Mode solving anisotropic

Contents

Mode solving anisotropic#

[1]

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 = 0.8
wg_thickness = 0.6076
core = shapely.geometry.box(-wg_width / 2, 0, +wg_width / 2, wg_thickness)
env = shapely.affinity.scale(core.buffer(5, resolution = 8), xfact = 0.5)

polygons = OrderedDict(
    core = core,
    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))

mesh = mesh_from_OrderedDict(
    polygons,
    resolutions,
    default_resolution_max = 0.1,
    filename = "mesh.msh",
)
Hide code cell output 
PyObject <meshio mesh object>
  Number of points: 10536
  Number of cells:
    line: 27
    line: 21
    line: 27
    line: 21
    line: 27
    line: 27
    triangle: 1442
    triangle: 7987
    triangle: 11363
  Cell sets: 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: core___box, core___clad, box___clad, core, box, clad

using LinearAlgebra
using SparseArrays

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

using Femwell.Maxwell.Waveguide

CairoMakie.inline!(true)
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_uHbpcs".
┌ 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/R7CtZ/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/a10jC/src/GLFW.jl:69
  [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/R7CtZ/src/gl_backend.jl:2
 [18] include(mod::Module, _path::String)
    @ Base ./Base.jl:495
 [19] include(x::String)
    @ GLMakie ~/.julia/packages/GLMakie/R7CtZ/src/GLMakie.jl:1
 [20] top-level scope
    @ ~/.julia/packages/GLMakie/R7CtZ/src/GLMakie.jl:90
 [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/R7CtZ/src/gl_backend.jl:1
in expression starting at /home/runner/.julia/packages/GLMakie/R7CtZ/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)

labels = get_face_labeling(model)

eye = diagonal_tensor(VectorValue([1.0, 1.0, 1.0]))
n2 = 2.302
Δ = 0.005
yig = TensorValue([n2^2 1im*Δ 0; -1im*Δ n2^2 0; 0 0 n2^2])
epsilons = ["core" => yig, "box" => 1.95^2 * eye, "clad" => 1.0^2 * eye]
ε(tag) = Dict(get_tag_from_name(labels, u) => v for (u, v) in epsilons)[tag]

τ = CellField(get_face_tag(labels, num_cell_dims(model)), Ω)

modes = calculate_modes(model, ε ∘ τ, λ = 1.3, num = 2, order = 1)

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

Bibliography#

[1]

Arman B. Fallahkhair, Kai S. Li, and Thomas E. Murphy. Vector finite difference modesolver for anisotropic dielectric waveguides. Journal of Lightwave Technology, 26(11):1423–1431, June 2008. URL: https://doi.org/10.1109/jlt.2008.923643, doi:10.1109/jlt.2008.923643.

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