This repository contains my thesis and its associated code. It's a Julia package, and can be installed with:

pkg> add https://github.com/mjg0/Mirrors.jl

The thesis, which goes into detail on the research that requires this code, can be built with make if you have bash, lualatex, and pygments installed.

This document will focus more on the code itself since the thesis covers the math and purpose behind Mirrors.jl. In short, a Mirror is a circular conducting mirror, possibly with some surface roughness:

using Mirrors, Plots

radius = 5.0 # wavelengths
N = 20       # number of rings; more rings means more precision and more memory use
rms = 0.1    # RMS surface roughness
sigma = 3.0  # standard deviation of surface roughness

M = Mirror(radius, N, rms, sigma)
heatmap(M) # plot the mirror's height

The impedance of the mirror (how each point on the mirror interacts with each other point when the mirror is charged) is a matrix of complex doubles, and scales quartically in memory use with the number of rings in the mirror:

Z = impedance(M)

Given the impedance matrix and an electric field on the mirror's surface:

# Profile of the illuminating beam; default is a uniform plane wave
sigma = 2.0 # wavelengths
function gaussianprofile(r, θ)
    return exp(-r^2/2sigma^2)
end
# Angle of incident beam relative to normal
angle = π/6
# Electric field
E = electricfield(M, angle, beamprofile=gaussianprofile)
heatmap(M, real.(E))

...the current on the mirror's surface can be found:

J = Z \ E
heatmap(M, real.(J))

Once the surface current is calculated, reflectance can be found:

R = Reflectance(M, J)
heatmap(R)

A Reflectance represents the far field reflectance from a Mirror in the mirror's entire upper hemisphere as an azimuthal equidistant projection, centered normal to the mirror and extending 90 degrees to the plane of the mirror.