Lithium niobate phase-shifter

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Lithium niobate phase-shifter#

Reproducing [1]

Hide code cell source 
using PyCall

py"""
from collections import OrderedDict

from shapely.geometry import box

from femwell.mesh import mesh_from_OrderedDict

core_width = 1.532
electrode_start_x = core_width / 2 + 2.629
electrode_width = 4.4

electrode_left = box(-electrode_start_x - electrode_width, 0.5, -electrode_start_x, 0.5 + 1.8)
electrode_right = box(electrode_start_x, 0.5, electrode_start_x + electrode_width, 0.5 + 1.8)
slab = box(-10, 0, 10, 0.5)
core = box(-core_width / 2, 0.5, core_width / 2, 0.8)
env = slab.buffer(20, resolution=8)

polygons = OrderedDict(
    electrode_left=electrode_left,
    electrode_right=electrode_right,
    slab=slab,
    core=core,
    env=env,
)

resolutions = dict(
    slab={"resolution": 0.1, "distance": 4},
    core={"resolution": 0.1, "distance": 4},
)

mesh_from_OrderedDict(polygons, resolutions, filename="mesh.msh", default_resolution_max=3)
"""

using Gridap
using Gridap.Geometry
using GridapGmsh
using Femwell.Maxwell.Waveguide
using Femwell.Maxwell.Electrostatic
using GridapMakie, CairoMakie

model = GmshDiscreteModel("mesh.msh")
Ω = Triangulation(model)
labels = get_face_labeling(model)
τ = CellField(get_face_tag(labels, num_cell_dims(model)), Ω)

conductivity = [
    "core" => 7.5,
    "slab" => 28.4,
    "electrode_left" => 3.9,
    "electrode_right" => 3.9,
    "env" => 3.9,
]
σ(tag) = Dict(get_tag_from_name(labels, u) => v for (u, v) in conductivity)[tag]

p0 = compute_potential(
    σ ∘ τ,
    Dict("electrode_left___slab" => 1.0, "electrode_right___slab" => 0.0),
    order = 2,
)

plot_potential(p0)

fig, _, plt =
    plot(get_triangulation(potential(p0)), (σ ∘ τ) * ∇(potential(p0)) ⋅ VectorValue(1, 0))
Colorbar(fig[1, 2], plt)
display(fig)

voltages = 0:10:100
voltages_neffs = []

for voltage in voltages
    epsilons = [
        "core" => 1.989,
        "env" => 1.445,
        "slab" => 2.211,
        "electrode_left" => 1.445,
        "electrode_right" => 1.445,
    ]
    ε(tag) = Dict(get_tag_from_name(labels, u) => v for (u, v) in epsilons)[tag]

    ε_perturbation =
        0.5 * 2.211^3 * 31e-6 * ∇(potential(p0)) ⋅ VectorValue(-1, 0) *
        voltage *
        ((tag -> get_tag_from_name(labels, "slab") == tag) ∘ τ)

    modes = calculate_modes(
        model,
        (ε ∘ τ + ε_perturbation) * (ε ∘ τ + ε_perturbation),
        λ = 1.55,
        order = 0,
    )
    push!(voltages_neffs, n_eff(modes[1]))
end

The following 1 direct dependency failed to precompile:

GLMakie [e9467ef8-e4e7-5192-8a1a-b1aee30e663a]

Failed to precompile GLMakie [e9467ef8-e4e7-5192-8a1a-b1aee30e663a] to "/home/runner/.julia/compiled/v1.10/GLMakie/jl_ZSbG1p".
┌ Warning:     OpenGL/GLFW wasn't loaded correctly or couldn't be initialized.
│     This likely means, you're on a headless server without having OpenGL support setup correctly.
│     Have a look at the troubleshooting section in the readme:
│     https://github.com/MakieOrg/Makie.jl/tree/master/GLMakie#troubleshooting-opengl.
└ @ GLMakie ~/.julia/packages/GLMakie/xG4T9/src/gl_backend.jl:4
ERROR: LoadError: InitError: Exception[GLFW.GLFWError(65550, "X11: The DISPLAY environment variable is missing"), ErrorException("glfwInit failed")]
Stacktrace:
  [1] __init__()
    @ GLFW ~/.julia/packages/GLFW/wmoTL/src/GLFW.jl:35
  [2] run_module_init(mod::Module, i::Int64)
    @ Base ./loading.jl:1134
  [3] register_restored_modules(sv::Core.SimpleVector, pkg::Base.PkgId, path::String)
    @ Base ./loading.jl:1122
  [4] _include_from_serialized(pkg::Base.PkgId, path::String, ocachepath::String, depmods::Vector{Any})
    @ Base ./loading.jl:1067
  [5] _require_search_from_serialized(pkg::Base.PkgId, sourcepath::String, build_id::UInt128)
    @ Base ./loading.jl:1581
  [6] _require(pkg::Base.PkgId, env::String)
    @ Base ./loading.jl:1938
  [7] __require_prelocked(uuidkey::Base.PkgId, env::String)
    @ Base ./loading.jl:1812
  [8] #invoke_in_world#3
    @ ./essentials.jl:926 [inlined]
  [9] invoke_in_world
    @ ./essentials.jl:923 [inlined]
 [10] _require_prelocked(uuidkey::Base.PkgId, env::String)
    @ Base ./loading.jl:1803
 [11] macro expansion
    @ ./loading.jl:1790 [inlined]
 [12] macro expansion
    @ ./lock.jl:267 [inlined]
 [13] __require(into::Module, mod::Symbol)
    @ Base ./loading.jl:1753
 [14] #invoke_in_world#3
    @ ./essentials.jl:926 [inlined]
 [15] invoke_in_world
    @ ./essentials.jl:923 [inlined]
 [16] require(into::Module, mod::Symbol)
    @ Base ./loading.jl:1746
 [17] top-level scope
    @ ~/.julia/packages/GLMakie/xG4T9/src/gl_backend.jl:2
 [18] include(mod::Module, _path::String)
    @ Base ./Base.jl:495
 [19] include(x::String)
    @ GLMakie ~/.julia/packages/GLMakie/xG4T9/src/GLMakie.jl:1
 [20] top-level scope
    @ ~/.julia/packages/GLMakie/xG4T9/src/GLMakie.jl:87
 [21] include
    @ ./Base.jl:495 [inlined]
 [22] include_package_for_output(pkg::Base.PkgId, input::String, depot_path::Vector{String}, dl_load_path::Vector{String}, load_path::Vector{String}, concrete_deps::Vector{Pair{Base.PkgId, UInt128}}, source::Nothing)
    @ Base ./loading.jl:2222
 [23] top-level scope
    @ stdin:3
during initialization of module GLFW
in expression starting at /home/runner/.julia/packages/GLMakie/xG4T9/src/gl_backend.jl:1
in expression starting at /home/runner/.julia/packages/GLMakie/xG4T9/src/GLMakie.jl:1
in expression starting at stdin:

Stacktrace:
  [1] pkgerror(msg::String)
    @ Pkg.Types /opt/hostedtoolcache/julia/1.10.3/x64/share/julia/stdlib/v1.10/Pkg/src/Types.jl:70
  [2] precompile(ctx::Pkg.Types.Context, pkgs::Vector{Pkg.Types.PackageSpec}; internal_call::Bool, strict::Bool, warn_loaded::Bool, already_instantiated::Bool, timing::Bool, _from_loading::Bool, kwargs::@Kwargs{io::IJulia.IJuliaStdio{Base.PipeEndpoint}})
    @ Pkg.API /opt/hostedtoolcache/julia/1.10.3/x64/share/julia/stdlib/v1.10/Pkg/src/API.jl:1659
  [3] precompile(pkgs::Vector{Pkg.Types.PackageSpec}; io::IJulia.IJuliaStdio{Base.PipeEndpoint}, kwargs::@Kwargs{_from_loading::Bool})
    @ Pkg.API /opt/hostedtoolcache/julia/1.10.3/x64/share/julia/stdlib/v1.10/Pkg/src/API.jl:159
  [4] precompile
    @ /opt/hostedtoolcache/julia/1.10.3/x64/share/julia/stdlib/v1.10/Pkg/src/API.jl:147 [inlined]
  [5] #precompile#114
    @ /opt/hostedtoolcache/julia/1.10.3/x64/share/julia/stdlib/v1.10/Pkg/src/API.jl:146 [inlined]
  [6] #invokelatest#2
    @ ./essentials.jl:894 [inlined]
  [7] invokelatest
    @ ./essentials.jl:889 [inlined]
  [8] _require(pkg::Base.PkgId, env::String)
    @ Base ./loading.jl:1963
  [9] __require_prelocked(uuidkey::Base.PkgId, env::String)
    @ Base ./loading.jl:1812
 [10] #invoke_in_world#3
    @ ./essentials.jl:926 [inlined]
 [11] invoke_in_world
    @ ./essentials.jl:923 [inlined]
 [12] _require_prelocked(uuidkey::Base.PkgId, env::String)
    @ Base ./loading.jl:1803
 [13] macro expansion
    @ ./loading.jl:1790 [inlined]
 [14] macro expansion
    @ ./lock.jl:267 [inlined]
 [15] __require(into::Module, mod::Symbol)
    @ Base ./loading.jl:1753
 [16] #invoke_in_world#3
    @ ./essentials.jl:926 [inlined]
 [17] invoke_in_world
    @ ./essentials.jl:923 [inlined]
 [18] require(into::Module, mod::Symbol)
    @ Base ./loading.jl:1746
Hide code cell source 
f = Figure()
ax = Axis(f[1, 1], xlabel = "Voltage / V", ylabel = "Effective refractive index")
lines!(ax, voltages, real(voltages_neffs))
plot!(ax, voltages, real(voltages_neffs))
display(f)

Bibliography#

[1]

Huangpu Han, Fan Yang, Chenghao Liu, Zhengfang Wang, Yunpeng Jiang, Guangyue Chai, Shuangchen Ruan, and Bingxi Xiang. High-performance electro-optical mach–zehnder modulators in a silicon nitride–lithium niobate thin-film hybrid platform. Photonics, 9(7):500, July 2022. URL: https://doi.org/10.3390/photonics9070500, doi:10.3390/photonics9070500.

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