# Public Documentation

These functions and types are to be used for transfer matrix calculation based on the sources used. If you wish to modify any of the steps in the calculation, refer to the private API.

## Index

`TransferMatrix.Layer`

`TransferMatrix.Structure`

`TransferMatrix.angle_resolved`

`TransferMatrix.calculate_tr`

`TransferMatrix.dielectric_constant`

`TransferMatrix.dielectric_constant`

`TransferMatrix.dielectric_constant`

`TransferMatrix.dielectric_tensor`

`TransferMatrix.electric_field`

`TransferMatrix.find_layerbounds`

`TransferMatrix.initialize`

`TransferMatrix.load_from_yaml`

`TransferMatrix.printstruct`

`TransferMatrix.propagation_matrix`

`TransferMatrix.read_refractive`

## Transfer Matrix Functions

`TransferMatrix.angle_resolved`

— Method`angle_resolved(s::Structure)`

Iterate through each angle provided in the structure to find the reflectance and transmittance spectra from the calculated transfer matrices and Poynting vectors.

`TransferMatrix.calculate_tr`

— Function`calculate_tr(s::Structure, θ=0.0)`

Calculate the transmittance and reflectance spectrum of the structure at a single incidence angle θ. Accurate transmittance must be calculated via the Poynting vector. Reflectance is calculated directly from the transfer matrix elements.

`TransferMatrix.dielectric_constant`

— Method`dielectric_constant(n::Complex)`

Return the complex dielectric function from the complex index of refraction.

`TransferMatrix.dielectric_constant`

— Method`dielectric_constant(layer::Layer)`

Return a complex dielectric function from the index of refraction in a `Layer`

` type.

`TransferMatrix.dielectric_constant`

— Method`dielectric_constant(n::Real, κ::Real)`

Return the complex dielectric function from the real and imaginary parts of the index of refraction.

The complex index of refraction, given by

` n' = n + iκ`

(in terms of n and κ), can be used to obtain the frequency-dependent complex dielectric function

` ε_r(ω) = ε' + iε''`

via the relation

` (n + iκ)^2 = ε' + iε''.`

`TransferMatrix.dielectric_tensor`

— Method`dielectric_tensor(ε1, ε2, ε3)`

Return the diagonal complex dielectric tensor

\[\varepsilon = \begin{pmatrix}\ \varepsilon_1 & 0 & 0 \ 0 & \varepsilon_2 & 0 \ 0 & 0 & \varepsilon_3 \end{pmatrix}\]

`TransferMatrix.electric_field`

— Function`electric_field(s::Structure, λ, θ; numpoints)`

Calculate the electric field profile for the entire structure as a function of z for a given incidence angle θ.

`TransferMatrix.find_layerbounds`

— Method`find_layerbounds(s::Structure)`

Find the unitful z coordinate for all layer-layer interfaces in the structure, with the first interface starting at z = 0. (negative z corresponds to positions inside the first layer.)

`TransferMatrix.initialize`

— Method`initialize(structure::Structure, λs)`

Initializing a `Structure`

interpolates the wavelength-dependent refractive index data using the given `λs`

Vector for all `Layer`

s in the `Structure`

, returning a new structure with the interpolated data.

`TransferMatrix.printstruct`

— Function`printstruct(s::Structure, unit=1e9)`

Print each layer and its thickness in a somewhat visually useful way. Change the default unit multiplier to switch from nanometers to micrometers. This does not affect any calculations, only what is printed to the command line when using `printstruct`

.

`TransferMatrix.propagation_matrix`

— Method`propagation_matrix(ω, q)`

Returns a function that propagates the electromagnetic field a distance z through a material for a frequency ω and wavevector $q$.

## Types

`TransferMatrix.Layer`

— Type`Layer(material::String, thickness::Float64, λ::Vector{Float64}, n::Vector{Float64}, κ::Vector{Float64})`

A `Layer`

stores information about a single layer, including its material name, thickness, a list of electric field wavelengths, and the real and imaginary parts of the refractive index associated with these wavelengths.

Initializing a `Layer`

with no arguments makes a 1 μm thick layer of Air.

`TransferMatrix.Structure`

— Type`Structure`

The `Structure`

is a mutable type that stores a Vector of `Layer`

types, along with a list of field wavelengths and incident angles to calculate on.

## Data Read/Write Functions

`TransferMatrix.load_from_yaml`

— Function`read_yaml(file::String)`

Read a yaml file with Structure parameters to perform transfer matrix calculations.

`TransferMatrix.read_refractive`

— Method`read_refractive(f::String, material::String, thickness; div=1.0, freq=false)`

Reads a csv file from the database website refractiveindex.info containing a wavelength column in units of micrometers, and two refractive index columns: one for the real part and the other for the imaginary part.

The header names are:

"Wavelength, μm", "n", "k"

Note that if you put a file in the `refractive_index_data`

folder, then this function can automatically find it if you simply put the file name (with .csv extension) in the `refractive_filename`

field in the yaml file. If you put the file somewhere else, you must provide the full path to that file (or relative path).

For some reason, the wavelength column cannot be normalized (so as to be a valid Julia identifier) using `normalizednames = true`

in `CSV.File`

, so the header is skipped.