notebook2.jl

### A Pluto.jl notebook ###
# v0.19.42

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
        el
    end
end

# ╔═╡ ca7d5367-a80d-4e87-b0aa-46b420c0a457
using Plots, OpticalFibers,Gridap, PlutoUI

# ╔═╡ 41c9ddce-87cb-49d7-8eeb-9ff9182bdb7b
using OpticalFibers.ModeSolvers

# ╔═╡ 8ff76d1a-678b-4d3e-b2f5-409438548b18
using GridapGmsh

# ╔═╡ e3f289c2-6e50-4377-9119-8adfbd502926
using OpticalFibers.PhysicalData

# ╔═╡ f41f5c2b-757b-4d36-9b33-1a369b4351b6
using Polynomials

# ╔═╡ b4e1973a-e0d7-4fb3-add5-c4d7feb93d5d
using FFTW

# ╔═╡ 3c4939c0-1ccd-11ef-2cfb-1d00743534a1
md"""
# Fibre à gradient d'indice et dispersion
## Calcul des modes scalaires avec FEM 1D
Fibre possédant un coeur à profil parabolique d'indice maximal 1.47 et de rayon 2 µm avec une gaine d'indice 1.45. Le calcul sera effectué avec la méthode des éléments finis.
"""

# ╔═╡ b9c70e35-43d2-4794-b355-24551c87980e
begin
	ng=1.45
	nc=1.47
	a = 2
	lambda=1.2
	k0=2*pi/lambda
end;

# ╔═╡ b8b113e4-b724-474f-914c-13d78fdec137
md"Fonction définissant la permittivité :"

# ╔═╡ 71076db9-c55e-4980-ac56-cc3b8b2c7e99
epsilon=x->(ng+(nc-ng)*(x[1]<=a)*(1-x[1]^2/a^2))^2;

# ╔═╡ 19c4d701-4a9a-4faa-8a02-818575e3c728
md"Création du maillage entre 0 et 5$\times$a avec 1000 éléments"

# ╔═╡ ab9c19dd-5479-401d-ad82-5d6f16fa16fc
model = CartesianDiscreteModel((0,5*a),1000);

# ╔═╡ b62fbf84-7747-4105-bcc0-e8cba1c50331
l=0;

# ╔═╡ 021f2947-2941-4254-b024-360edafb0c23
V=k0*a*sqrt(nc^2-ng^2)

# ╔═╡ db9b95c6-6ebc-4104-9ab3-e25aaa90bccd
ms=FEM1D(lambda,l,epsilon,model,field=true,neigs=4)

# ╔═╡ ad5f6b28-b954-43be-b983-c2412af915f7
md"Numéro du mode (m) :"

# ╔═╡ 9fd70241-55fe-4a27-aa88-4de9b7b2c480
if (isempty(ms))
	md"Pas de mode"
else
	@bind nmode NumberField(1:length(ms), default=1)
end

# ╔═╡ 6873d3ad-fe9f-456a-8c05-740d796c823e
begin
	if (@isdefined nmode)
		rmax=maximum(model.grid_topology.vertex_coordinates)[1]
		r=0:rmax/200:rmax
		plot(r,sqrt.(epsilon.(r)),xlabel="r (µm)",ylabel="Indice de réfraction",label="RIP",xlims=(minimum(r),maximum(r)),legend=:top)
		plot!([minimum(r),maximum(r)],[ms[nmode].neff,ms[nmode].neff],linestyle=:dash,label="neff(FM)",legend=:top)
		plot!(twinx(),r,-real.(computeField(ms[nmode],r)),color=:green,label="FM",xlims=(minimum(r),maximum(r)),legend=:right,ylabel="E")
	end
end

# ╔═╡ 393f8f7d-f895-439f-afda-8f0955a17191
md"""
## Exercice
Utiliser la méthode des éléments finis pour retrouver les modes de la fibre à 3 couches décrite dans le calul ci-dessous.
"""

# ╔═╡ 28ba7674-771d-4fd0-a543-9825873b53f7
ms2_step=multi_step_fiber_modes.(1,[0,1],Ref([0.5,2]),Ref([1.48,1.47,1.45]))

# ╔═╡ 82ff2d54-70e4-4482-8270-e6f00a2ea5b6


# ╔═╡ 790eb6b8-9753-4b16-99c1-2c778c95beda
md"## Calcul des modes scalaires avec FEM 2D"

# ╔═╡ bc883cf0-8b6e-40fe-9668-1b1dded0efbd
md"Pour cette partie, le rayon `a` doit impérativement valoir 2 car le maillage est réalisé pour cette valeur de rayon de coeur."

# ╔═╡ a005da69-2a18-48a5-ac96-931a29ba0249
md"En premier lieu, le maillage généré à l'aide de GMSH est chargé en mémoire."

# ╔═╡ 87e030da-f31f-4f99-b52d-70e14ebbb16b
model2D = GmshDiscreteModel("example1.msh");

# ╔═╡ ddc08e2c-6765-4f03-9410-eb8cf47df361
md"La permittivité en 2D est définie à partir de celle en 1D"

# ╔═╡ 5ae2d6d0-ff92-4354-974b-65ac7ac834de
epsilon2D=x->epsilon(hypot(x[1],x[2]));

# ╔═╡ e14125de-f7dd-4e66-99e1-303e88c7275a
x=-5:0.02:5;

# ╔═╡ 5377121f-89be-4f6d-bb49-18b8fe0fa8dc
contourf(x,x,(sqrt.(epsilon2D.(tuple.(x,x'))))',linewidth=0,levels=100,title="Profil d'indice",aspect_ratio=:equal,xlims=(minimum(x),maximum(x)),ylims=(minimum(x),maximum(x)))

# ╔═╡ 1f7c07e7-1dd9-4ac3-9ff7-3c736d500116
ms2D=FEM2D(lambda,epsilon2D,model2D,field=true,neigs=4)

# ╔═╡ 982a78c9-f93b-4bb3-8e98-812d738d5437
contourf(x,x,abs.(computeField(ms2D[1],x,x'))',levels=100,linewidth=0,aspect_ratio=:equal,xlims=(minimum(x),maximum(x)),ylims=(minimum(x),maximum(x)),title="Mode 1 - |E|")

# ╔═╡ 6313ffeb-2ef0-4700-b1a3-cc7de886f3c2
md"Sauvegarde du mode dans un fichier pouvant être lu par paraview"

# ╔═╡ 1e9337e8-e59b-49f8-9186-e625cefdd27d
writevtk("mode1",ms2D[1])

# ╔═╡ 4e7f5197-7c62-4181-a916-4893997eca98
md"""
## Calcul de l'aire effective, du MFD et du coefficient non-linéaire
Pour les modes scalaires l'aire effective est définie par $A_{\text{eff}}=\frac{\left( \iint \vert E \vert^2 dS \right)^2}{\iint \vert E \vert^4 dS}$
"""

# ╔═╡ 4d0b13e5-6d3f-45c8-b554-0219f3b6fd85
Aeff(ms[1]) #en µm²

# ╔═╡ fc85b433-eda0-474f-bd11-41a7574cdc46
Aeff(ms2D[1]) #en µm²

# ╔═╡ 3922b817-e53c-491c-bd4e-4564b0af89b2
md"Le diamètre de mode correspond à la largeur en $1/e^2$ de l'intensité"

# ╔═╡ 05cf161f-b94f-465e-a5ac-9a6b11960776
MFD(ms[1]) #en µm

# ╔═╡ 0c8a016b-7f69-4f14-a9a3-3b62c1b26892
MFD(ms2D[1]) #en µm

# ╔═╡ 6906fc28-aa3c-4847-9dab-fe1992431db3
md"Pour les modes scalaires, le coefficient non-linéaire vaut $\frac{n_2\omega}{cA_{\text{eff}}}$"

# ╔═╡ 1a7630fd-8d4e-4184-9dd4-3a5a5b341693
nonLinearCoefficient(ms[1],2.53E-20)*1E21 #en 1/W/km

# ╔═╡ 6c0fd10e-74ea-4196-a7a2-2a9f0029a2a3
nonLinearCoefficient(ms2D[1],2.53E-20)*1E21 #en 1/W/km

# ╔═╡ 9f04996c-1718-4d22-b160-3e7382e27c13
md"""
## Prise en compte de la dispersion du matériau
Nous allons maintenant considérer la dispersion de la silice constituant la gaine de la fibre précédente. En première approximation, nous supposerons que la différence d'indice coeur/gaine ne varie pas avec la longueur d'onde et reste fixe à 0.02.
"""

# ╔═╡ 3996bfff-c73e-4187-a033-fcda4c8d6a18
epsilon_dispersif=(l,x)->(n_Ge_Doped_Silica(l*1e-6,0)+0.02*(x[1]<=2)*(1-x[1]^2/2^2))^2;

# ╔═╡ d8969846-66c2-4fce-b33a-e9885580fd7b
#Longueur d'onde d'étude
lambda2=1.2;

# ╔═╡ 46c42a19-70c2-4a50-9f86-ec70802e1514
md"Calcul du mode fondamental :"

# ╔═╡ 03a57dfe-1726-4d5e-a3f4-bc64a7b186e8
ms_dispersif=FEM1D(lambda2,0,x->epsilon_dispersif(lambda2,x),model,field=true)

# ╔═╡ fa8afffa-6cbf-45ee-afe2-37cdb06c8509
begin
	r2=0:0.05:10
	plot(r2,sqrt.(epsilon_dispersif.(lambda2,r2)),xlabel="r (µm)",ylabel="Indice de réfraction",label="RIP",xlims=(minimum(r2),maximum(r2)),legend=:top)
	plot!([minimum(r2),maximum(r2)],[ms_dispersif[1].neff,ms_dispersif[1].neff],linestyle=:dash,label="neff(FM)",legend=:top)
	plot!(twinx(),r2,abs.(computeField(ms_dispersif[1],r2)),color=:green,label="FM",xlims=(minimum(r2),maximum(r2)),legend=:right)
end

# ╔═╡ ac69c724-4581-420f-a474-5c0b15d25880
md"Pour tracer l'évolution de l'indice effectif en fonction de la longueur d'onde, il faut créer un vecteur de longueur d'onde et un vecteur de fonctions représentant le profil d'indice."

# ╔═╡ 5d8ca80e-c826-45cf-a384-af0bd81ea23a
begin
	vlambda=0.4:0.005:1
	vepsilon=[x->epsilon_dispersif(l,x) for l in vlambda]
end;

# ╔═╡ 50cae966-3406-4fe3-a180-504cf0e445f5
m=FEM1D.(vlambda,[0,1,2]',vepsilon,Ref(model),neigs=2);

# ╔═╡ e8a7b3cc-0e79-4ee3-ab0e-b6801fd47005
begin
	#mode LP01 always exists
	neff01=[real(m[j,1][1].neff) for j in 1:length(vlambda)];
	N02=sum((length.(m[:,1])).>=2);
	neff02=[real(m[j,1][2].neff) for j in 1:N02]
	N11=sum((length.(m[:,2])).>=1);
	neff11=[real(m[j,2][1].neff) for j in 1:N11]
	N21=sum((length.(m[:,3])).>=1);
	neff21=[real(m[j,3][1].neff) for j in 1:N21]
end;

# ╔═╡ 78e2152c-116a-4f57-8f98-fdc13630dc0a
begin
	plot(vlambda,n_Ge_Doped_Silica.(vlambda*1E-6,0),label="Cladding",xlabel="λ (µm)",ylabel="Effective index",color=:black,xlims=(minimum(vlambda),maximum(vlambda)));
	plot!(vlambda,n_Ge_Doped_Silica.(vlambda*1E-6,0).+0.02,label="Core max",color=:black,line=:dash);
	plot!([vlambda,vlambda[1:N11],vlambda[1:N02],vlambda[1:N21]],[neff01,neff11,neff02,neff21],label=["LP01" "LP11" "LP02" "LP21"])
end

# ╔═╡ cf1507ff-817c-48e4-ba49-66d152d44156
md"""
## Exercice : Dispersion modale
Caluler l'indice de groupe du mode LP$_{01}$ et du mode LP$_{11}$ pour la longueur d'onde `vlambda[61]`=700 nm en effectuant une dérivée discrète.
"""

# ╔═╡ b3983b11-ac10-4806-b39f-70be6f44ae8e
begin
	vomega=2*pi*(PhysicalData.c)./(vlambda*1e-6) #vecteur de pulsation
	vbeta01=neff01*2*pi./(vlambda*1E-6) #vecteur de beta pour le mode LP01
	vbeta11=neff11*2*pi./(vlambda[1:N11]*1E-6) #vecteur de beta pour le mode LP11
end;

# ╔═╡ 2b135708-0b52-49a5-8ca9-1664447b19ff


# ╔═╡ f2ec3390-b83f-4e8e-8bbb-ef71616ba567
md"""
## Calcul de la dispersion de vitesse de groupe
A titre d'exemple,nous allons calculer $\beta_2$ pour la mode fondamental de la fibre précédente.
"""

# ╔═╡ b0d9cc2e-21a2-4775-b9a7-35fcbe810531
md"On comme d'abord par calculer la constante de propagation $\beta$ en fonction de la pulsation $\omega$ :"

# ╔═╡ a285e502-a82e-4c2b-965f-483c00727ab2
begin
	omega=2*pi*(PhysicalData.c)./(vlambda*1e-6)
	beta01=neff01*2*pi./(vlambda*1E-6)
	omega0=2*pi*(PhysicalData.c)./(0.8*1e-6)
end;

# ╔═╡ a85f83e9-9b88-4fc5-a86c-3346b9117ed7
md"On peut ensuite procéder à un fit polynomial qui devra être dérivé deux fois"

# ╔═╡ dab0dcc9-b969-4594-808c-9eefda454f3c
p =  fit((omega.-omega0)*1E-15, beta01,4)

# ╔═╡ 5b10de7b-0bae-466a-98d9-f0dad3758b25
p2=Polynomials.derivative(p,2)

# ╔═╡ 7eb60260-9930-45f8-b8d1-25018ebd87ef
beta2_800nm=p2(0)*1E-30 #en s²/m

# ╔═╡ ecc91321-29a5-4c96-b44a-6e7261b1de52
md"""
## Exercice
Utiliser la fonction `diff` pour retrouver $\beta_2(\lambda)$ en effectuant une dérivée discrète.
"""

# ╔═╡ 5b00e1e2-fabe-4d47-b0bd-d2b4a5fe269d


# ╔═╡ 98431fcd-8e85-4dea-94ad-d368ff3e0717
begin
	plot(vlambda,p2.((omega.-omega0)*1E-15)*1E-4,xlabel="Longueur d'onde (µm)",ylabel="β₂ (x10⁻²⁶ s²/m)",label="Fit polynomial")
	#plot!(lambdabis*1E6,beta2*1E26,label="Dérivée discrète")
end

# ╔═╡ cd3a11da-bb1b-480f-a793-9c54f30fe8d2
md"""
## Effet de la dispersion de vitesse de groupe sur une impulsion
A titre d'exemple nous allons étudier une impulsion gaussienne de durée $T_0 = 1$ ps dans une fibre possédant une dispersion $\beta_2=10^{-26}$ s²/m.
"""

# ╔═╡ e85c3896-e4b5-4532-a1b4-1d9b51c0cb3e
md"On définit les fenêtres spectrales et temporelles :"

# ╔═╡ cb4f54bf-4988-47b7-a45f-5ddf87417982
begin
	Tmax=80e-12
	N=2^10
	dtau=2*Tmax/N
	tau=(-div(N,2):1:(div(N,2)-1))*dtau
	dOmega=pi/Tmax;
	Omega=(-div(N,2):1:(div(N,2)-1))*dOmega
end;

# ╔═╡ a23e43b9-c6f4-474f-9e6f-17d6bd474ddf
md"Impulsion initiale :"

# ╔═╡ 2aecbc0f-9f06-4818-b660-627c6b8d39cf
begin
	T0=1E-12
	A0=exp.(-tau.^2/2/T0^2)
end;

# ╔═╡ 8a654153-2023-4677-b264-2359df755569
md"Dispersion de la fibre :"

# ╔═╡ 1e30db37-7797-41b5-8a93-7fc2669e1106
begin
	b2=1E-26
	LD=T0^2/b2
end

# ╔═╡ 3e14a9b1-2f38-4aec-9a7b-7353520b2f05
md"Effet de la dispersion :"

# ╔═╡ 0d17994f-334e-4b1e-a2e6-d3a04cf37c20
begin
	z=4*LD
	B0=fftshift(ifft(A0))
	B=B0.*exp.(im*0.5*b2*Omega.^2*z)
	A=fft(fftshift(B))
end;

# ╔═╡ 1098a6a7-5e75-4eab-bb5e-ec4d9fccc8ea
md"**Exercice :** Calculer l'effet de l'ajout d'une dispersion d'ordre 3 positive et dont la valeur donne une longueur caractéristique qui est la moitié de celle de la dispersion d'ordre 2"

# ╔═╡ 134c416a-80e1-4fa0-a038-ba5e3d78af2a
begin
	LD3=LD/2
	b3=T0^3/LD3
	B2=B0.*exp.(im*(0.5*b2*Omega.^2+1/6.0*b3*Omega.^3)*z)
	A2=fft(fftshift(B2))
end;

# ╔═╡ c04a8725-c19f-4a89-820e-5b7d6d789d17
begin
	plot(tau*1E12,abs2.(A0),label="z=0",xlabel="T (ps)",ylabel="|A|²",xlims=(-30,30))
	plot!(tau*1E12,abs2.(A),label="z - β₂")
	plot!(tau*1E12,abs2.(A2),label="z - β₂+β₃")
end

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uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.10.9"
weakdeps = ["Random", "Test"]

    [deps.TranscodingStreams.extensions]
    TestExt = ["Test", "Random"]

[[deps.Trapz]]
git-tree-sha1 = "79eb0ed763084a3e7de81fe1838379ac6a23b6a0"
uuid = "592b5752-818d-11e9-1e9a-2b8ca4a44cd1"
version = "2.0.3"

[[deps.Tricks]]
git-tree-sha1 = "eae1bb484cd63b36999ee58be2de6c178105112f"
uuid = "410a4b4d-49e4-4fbc-ab6d-cb71b17b3775"
version = "0.1.8"

[[deps.URIs]]
git-tree-sha1 = "67db6cc7b3821e19ebe75791a9dd19c9b1188f2b"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.5.1"

[[deps.UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[deps.UnPack]]
git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
version = "1.0.2"

[[deps.Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[deps.UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
version = "0.4.1"

[[deps.Unitful]]
deps = ["Dates", "LinearAlgebra", "Random"]
git-tree-sha1 = "dd260903fdabea27d9b6021689b3cd5401a57748"
uuid = "1986cc42-f94f-5a68-af5c-568840ba703d"
version = "1.20.0"
weakdeps = ["ConstructionBase", "InverseFunctions"]

    [deps.Unitful.extensions]
    ConstructionBaseUnitfulExt = "ConstructionBase"
    InverseFunctionsUnitfulExt = "InverseFunctions"

[[deps.UnitfulLatexify]]
deps = ["LaTeXStrings", "Latexify", "Unitful"]
git-tree-sha1 = "e2d817cc500e960fdbafcf988ac8436ba3208bfd"
uuid = "45397f5d-5981-4c77-b2b3-fc36d6e9b728"
version = "1.6.3"

[[deps.Unzip]]
git-tree-sha1 = "ca0969166a028236229f63514992fc073799bb78"
uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
version = "0.2.0"

[[deps.VTKBase]]
git-tree-sha1 = "c2d0db3ef09f1942d08ea455a9e252594be5f3b6"
uuid = "4004b06d-e244-455f-a6ce-a5f9919cc534"
version = "1.0.1"

[[deps.Vulkan_Loader_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Wayland_jll", "Xorg_libX11_jll", "Xorg_libXrandr_jll", "xkbcommon_jll"]
git-tree-sha1 = "2f0486047a07670caad3a81a075d2e518acc5c59"
uuid = "a44049a8-05dd-5a78-86c9-5fde0876e88c"
version = "1.3.243+0"

[[deps.Wayland_jll]]
deps = ["Artifacts", "EpollShim_jll", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "7558e29847e99bc3f04d6569e82d0f5c54460703"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.21.0+1"

[[deps.Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "93f43ab61b16ddfb2fd3bb13b3ce241cafb0e6c9"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.31.0+0"

[[deps.WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "c1a7aa6219628fcd757dede0ca95e245c5cd9511"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "1.0.0"

[[deps.WriteVTK]]
deps = ["Base64", "CodecZlib", "FillArrays", "LightXML", "TranscodingStreams", "VTKBase"]
git-tree-sha1 = "48b9e8e9c83865e99e57f027d4edfa94e0acddae"
uuid = "64499a7a-5c06-52f2-abe2-ccb03c286192"
version = "1.19.1"

[[deps.XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Zlib_jll"]
git-tree-sha1 = "52ff2af32e591541550bd753c0da8b9bc92bb9d9"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.12.7+0"

[[deps.XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.34+0"

[[deps.XZ_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "ac88fb95ae6447c8dda6a5503f3bafd496ae8632"
uuid = "ffd25f8a-64ca-5728-b0f7-c24cf3aae800"
version = "5.4.6+0"

[[deps.Xorg_libICE_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "326b4fea307b0b39892b3e85fa451692eda8d46c"
uuid = "f67eecfb-183a-506d-b269-f58e52b52d7c"
version = "1.1.1+0"

[[deps.Xorg_libSM_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libICE_jll"]
git-tree-sha1 = "3796722887072218eabafb494a13c963209754ce"
uuid = "c834827a-8449-5923-a945-d239c165b7dd"
version = "1.2.4+0"

[[deps.Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "afead5aba5aa507ad5a3bf01f58f82c8d1403495"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.8.6+0"

[[deps.Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "6035850dcc70518ca32f012e46015b9beeda49d8"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.11+0"

[[deps.Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.0+4"

[[deps.Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "34d526d318358a859d7de23da945578e8e8727b7"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.4+0"

[[deps.Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "d2d1a5c49fae4ba39983f63de6afcbea47194e85"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.6+0"

[[deps.Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "5.0.3+4"

[[deps.Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"

[[deps.Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"

[[deps.Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"

[[deps.Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "47e45cd78224c53109495b3e324df0c37bb61fbe"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.11+0"

[[deps.Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "8fdda4c692503d44d04a0603d9ac0982054635f9"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.1+0"

[[deps.Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "b4bfde5d5b652e22b9c790ad00af08b6d042b97d"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.15.0+0"

[[deps.Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libX11_jll"]
git-tree-sha1 = "730eeca102434283c50ccf7d1ecdadf521a765a4"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.2+0"

[[deps.Xorg_xcb_util_cursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_jll", "Xorg_xcb_util_renderutil_jll"]
git-tree-sha1 = "04341cb870f29dcd5e39055f895c39d016e18ccd"
uuid = "e920d4aa-a673-5f3a-b3d7-f755a4d47c43"
version = "0.1.4+0"

[[deps.Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"

[[deps.Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"

[[deps.Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[deps.Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "330f955bc41bb8f5270a369c473fc4a5a4e4d3cb"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.6+0"

[[deps.Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "691634e5453ad362044e2ad653e79f3ee3bb98c3"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.39.0+0"

[[deps.Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "e92a1a012a10506618f10b7047e478403a046c77"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.5.0+0"

[[deps.Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.13+1"

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "e678132f07ddb5bfa46857f0d7620fb9be675d3b"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.6+0"

[[deps.eudev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "gperf_jll"]
git-tree-sha1 = "431b678a28ebb559d224c0b6b6d01afce87c51ba"
uuid = "35ca27e7-8b34-5b7f-bca9-bdc33f59eb06"
version = "3.2.9+0"

[[deps.fzf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "a68c9655fbe6dfcab3d972808f1aafec151ce3f8"
uuid = "214eeab7-80f7-51ab-84ad-2988db7cef09"
version = "0.43.0+0"

[[deps.gmsh_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9554bb1cad1926e7d3afb68b0ab117d0b9bb73ee"
uuid = "630162c2-fc9b-58b3-9910-8442a8a132e6"
version = "4.9.3+0"

[[deps.gperf_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3516a5630f741c9eecb3720b1ec9d8edc3ecc033"
uuid = "1a1c6b14-54f6-533d-8383-74cd7377aa70"
version = "3.1.1+0"

[[deps.libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "1827acba325fdcdf1d2647fc8d5301dd9ba43a9d"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.9.0+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.8.0+1"

[[deps.libevdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "141fe65dc3efabb0b1d5ba74e91f6ad26f84cc22"
uuid = "2db6ffa8-e38f-5e21-84af-90c45d0032cc"
version = "1.11.0+0"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[deps.libinput_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "eudev_jll", "libevdev_jll", "mtdev_jll"]
git-tree-sha1 = "ad50e5b90f222cfe78aa3d5183a20a12de1322ce"
uuid = "36db933b-70db-51c0-b978-0f229ee0e533"
version = "1.18.0+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "d7015d2e18a5fd9a4f47de711837e980519781a4"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.43+1"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"

[[deps.mtdev_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "814e154bdb7be91d78b6802843f76b6ece642f11"
uuid = "009596ad-96f7-51b1-9f1b-5ce2d5e8a71e"
version = "1.1.6+0"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.52.0+1"

[[deps.oneTBB_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "7d0ea0f4895ef2f5cb83645fa689e52cb55cf493"
uuid = "1317d2d5-d96f-522e-a858-c73665f53c3e"
version = "2021.12.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+2"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[deps.xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "9c304562909ab2bab0262639bd4f444d7bc2be37"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.4.1+1"
"""

# ╔═╡ Cell order:
# ╟─3c4939c0-1ccd-11ef-2cfb-1d00743534a1
# ╠═ca7d5367-a80d-4e87-b0aa-46b420c0a457
# ╠═41c9ddce-87cb-49d7-8eeb-9ff9182bdb7b
# ╠═b9c70e35-43d2-4794-b355-24551c87980e
# ╟─b8b113e4-b724-474f-914c-13d78fdec137
# ╠═71076db9-c55e-4980-ac56-cc3b8b2c7e99
# ╟─19c4d701-4a9a-4faa-8a02-818575e3c728
# ╠═ab9c19dd-5479-401d-ad82-5d6f16fa16fc
# ╠═b62fbf84-7747-4105-bcc0-e8cba1c50331
# ╠═021f2947-2941-4254-b024-360edafb0c23
# ╠═db9b95c6-6ebc-4104-9ab3-e25aaa90bccd
# ╟─ad5f6b28-b954-43be-b983-c2412af915f7
# ╟─9fd70241-55fe-4a27-aa88-4de9b7b2c480
# ╟─6873d3ad-fe9f-456a-8c05-740d796c823e
# ╟─393f8f7d-f895-439f-afda-8f0955a17191
# ╠═28ba7674-771d-4fd0-a543-9825873b53f7
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