Problem 1. (35 points) Write a software program (e.g. Matlab) that solves a symmetric dielectric slab waveguide n other words, starting from the lecture note equations, below link X vs Vand Y vs Vin your program for TE waves: Your program should be able to provide the values of X and Y for a given Vvalue. Alternatively, you can write a program so that it prompts the users to enter d, n1, n2, and .values and then calculates V value internally. You can use d 6 Hm, n1 1.50, n2 1.49, and 1.55 um Using this program, (a) obtain the plot of X vs. Vin the range of V 0 to 6. The actual computation does not need to go a set of tabulated solutions (v, x) and a plot interpolating the solutions. Complete this for the lowest TE mode. Save this design curve for later purposes. (b) Repeat (a) and plotYvs. V. (c) Repeat (b) and plot Zvs. V where Z3Ba (d) For a symmetric waveguide of total thickness d 6 um, wavelength 1.55 um, core optical index n1-1.50, cladding index n2-1.49, what is the value of B? What is the angle 01