Student name: Project#1: Dispersion modeling of optical fiber Florida Institute of Technology Department of Electrical Engineering and Computer Science Total points: 100 Points Obtained: • You have to write the answers in MS word or Latex, handwritten answers will not be accepted • You must have to attach the code • You have to submit the project in pdf format • The report should have: o High quality figures such as vector format o Text of the figure should be readable o • If you use Overleaf, you should use figures in .pdf format or .eps format Show all the steps to get full credits and attach this sheet Problem 1 (50 points). Consider, an electromagnetic wave (light) is traveling inside a silica optical fiber. When light travels inside optical fiber, the output signal broadens/spreads compared to the input signal, a common phenomenon in optical fiber communication or electromagnetics is known as dispersion. One of the main reasons for the pulse broadening is due to the material dispersion of silica determined using a well-known Sellmeier equation. The Sellmeier equation is an empirical relationship between refractive index and wavelength for a particular transparent medium. A three-term Sellmeier equation is given by: 𝑛𝑛(λ) = �1 + 𝐵𝐵2 λ 2 𝐵𝐵3 λ 2 𝐵𝐵1 λ 2 + + , λ 2 − 𝐶𝐶1 λ 2 − 𝐶𝐶2 λ 2 − 𝐶𝐶3 Where, n(λ) is the refractive index of silica, λ is the wavelength and B1, B2, B3, C1, C2, and C3 are the Sellmeier coefficients. As an example, the coefficients for a common silica glass are shown below: Coefficient Value B1 0.696166300 B2 0.407942600 B3 0.897479400 C1 (μm2) 4.67914826×10−3 C2 (μm2) 1.35120631×10−2 C3 (μm2) 97.9340025 1 (a) Write a computer code using MATLAB® or Python or C/C++ to draw the refractive index, n(λ) vs. wavelength, λ (μm). Consider the wavelength, λ = 0.4 to 2 μm. You have to attach the code. (b) Write a computer code using MATLAB® or Python or C/C++ to draw the group refractive index, ng(λ) vs. wavelength, λ (μm). Consider the wavelength, λ = 0.4 to 2 μm. You have to attach the code. (c) The dispersion can be calculated the following formulae: 2 Where, 𝑑𝑑2 𝑛𝑛 𝑑𝑑λ2 𝐷𝐷 = − λ𝑐𝑐 𝑑𝑑𝑑𝑑λ𝑛𝑛2 , unit: s/m2 is the double-derivative of refractive index with respect of wavelength. Draw the dispersion vs. wavelength. Tips: (i) if you are using MATLAB, use gradient function for the derivative, (ii) In electromagnetics, we prefer to write the unit of dispersion ps.nm-1.km-1. In order to convert the dispersion unit from s/m2 to ps.nm-1.km-1, you need to multiply 106 with the dispersion equation. Problem 2 (50 points). Consider, an electromagnetic wave (light) is traveling inside a Chalcogenide (As2S3) optical fiber. When light travels inside optical fiber, the output signal broadens/spreads compared to the input signal, a common phenomenon in optical fiber communication or electromagnetics is known as dispersion. One of the main reasons for the pulse broadening is due to the material dispersion of material determined using a well-known Sellmeier equation. The Sellmeier equation is an empirical relationship between refractive index and wavelength for a particular transparent medium. A five-term Sellmeier equation is given by: (a) Write a computer code using MATLAB® or Python or C/C++ to draw the refractive index, n(λ) vs. wavelength, λ (μm). Consider the wavelength, λ = 0.5 to 3 μm. You have to attach the code. (b) The dispersion can be calculated the following formulae: 2 Where, 𝑑𝑑2 𝑛𝑛 𝑑𝑑λ2 𝐷𝐷 = − λ𝑐𝑐 𝑑𝑑𝑑𝑑λ𝑛𝑛2 , unit: s/m2 is the double-derivative of refractive index with respect of wavelength. Draw the dispersion vs. wavelength. Tips: (i) if you are using MATLAB, use gradient function for the derivative, (ii) In electromagnetics, we prefer to write the unit of dispersion ps.nm-1.km-1. In order to convert the dispersion unit from s/m2 to ps.nm-1.km-1, you need to multiply 106 with the dispersion equation. 2

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