(Answered): Part A: Material Dispersion The empirical expression shown below is the Sellmeier dispersion equati ...

Part A: Material Dispersion The empirical expression shown below is the Sellmeier dispersion equation for the refractive index of glass in terms of wavelength 2. The constants G1, G2, G3, 21, 22, and 23 are called the Sellmeier coefficients and are determined by fitting this expression to experimental data. 6722 G222 G?2² n2 – 1 = + + 2²-23 2² - 22 2²-23 The following table shows the Sellmeier coefficients for Pure Silica (SiO2) and SiO2-13.5% GeO2 extracted experimentally. The Sellmeier coefficients for SiO2 and SiO2-13.5% Ge02. G G3 21 (um) 22(um) SiO2 0.6967490.408218 0.890815 0.0690660 0.115662 SiO2-13.5%Ge02. 0.711040 0.451885 0.704048 0.0642700 0.129408 23 (um) 9.900559 9.425478 1. Using Matlab, write a program to obtain the refractive index as a function of a from 0.5 um to 1.8 um for both SiO2 and SiO2-13.5% GeO2 2. Using Matlab, write a program to obtain the group index, Ng, as a function of 2 from 0.5 um to 1.8 um for both SiO2 and SiO2-13.5% GeO2 and plot them on the same plot of part (1). 3. Using Matlab, write a program to obtain the material dispersion as a function of 2. from 0.5 pm to 1.8 um for both SiO2 and SiO2-13.5% GeO2 4. Find the wavelength at which the material dispersion becomes zero in each material. The purpose of this project is to provide simulation-based validation of the theory being studied in class. The project should be handed in as a report showing the following: 1- The Matlab source code used for each question. Note: the code that you submit must be well documented and commented so that it is easily understood by a novice Matlab programmer. 2- The necessary derivations/equations used in the Matlab code along with your reasons for using them. All the assumptions must be stated clearly in your report before using them. 3- The resulting figures of the various questions with clear titles and legend. 4- Answers and analysis of each question. 5- The format of the report must be clear and will be part of the grade. Part B: Dielectric Slab waveguide Design a dielectric slab with core made of Si02-13.5% eO2 and cladding made of Pure Silica for wavelength of 0.82 um. 1. Write a program using Matlab to produce a mode chart for varying core diameter d of the dielectric slab waveguide. Use the TE ray analysis and plot the modes against (d/). 2. Re-produce part (1) by plotting the left-hand side against the right-hand side of the TE transcendental mode equation. Use the ray analysis and plot the modes against (0). Take d = 20 um. 3. Compare the angle solutions of part (1) to part (2), Part C Fiber Optics For a single mode fiber step-index fiber made of SiO2-13.5% GeO2 core and cladding of pure Silica. 1. For the fiber to have NA = 0.1, and a core diameter of 9um operating at 1.3 um.. How should the cladding composition be modified to accommodate those properties (assume a linear relationship between the refractive index and the addition of GeO2)? 2. Write a program using Matlab to produce the attenuation tails of the fiber as a function of à from 0.5 um to 2 um (Consider intrinsic and Rayleigh losses). Plot each loss and the total loss in the same figure. What is the best operating wavelength? 3. Waveguide and polarization dispersion of the fiber can be approximated by the equations in the table below Waveguide Dispersion 1.984 Dw(s m-2) = 2 c(2na)2n2 Polarization Dispersion Ng1 (1.984 dA - ? V2 Using Matlab, write a program to obtain the waveguide, polarization, and chromatic dispersion (in ps nm-km-?) as a function of from 0.5 um to 1.8 um for a fiber of SiO2 cladding and SiO2-13.5% GeO2 core. Take the core diameter to be 8 um.