 5, 8, 9, 14 a) 5 λ c = 542 nm Is 870 nm wavelength single mode operation? Ignore rest of the question (do not answer penetration depth or MFD) 8 a) V = 89.47 and the number of modes is? b) λ c = 31.6 µ m c) NA = 0.242 d) α max = 14 ° e) ∆τ /L = 67.6 ns per km and BL 13 Mb/sec km 9 a) V = 2.094 b) λ 1.12 µ m c) NA = 0.108 d) α max = 6.2 ° e) ∆τ /L = 0.025 ns/km and BL 23.6 Gb/sec km use Dm = -7.5 ps/km nm and Dw = -5 ps/km nm 14 a) σ intermodal = 0.029 ns for 1 km of fiber ∆τ material = 0.015 ns for 1 km of fiber ∆τ material(rms) = 0.425 ∆τ material = 0.00638 ns σ total = 0.0295 ns b = 0.25/ σ total = 8.5 Gb Now for multimode step index ∆τ /L(rms) = 72 ns/km BL = 12.8 Mb/sec km With LED source σ material = 0.17 ns for 1 km of fiber σ total = 0.172 ns for 1 km of fiber B = 1.45 Gb
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2.5 Dielectric slab waveguide Consider a dielectric slab waveguide which has a thin GaAs layer of thickness 0.2 µ m between two AlGaAs layers. The refractive index of GaAs is 3.66 and that of the AlGaAs layers is 3.40. What is the cut-off wavelength beyond which only a single mode can propagate in the waveguide assuming that the refractive index does not vary greatly with the wavelength? If a radiation of wavelength 870 nm (corresponding to bandgap radiation) is propagating in the GaAs layer, what is the penetration of the evanescent wave into the AlGaAs layers? What is the mode field distance of this radiation? Solution Given n 1 = 3.66 (AlGaAs), n 2 = 3.4 (AlGaAs), 2 a = 2 × 10 -7 m or a = 0.1 µ m, for only a single mode we need V = 2 π a λ n 1 2 n 2 2 () 1/ 2 < π 2 > 2 π an 1 2 n 2 2 π 2 = 2 π (0.1 µ m) 3.66 2 3.40 2 ( ) 1/2 π 2 = 0. 542 µ m. The cut-off wavelength is 542 nm. When = 870 nm, V = 2 π (1 µ m) 3.66 2 3.40 2 (0.870 µ m) = 0.979 < π /2 Therefore, = 870 nm is a single mode operation.
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Homework_Chapter_02 - EEE 165 CSUS Instructor: Russ Tatro...

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