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MultilayerStructure.jl
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MultilayerStructure.jl
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mutable struct MultilayerStructure{T} <: AbstractPropagationComponent{T}
n_A::Vector{Material{T}}
h_A::Vector{T}
ref::ReferenceFrame{T}
function MultilayerStructure{T}(n_A, h_A, ref) where T
length(n_A) != length(h_A) + 2 && error("The length of n_A must be equal to the length of h_A + 2")
new{T}(n_A, h_A, ref)
end
end
n1(mls::MultilayerStructure, λ) = first(mls.n_A)(λ)
n2(mls::MultilayerStructure, λ) = last(mls.n_A)(λ)
function n(mls::MultilayerStructure{T}, λ) where T
n_A = Vector{Complex{T}}(undef, length(mls.n_A))
for i in eachindex(mls.n_A)
n_A[i] = mls.n_A[i](λ)
end
return n_A
end
"""
MultilayerStructure(T, n, h, ref)
Initializes a multilayer structure.
- `T` number type specifing data precision. Ex: `Float32`, `BigFloat`, ... The default is Float64;
- `n` - vector specifying the refractive index of each layer. A function or interpolation object can be used to describe a refractive index wavelength dependent.
- `h` - vector specifying the thickness of each layer. The layer with refractive index `n[i]` has a thickness of `h[i-1]` meters;
- `ref` - `ReferenceFrame` specifying the multilayer position and orientation. The first interface of the multilayer structure is intersect the reference frame.
**Examples:**
```julia
mls = MultilayerStructure([1, 2, 3], [100E-9], ReferenceFrame(0,0,0.,0,0))
```
```julia
n_1(λ) = √(complex(8.393 + .14383 / ((λ*1E6)^2 - 0.2421^2) + 4430.99 / ((λ*1E6)^2 - 36.71^2)))
mls = MultilayerStructure([1, n_1], [], ReferenceFrame(0,0,0.,0,0))
```
"""
MultilayerStructure(::Type{T}, n_A, h_A, ref) where T = MultilayerStructure{T}(n_A, h_A, ref)
MultilayerStructure(n_A, h_A, ref) = MultilayerStructure{Float64}(n_A, h_A, ref)
reflectioncoefficientinterfacep(n1, sz1, n2, sz2) = (n2 * sz1 - n1 * sz2) / (n2 * sz1 + n1 * sz2);
reflectioncoefficientinterfaces(n1, sz1, n2, sz2) = (n1 * sz1 - n2 * sz2) / (n1 * sz1 + n2 * sz2);
transmissioncoefficientinterfaces(n1, sz1, n2, sz2) = (2 * n1 * sz1) / (n1 * sz1 + n2 * sz2);
transmissioncoefficientinterfacep(n1, sz1, n2, sz2) = (2 * n1 * sz1) / (n2 * sz1 + n1 * sz2);
function rtss₁₂(nsr::Real, n_A::AbstractVector{<:Number}, h_A::AbstractVector{<:Real}, λ::Real)
sizeA = length(n_A)
sizeA == length(h_A) + 2 || error("Length n_A must be length h_A + 2")
sz₂ = √(complex(1 - (nsr / n_A[sizeA])^2))
sz₁ = √(complex(1 - (nsr / n_A[sizeA-1])^2))
ri = reflectioncoefficientinterfaces(n_A[sizeA-1], sz₁, n_A[sizeA], sz₂)
ti = transmissioncoefficientinterfaces(n_A[sizeA-1], sz₁, n_A[sizeA], sz₂)
imk= im * 2π / λ
@inbounds for iA in (sizeA-2):-1:1
sz₂ = sz₁
sz₁ = √(complex(1 - (nsr / n_A[iA])^2))
propagationTerm = exp(imk * n_A[iA+1] * sz₂ * h_A[iA])
rinterface = reflectioncoefficientinterfaces(n_A[iA], sz₁, n_A[iA+1], sz₂)
tinterface = transmissioncoefficientinterfaces(n_A[iA], sz₁, n_A[iA+1], sz₂)
ti = tinterface * ti * propagationTerm / (1 + rinterface * ri * propagationTerm^2)
ri = (rinterface + ri * propagationTerm^2) / (1 + rinterface * ri * propagationTerm^2)
end
return (ri, ti)
end
function rtpp₁₂(nsr::Real, n_A::AbstractVector{<:Number}, h_A::AbstractVector{<:Real}, λ::Real)
sizeA = length(n_A)
sizeA == length(h_A) + 2 || error("Length n_A must be length h_A + 2")
sz₂ = √(complex(1 - (nsr / n_A[sizeA])^2))
sz₁ = √(complex(1 - (nsr / n_A[sizeA-1])^2))
ri = reflectioncoefficientinterfacep(n_A[sizeA-1], sz₁, n_A[sizeA], sz₂)
ti = transmissioncoefficientinterfacep(n_A[sizeA-1], sz₁, n_A[sizeA], sz₂)
imk = im * 2π / λ
@inbounds for iA in (sizeA-2):-1:1
sz₂ = sz₁;
sz₁ = √(complex(1 - (nsr / n_A[iA])^2))
propagationTerm = exp(imk * n_A[iA+1] * sz₂ * h_A[iA])
rinterface = reflectioncoefficientinterfacep(n_A[iA], sz₁, n_A[iA+1], sz₂)
tinterface = transmissioncoefficientinterfacep(n_A[iA], sz₁, n_A[iA+1], sz₂)
ti = tinterface * ti * propagationTerm / (1 + rinterface * ri * propagationTerm^2)
ri = (rinterface + ri * propagationTerm^2) / (1 + rinterface * ri * propagationTerm^2)
end
return (ri, ti)
end
"""
coefficient_general(::MultilayerStructure, ::FieldAngularSpectrumScalar)
Calculates the scattering matrix of a multilayer structure for an incident angular spectrum
- **Type:** Transmission and reflection matrices are diagonal
- **Time:** very short; scales with Nx Ny
- **RAM:** very small; scales with Nx Ny
- **Convergence** sampling of nsx and nsy
"""
function coefficient_general(mls::MultilayerStructure{T}, fieldi::FieldAngularSpectrumScalar) where T
checkapplicability(mls, fieldi)
n_A = n(mls, fieldi.λ)
inv_n_A = n_A[end:-1:1]
inv_h_A = mls.h_A[end:-1:1]
scat = get_scatteringmatrixtype(mls, fieldi)
cart = CartesianIndices(fieldi)
@inbounds Threads.@threads for i in iterator_index(fieldi)
nsr = √(fieldi.nsx_X[cart[i][2]]^2 + fieldi.nsy_Y[cart[i][3]]^2)
(scat.r₁₂.diag[i], scat.t₁₂.diag[i]) = rtss₁₂(nsr, n_A, mls.h_A, fieldi.λ)
(scat.r₂₁.diag[i], scat.t₂₁.diag[i]) = rtss₁₂(nsr, inv_n_A, inv_h_A, fieldi.λ)
end
correctscatteringmatrix_referenceframes!(scat, mls, fieldi)
return scat
end
"""
coefficient_general(::MultilayerStructure, ::FieldAngularSpectrumScalarRadialSymmetric)
Calculates the scattering matrix of a multilayer structure for an incident angular spectrum
- **Type:** Transmission and reflection matrices are diagonal
- **Time:** very short; scales with Nr
- **RAM:** very small; scales with Nr
- **Convergence** sampling of nsr
"""
function coefficient_general(mls::MultilayerStructure{T}, fieldi::FieldAngularSpectrumScalarRadialSymmetric) where T
checkapplicability(mls, fieldi)
n_A = n(mls, fieldi.λ)
inv_n_A = n_A[end:-1:1]
inv_h_A = mls.h_A[end:-1:1]
scat = get_scatteringmatrixtype(mls, fieldi)
cart = CartesianIndices(fieldi)
@inbounds Threads.@threads for i in iterator_index(fieldi)
(scat.r₁₂.diag[i], scat.t₁₂.diag[i]) = rtss₁₂(fieldi.nsr_R[i], n_A, mls.h_A, fieldi.λ)
(scat.r₂₁.diag[i], scat.t₂₁.diag[i]) = rtss₁₂(fieldi.nsr_R[i], inv_n_A, inv_h_A, fieldi.λ)
end
correctscatteringmatrix_referenceframes!(scat, mls, fieldi)
return scat
end
"""
lightinteraction(::MultilayerStructure, ::FieldAngularSpectrumScalar)
Calculates the reflected and transmitted fields from a multilayer structure for an incident angular spectrum
- **Time:** very short; scales with Nx Ny
- **RAM:** None
- **Convergence** sampling of nsx and nsy
"""
function lightinteraction(mls::MultilayerStructure{T}, fieldi::FieldAngularSpectrumScalar) where T
checkapplicability(mls, fieldi)
(fieldl, fieldr) = getfields_lr(mls, fieldi)
fieldi_newref = changereferenceframe(fieldi, dir(fieldi) > 0 ? ref1(mls) : ref2(mls))
n_A = n(mls, fieldi.λ)
inv_n_A = n_A[end:-1:1]
inv_h_A = mls.h_A[end:-1:1]
cart = CartesianIndices(fieldi)
@inbounds Threads.@threads for i in iterator_index(fieldi)
nsr = √(fieldi_newref.nsx_X[cart[i][2]]^2 + fieldi_newref.nsy_Y[cart[i][3]]^2)
if dir(fieldi_newref) > 0
(r, t) = rtss₁₂(nsr, n_A, mls.h_A, fieldi.λ)
fieldl.e_SXY[i] = fieldi_newref.e_SXY[i] * r
fieldr.e_SXY[i] = fieldi_newref.e_SXY[i] * t
else
(r, t) = rtss₁₂(nsr, inv_n_A, inv_h_A, fieldi.λ)
fieldl.e_SXY[i] = fieldi_newref.e_SXY[i] * t
fieldr.e_SXY[i] = fieldi_newref.e_SXY[i] * r
end
end
return (fieldl, fieldr)
end
"""
lightinteraction(::MultilayerStructure, ::FieldAngularSpectrumScalarRadialSymmetric)
Calculates the reflected and transmitted fields from a multilayer structure for an incident angular spectrum
- **Time:** very short; scales with Nr
- **RAM:** None
- **Convergence** sampling of nsr
"""
function lightinteraction(mls::MultilayerStructure{T}, fieldi::FieldAngularSpectrumScalarRadialSymmetric) where T
checkapplicability(mls, fieldi)
(fieldl, fieldr) = getfields_lr(mls, fieldi)
fieldi_newref = changereferenceframe(fieldi, dir(fieldi) > 0 ? ref1(mls) : ref2(mls))
n_A = n(mls, fieldi.λ)
inv_n_A = n_A[end:-1:1]
inv_h_A = mls.h_A[end:-1:1]
@inbounds Threads.@threads for i in iterator_index(fieldi)
if dir(fieldi_newref) > 0
(r, t) = rtss₁₂(fieldi.nsr_R[i], n_A, mls.h_A, fieldi.λ)
fieldl.e_SXY[i] = fieldi_newref.e_SXY[i] * r
fieldr.e_SXY[i] = fieldi_newref.e_SXY[i] * t
else
(r, t) = rtss₁₂(fieldi.nsr_R[i], inv_n_A, inv_h_A, fieldi.λ)
fieldl.e_SXY[i] = fieldi_newref.e_SXY[i] * t
fieldr.e_SXY[i] = fieldi_newref.e_SXY[i] * r
end
end
return (fieldl, fieldr)
end
function get_scatteringmatrixtype(mls::MultilayerStructure, fieldi::FieldAngularSpectrumScalar{T,D,X,B}) where {T,D,X,B}
sizeXY = length(fieldi.e_SXY)
r12 = Diagonal(Vector{Complex{T}}(undef, sizeXY))
t12 = Diagonal(Vector{Complex{T}}(undef, sizeXY))
r21 = Diagonal(Vector{Complex{T}}(undef, sizeXY))
t21 = Diagonal(Vector{Complex{T}}(undef, sizeXY))
(fieldl, fieldr) = getfields_lr(mls, fieldi)
return ScatteringMatrix{T, FieldAngularSpectrumScalar{T,-1,X,B}, FieldAngularSpectrumScalar{T,1,X,B}, Diagonal{Complex{T},Vector{Complex{T}}}, Diagonal{Complex{T},Vector{Complex{T}}}}(r12, t12, r21, t21, fieldl, fieldr)
end
function get_scatteringmatrixtype(mls::MultilayerStructure, fieldi::FieldAngularSpectrumScalarRadialSymmetric{T,D,X,B}) where {T,D,X,B}
sizeXY = length(fieldi.e_SXY)
r12 = Diagonal(Vector{Complex{T}}(undef, sizeXY))
t12 = Diagonal(Vector{Complex{T}}(undef, sizeXY))
r21 = Diagonal(Vector{Complex{T}}(undef, sizeXY))
t21 = Diagonal(Vector{Complex{T}}(undef, sizeXY))
(fieldl, fieldr) = getfields_lr(mls, fieldi)
return ScatteringMatrix{T, FieldAngularSpectrumScalarRadialSymmetric{T,-1,X,B}, FieldAngularSpectrumScalarRadialSymmetric{T,1,X,B}, Diagonal{Complex{T},Vector{Complex{T}}}, Diagonal{Complex{T},Vector{Complex{T}}}}(r12, t12, r21, t21, fieldl, fieldr)
end
function getfields_lr(mls::MultilayerStructure, fieldi::FieldAngularSpectrumScalar{T,A,X,B}) where {T,X,A,B}
fieldl = FieldAngularSpectrumScalar{T,-1,X,B}(deepcopy(fieldi.nsx_X), deepcopy(fieldi.nsy_Y), deepcopy(fieldi.e_SXY), fieldi.λ, n1(mls, fieldi.λ), ref1(mls))
fieldr = FieldAngularSpectrumScalar{T,1,X,B}(deepcopy(fieldi.nsx_X), deepcopy(fieldi.nsy_Y), deepcopy(fieldi.e_SXY), fieldi.λ, n2(mls, fieldi.λ), ref2(mls))
return (fieldl, fieldr)
end
function getfields_lr(mls::MultilayerStructure, fieldi::FieldAngularSpectrumScalarRadialSymmetric{T,A,X,B}) where {T,X,A,B}
fieldl = FieldAngularSpectrumScalarRadialSymmetric{T,-1,X,B}(deepcopy(fieldi.nsr_R), deepcopy(fieldi.e_SXY), fieldi.λ, n1(mls, fieldi.λ), ref1(mls))
fieldr = FieldAngularSpectrumScalarRadialSymmetric{T,1,X,B}(deepcopy(fieldi.nsr_R), deepcopy(fieldi.e_SXY), fieldi.λ, n2(mls, fieldi.λ), ref2(mls))
return (fieldl, fieldr)
end
function ref2(mls::MultilayerStructure)
totalh = sum(mls.h_A);
return mls.ref + ReferenceFrame(sin(mls.ref.θ) * cos(mls.ref.ϕ) * totalh, sin(mls.ref.θ) * sin(mls.ref.ϕ) * totalh, cos(mls.ref.θ) * totalh, mls.ref.θ, mls.ref.ϕ);
end
function checkapplicability(mls::MultilayerStructure, fieldi::AbstractFieldAngularSpectrum)
isapprox(fieldi.n, dir(fieldi) > 0 ? n1(mls, fieldi.λ) : n2(mls, fieldi.λ), atol = @tol) || error("Field medium and multilayer structure medium are different")
checkorientation(fieldi.ref, mls.ref) || errorToDo()
end