Overview: There are various methods to analyze silicon-on-insulator (SOI) waveguides in silicon photonics. Among such methods, the Effective Index Method (EIM) is widely used due to its relatively high accuracy and, most importantly, high computational efficiency. In this lab, we aim at implementing the EIM method and then use it to study different characteristics in SOI waveguides of different sizes. Feel free to use the codes from the textbook for this lab assignment (but you must reference the source if you use any): https://github.com/lukasc- ubc/SiliconPhotonicsDesign/tree/master/siliconphotonicsdesign_book_scripts Problem Description: Implement the Effective Index Method (EIM) for 2D Strip AND Ridge SOI waveguides in MATLAB (or Python, etc.). Your implementation should calculate the effective index and the group index under different optical wavelengths and for different waveguide dimensions as well as for TE and TM modes. You should consider the following parameters in the input (user can define such parameters). Use the parametersotations described below: Waveguide dimensions: Width (w), SOI thickness (t), and slab thickness (t_sl) in case of ridge waveguides; Wavelength range: (wvl_start) 1500 to (wvl_stop) 1600 nm in this case; Wavelength step (wvl_res): Determines the number of simulations you need to perform. For example, wvl_res= 1 nm means you should calculate waveguide properties at 1500, 1501, 1502, 1600. Polarization (pol): Defines the polarization of interest. pol=TE OR pol=TM. Material: You can consider Silicon (n_si) and Silicon Dioxide (n_sio2). Use the Lorentz model to calculate the material refractive indices at various optical wavelengths (material dispersion should be considered). In the output: Effective Index Plot: This should indicate the effective index in a waveguide under different wavelengths; Activate Group Index Plot: This should indicate the group index in a waveguide under different Go to Setting wavelengths.Hint: You should implement the Lorentz model to calculate the refractive index of Silicon at different wavelength points. You can find the model in the textbook (eq. 3.2). Note that Silicon is almost lossless at wavelength of 1550 nm. Report the plot of refractive index against the wavelength. 1- Plot effective index vs. wavelength as well as group index vs. wavelength using EIM for the following parameters (two plots in total) listed in Table I. Table I: Strip waveguide parameters 500 nm 220 nm t sl 0 nm wvl start 1500 nm wvl_stop 1600 nm pol TE n si Si (dispersive) n_sioz Si02 (dispersive) 2- Plot effective index vs. wavelength as well as group index vs. wavelength using EIM for the following parameters (two plots in total) listed in Table II. Table II: Ridge waveguide parameters W 500 nm 220 nm t sl 90 nm wvl_start 1500 nm wvl stop 1600 nm pol TE n si Si (dispersive) n sio2 Si02 (dispersive) 3- Repeat 1 and 2 for TM polarization. Compare the effective and group indices between TE and TM modes. Which polarization has a higher effective index? Why? Which polarization has a higher group index? Why? 4- Consider an optical wavelength at 1550 nm. Using the parameters in Table I, sweep the waveguide width from 300 nm to 1200 nm (consider 5 nm increase in the width in each simulation: i.e., 300 nm, 305 nm, ..., 1200 nm) and plot the effective index and group index vs. waveguide width. What do you learn from the results? Download the template: https://www.icee.org/conferences/publishing/templates.htmlHint: You can do the sweep for effective index for different wavelengths at each design point and use ng = nerr - 1-" to calculate the group index. $read Ist, lambda [um], and 2nd column (neff) from the text file lambda=A ( : , 1) ; $assign lambda to a vector neff=A ( : , 2) ; Bassign neff to a vector dneffdlambda=gradient (neff, lambda) ; $numerical derivative ng=neff-lambda. *dneffdlambda; $group index mean (ng) $average value on the interval 5- Consider an optical wavelength at 1550 nm. Using the parameters in Table II, sweep the waveguide width from 300 nm to 1200 nm (consider 5 nm increase in the width in each simulation: i.e., 300 nm, 305 nm, ..., 1200 nm) and plot the effective index and group index vs. waveguide width. What do you learn from the results? 6- Consider the parameters in the table below. Given a SOI thickness of 300 nm, what is the waveguide width range that supports only a single TE and TM mode (fundamental modes)? Does such waveguide with t=300 nm exist? Table III: Strip waveguide parameters with t= 300 nm w 100 nm to 1200 nm 300 nm t sl 0 nm wvl 1550 nm pol TE n si Si (dispersive) n sio2 Si02 (dispersive) 7- Using the parameters in Table I. For n_si, instead of using the conventional Si (dispersive) model, use the Si - Temp (n = 3.47+1.86e-4*x1) where 3.47 is the refractive index of Si 1.86e-4 is the thermo-optic coefficient related to Silicon. Plot the effective index at 1550 nm where x1 (temperature) changes from 10 to 100 degrees. Do the same for group index. Explain the results