520.624 Integrated Photonics
Group-velocity dispersion calculations
Homework #4 due 3/29/18 at 11:59 PM
This assignment is based mostly on utilizing the finite-difference mode-solver that we are using in class. (You can download this from Professor Thomas Murphy’s website http://www.photonics.umd.edu/software/wgmodes/) You will need to alter the code to incorporate group- velocity dispersion simulations. The code basic_fullvector.m that we are using in class is altered from what is available on his website, so you should save this code for your use.
Model the total group-velocity dispersion (GVD) of a waveguide for one mode (either the fundamental TE, or the fundamental TM). Total GVD incorporates BOTH material AND waveguiding dispersion and can be implemented by solving the waveguide mode over a wavelength range (maybe 100 different wavelength values) while using a Sellmeier or Cauchy fit to the material dispersion (you will need to find these expressions for the materials you choose) to represent the refractive indices of all materials involved at each wavelength. After determining the effective refractive index for the particular mode of interest for each wavelength over the range, you must take a numerical second derivative. See reference 1 for guidance.
You will show that you can calculate the D-parameter of the GVD by iteratively solving the mode at different wavelengths. You should do this for two different waveguide geometries so you can compare how changing the geometry moves the zero-GVD point. You will need use some sort of loop (ex: for loop) in the code and include the working code in the assignment, and as a .m file in blackboard so I can try running it as well. The submitted work should include:
a. A diagram with your waveguide geometry and materials as well as a description of the two sizes that you have simulated. Make sure your simulation domain is defined properly so you have reached convergence!
b. Aplot of the 1) effective index of the fundamental mode, 2) the group index, and 3) the D-parameter of the GVD as a function of wavelength for the respective waveguides (these should be on the same plot for comparison).
c. A quick explanation of your results. It doesn’t have to be extremely formal, it just has to stand on its own so that I can understand what you designed and why.
d. The code that you created as a .m file submitted to blackboard
(Note that you can choose silicon as your waveguiding material, or some other material if it is silicon- based):
References:
[1] Turner, A.C., Manolatou, C., Schmidt, B.S., Lipson, M., Foster, M.A., Sharping, J.E. and Gaeta, A.L., “Tailored anomalous group-velocity dispersion in silicon channel waveguides,” Optics Express, Vol. 14, No. 10, p. 4357-4362 ,15 May 2006.