Computational physics report
Reflectance in dielectric structures
Transfer-matrix modelling of thin-film optical coatings
Of the many triumphs of human understanding, the ability to predict how light behaves inside structured materials remains one of the most elegant links between physics, mathematics, and computation. Thin-film dielectric coatings are a particularly good example of this, because their behaviour follows from the interference of reflected waves at each interface, yet the final optical response can become highly non-trivial once multiple layers are combined.
During my undergraduate degree, I had the privilege of working on a computational physics project exploring reflectance in dielectric structures. This gave me the opportunity to demonstrate my ability to translate physical theory into working numerical code, using the transfer-matrix formalism to model normally incident light in single-layer, bilayer, and multilayer dielectric coatings. I implemented the calculations in C, using complex arithmetic to evaluate the reflectivity and generate reflectance spectra across the visible range.
The project was a useful exercise in connecting abstract electromagnetic theory to concrete computational results. A single low-index layer behaved mainly as an anti-reflection coating, while adding high-index layers introduced stronger interference effects. Repeating the bilayer structure produced the characteristic behaviour of a dielectric mirror, with reflectance approaching unity across a broad stop band as the number of bilayers increased. I was pleased to receive 75% for this work, which made it a strong demonstration of my computational physics, numerical modelling, and scientific programming skills.
The following report presents the finished analysis, showing how the transfer-matrix method can be used to predict and interpret the reflectance behaviour of dielectric coatings from simple single-layer structures through to high-reflectance multilayer mirrors.
Abstract
This report models single-layer, bilayer, and multilayer dielectric coatings using transfer matrices and complex amplitudes.
It records the implementation and physical interpretation of reflectance spectra across increasingly structured optical stacks.
Motivation
Thin-film optical coatings provide a compact example of how interference, boundary conditions, and numerical modelling combine into a practical engineering problem.
The project focused on reproducing reflectance behaviour across simple anti-reflection layers and repeated bilayer mirrors.
Method
The core model used the transfer-matrix formalism for normally incident light, implemented in C with complex arithmetic.
Reflectance spectra were generated across the visible range and compared across single-layer, bilayer, and repeated multilayer structures.
Outcome
The report demonstrates a clear progression from weak anti-reflection behaviour to broad high-reflectance stop bands as more bilayers are added.