Reference no: EM132965026

Question: The theory of transfer matrix applied to multilayers is a powerful tool for the simulation of 1D optical systems, such as optical filters, thin films, Bragg gratings, dielectric mirrors, and antireflective coatings. Compute and plot over the 400-700 nm visible band (with a step of 1 nm) the reflection coefficient, reflectance, transmission coefficient, transmittance, and absorptance (where needed) of the following antireflection coatings on glass (n=1.5) and exposed to air (n=1). The multilayer systems are defined by the isotropic refractive indices n and optical thicknesses L:

(a) n = [1.38], L = [138] nm

(b) n = [1.38, 1.63], L = [138, 275] nm

(c) n = [1.38, 2.2, 1.63], L = [138, 275, 138] nm

(d) n = [1.38, 2.08, 1.38, 2.08], L = [138, 290, 46, 31] nm

Evaluate and compare the coatings in terms of bandwidth and reflectance. Discuss your results in detail. The work should be handed in proper report format, for example, with a purpose, method, results, and discussion sections. Choose carefully how you display your data so that it connects to your discussion and makes your point clear. Do not just include many graphs without explanation. Please discuss all the code implementation and theoretical details in the methods section. The code can be written in Python or Matlab and should scale to an arbitrary number of layers.

1) Compare the performance of (a) against what you get by employing the strategy for the design of antireflective coatings presented during the course.

2) What happens if you replicate the system (b) 100 times?

3) What happens if in (d) you one of the layers has a complex refractive index, i.e., n = [1.38, 2.08, 1.38-0.1j, 2.08]?

4) What happens if you add a 10 nm layer of gold in the middle of system (d)? And if the layer is reduced to 5 nm? Use the complex refractive index of gold and consider the dispersion of the material. Fitting or interpolation of permittivity experimental data is needed. Choose your strategy and motivate it in the methods section.

5) What happens if to system (d) you add instead a 20 nm layer of amorphous silicon?

6) Consider an inverse design problem, where you set a desired input/output and determine the required transfer matrix. Thus, discuss strategies to implement the transfer matrix with discrete layers.