Mode solving

Caution

This example is under construction As Julia-Dicts are not ordered, the mesh might become incorrect when adjusted (for now, better do the meshing in python)

using PyCall
np = pyimport("numpy")
shapely = pyimport("shapely")
shapely.affinity = pyimport("shapely.affinity")
clip_by_rect = pyimport("shapely.ops").clip_by_rect
OrderedDict = pyimport("collections").OrderedDict
mesh_from_OrderedDict = pyimport("femwell.mesh").mesh_from_OrderedDict

wg_width = 0.5
wg_thickness = 0.22
slab_width = 3
slab_thickness = 0.11
core = shapely.geometry.box(-wg_width / 2, 0, wg_width / 2, wg_thickness)
slab = shapely.geometry.box(slab_width / 2, 0, slab_width / 2, slab_thickness)
env = shapely.affinity.scale(core.buffer(3, resolution = 8), xfact = 0.5)

polygons = OrderedDict(
    core = core,
    slab = slab,
    box = clip_by_rect(env, -np.inf, -np.inf, np.inf, 0),
    clad = clip_by_rect(env, -np.inf, 0, np.inf, np.inf),
)

resolutions = Dict(
    "core" => Dict("resolution" => 0.03, "distance" => 0.5),
    "slab" => Dict("resolution" => 0.03, "distance" => 0.5),
)

mesh = mesh_from_OrderedDict(
    polygons,
    resolutions,
    default_resolution_max = 1,
    filename = "mesh.msh",
)

Show code cell output Hide code cell output

PyObject <meshio mesh object>
  Number of points: 338
  Number of cells:
    vertex: 1
    vertex: 1
    line: 4
    line: 17
    line: 8
    line: 17
    line: 8
    line: 6
    line: 8
    line: 3
    triangle: 342
    triangle: 116
    triangle: 178
  Cell sets: slab_points, slab, core___box, core___clad, box___clad, core, box, clad, gmsh:bounding_entities
  Point data: gmsh:dim_tags
  Cell data: gmsh:physical, gmsh:geometrical
  Field data: slab_points, slab, core___box, core___clad, box___clad, core, box, clad

using Gridap
using Gridap.Geometry
using Gridap.Visualization
using Gridap.ReferenceFEs
using GridapGmsh
using GridapMakie, CairoMakie

using Femwell.Maxwell.Waveguide

CairoMakie.inline!(true)

Show code cell output Hide code cell output

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_ugYon7".
┌ 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/TH3rf/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/TH3rf/src/gl_backend.jl:2
 [18] include(mod::Module, _path::String)
    @ Base ./Base.jl:495
 [19] include(x::String)
    @ GLMakie ~/.julia/packages/GLMakie/TH3rf/src/GLMakie.jl:1
 [20] top-level scope
    @ ~/.julia/packages/GLMakie/TH3rf/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/TH3rf/src/gl_backend.jl:1
in expression starting at /home/runner/.julia/packages/GLMakie/TH3rf/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

model = GmshDiscreteModel("mesh.msh")
Ω = Triangulation(model)
#fig = plot(Ω)
#fig.axis.aspect=DataAspect()
#wireframe!(Ω, color=:black, linewidth=1)
#display(fig)

labels = get_face_labeling(model)

epsilons = ["core" => 3.5^2, "slab" => 1.44^2, "box" => 1.444^2, "clad" => 1.44^2]
ε(tag) = Dict(get_tag_from_name(labels, u) => v for (u, v) in epsilons)[tag]


#dΩ = Measure(Ω, 1)
τ = CellField(get_face_tag(labels, num_cell_dims(model)), Ω)

modes = calculate_modes(model, ε ∘ τ, λ = 1.55, num = 1, order = 1)
println(n_eff(modes[1]))
# write_mode_to_vtk("mode", modes[2])

plot_mode(modes[1])
#plot_mode(modes[2])
modes

Perturbations

Let’s add a minor perturbation and calculate the effective refractive index using perturbation theory:

epsilons_p = ["core" => -0.1im, "box" => -0.0im, "slab" => -0.0im, "clad" => -0.0im]
ε_p(tag) = Dict(get_tag_from_name(labels, u) => v for (u, v) in epsilons_p)[tag]

println(perturbed_neff(modes[1], ε_p ∘ τ))

For comparison, we also calculate directly the effective refractive index:

modes_p = calculate_modes(model, ε ∘ τ + ε_p ∘ τ, λ = 1.55, num = 2, order = 1)
println(n_eff(modes_p[1]))
plot_mode(modes_p[1])