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

Transfer Matrix Functions

TransferMatrix.angle_resolvedMethod
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.

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TransferMatrix.calculate_trFunction
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.

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TransferMatrix.electric_fieldFunction
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.

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TransferMatrix.find_layerboundsMethod
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.)

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TransferMatrix.initializeMethod
initialize(structure::Structure, λs)

Initializing a Structure interpolates the wavelength-dependent refractive index data using the given λs Vector for all Layers in the Structure, returning a new structure with the interpolated data.

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TransferMatrix.propagation_matrixMethod
propagation_matrix(ω, q)

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

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TransferMatrix.dielectric_constantMethod
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''.
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TransferMatrix.dielectric_tensorMethod
dielectric_tensor(ε1, ε2, ε3)

Return the diagonal complex dielectric tensor

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

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Types

TransferMatrix.LayerType
Layer(material, thickness, λ, n, κ)

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.

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TransferMatrix.StructureType
Structure(layers, λs, θs)

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.

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Data Read/Write Functions

TransferMatrix.load_refractive_dataFunction
load_refractivedata(material::RefractiveMaterial, thickness, wavelength_unit=1e-6)

Retrieves refractive index data from refractiveindex.info database via the RefractiveIndex.jl interface. Wavelengths are in units of micrometers by default. and two refractive index columns: one for the real part and the other for the imaginary part.

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TransferMatrix.printstructFunction
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.

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Miscellaneous Optics Functions

TransferMatrix.dbr_reflectivityMethod
dbr_reflectivity(no, n2, n1, n2, N)

Approximate the reflectivity of a DBR structure with originating medium with refractive index no, substrate with index ns, and alternating materials with indices n1 and n2 and number of repetitions N. The repeated pair of materials are assumed to have quarter-wave thickness $nd = \lambda / 4$, where $n$ is the refractive index, $d$ is the layer thickness, and $\lambda$ is the wavelength of the light.

Distributed Bragg reflector

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TransferMatrix.fresnelMethod
fresnel(θ, n1, n2)

Calculate the reflectance for s-polarized and p-polarized light given the incidence angle θ and indices of refraction of two media n1 and n2 at a plane interface.

Fresnel equations

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TransferMatrix.stopbandMethod
stopband(n1, n2)

Calculate the frequency bandwidth Δf of the photonic stopband for a distributed bragg reflector (DBR) with two alternating materials of refractive indices n1 and n2.

\[ \frac{\Delta f_0}{f_0} = \frac{4}{\pi} \arcsin \left( \frac{n_2 - n_1}{n_2 + n_1} \right)\]

Distributed Bragg reflector

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