Mode solving anisotropic

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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

 
InitError: could not load library "/home/runner/.julia/artifacts/b2e490a224990d92e99cc4463b8df48c8c454971/lib/libpangocairo-1.0.so"
/home/runner/.julia/artifacts/b2e490a224990d92e99cc4463b8df48c8c454971/lib/libpangoft2-1.0.so.0: undefined symbol: FcConfigSetDefaultSubstitute
during initialization of module Pango_jll

Stacktrace:
  [1] dlopen(s::String, flags::UInt32; throw_error::Bool)
    @ Base.Libc.Libdl ./libdl.jl:117
  [2] dlopen(s::String, flags::UInt32)
    @ Base.Libc.Libdl ./libdl.jl:116
  [3] macro expansion
    @ ~/.julia/packages/JLLWrappers/m2Pjh/src/products/library_generators.jl:63 [inlined]
  [4] __init__()
    @ Pango_jll ~/.julia/packages/Pango_jll/CWpUN/src/wrappers/x86_64-linux-gnu.jl:22
  [5] run_module_init(mod::Module, i::Int64)
    @ Base ./loading.jl:1134
  [6] register_restored_modules(sv::Core.SimpleVector, pkg::Base.PkgId, path::String)
    @ Base ./loading.jl:1122
  [7] _include_from_serialized(pkg::Base.PkgId, path::String, ocachepath::String, depmods::Vector{Any})
    @ Base ./loading.jl:1067
  [8] _tryrequire_from_serialized(modkey::Base.PkgId, path::String, ocachepath::String, sourcepath::String, depmods::Vector{…})
    @ Base ./loading.jl:1481
  [9] _require_search_from_serialized(pkg::Base.PkgId, sourcepath::String, build_id::UInt128)
    @ Base ./loading.jl:1574
 [10] _require(pkg::Base.PkgId, env::String)
    @ Base ./loading.jl:1938
 [11] __require_prelocked(uuidkey::Base.PkgId, env::String)
    @ Base ./loading.jl:1812
 [12] #invoke_in_world#3
    @ ./essentials.jl:926 [inlined]
 [13] invoke_in_world
    @ ./essentials.jl:923 [inlined]
 [14] _require_prelocked(uuidkey::Base.PkgId, env::String)
    @ Base ./loading.jl:1803
 [15] macro expansion
    @ ./loading.jl:1790 [inlined]
 [16] macro expansion
    @ ./lock.jl:267 [inlined]
 [17] __require(into::Module, mod::Symbol)
    @ Base ./loading.jl:1753
 [18] #invoke_in_world#3
    @ ./essentials.jl:926 [inlined]
 [19] invoke_in_world
    @ ./essentials.jl:923 [inlined]
 [20] 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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