OpticalFibers.jl

OpticalFibers is a package that allows to compute modes of optical fibers. Different methods are implemented to find scalar or vector modes: - A semi-analytical solver (based on Bessel functions) for multi-step index fibers. - Finite element method (using Gridap.jl) for any kind of isotropic or anisotropic fiber. A PML (Perfectly Matched Layer) is implemented to compute losses of leaky modes guided in trench-assisted fibers, PCF (Photonic Crystal Fibers), bent fiber, twisted fiber, etc. The FEM mode solver can also be used to find photonic bandgaps of a PCF cladding.

Installation

OpticalFibers requires at least julia 1.9 and can be installed with:

julia using Pkg Pkg.add("OpticalFibers")

Quickstart

Finding guided modes of a step-index fiber using the semi-analytical mode solver

Computation of the scalar fundamental mode (l=0) of a step index fiber with a core-radius of 2 µm, a refractive index of 1.47 for core and 1.45 for cladding at a wavelength of 1 µm: julia julia> using OpticalFibers julia> using OpticalFibers.ModeSolvers julia> ms=multi_step_fiber_modes(1,0,2,[1.47,1.45],field=true) 1-element Vector{Mode}: [LP 0,1,1.463179347605715,1,ScalarFieldFunction1D] julia> using Plots julia> plot(0:0.1:7,abs.(ms[1].field.E.(0:0.1:7)),xlabel="r (µm)",ylabel="|E|",label="Fundamental Mode")

Computation of the fundamental vector mode (l=1) of the same fiber: julia julia> mv=multi_step_fiber_modes(1,1,2,[1.47,1.45],type=:Vector) 1-element Vector{Mode}: [HE 1,1,1.4631371608572663,1,Nothing]

Finding guided modes of a graded-index fiber using the FEM mode solver

Computation of the scalar modes of a parabolic-index fiber with a core-radius of 4 µm, a refractive index of 1.48 for core center and 1.45 for cladding at a wavelength of 1 µm by using the finite element method with 1000 nodes between r=0 and r=20 µm: ```julia julia> using OpticalFibers julia> using OpticalFibers.ModeSolvers julia> using Gridap julia> m=FEM1D(1,0,x->(1.45+0.03(1-x[1]^2/16)(x[1]<=4))^2,CartesianDiscreteModel((0,20),1000),field=true,neigs=5) 2-element Vector{Mode{ScalarFieldFEM1D}}: [Mode LP n°1,1.471980656971672,1,ScalarFieldFEM1D] [Mode LP n°2,1.4561502566053002,1,ScalarFieldFEM1D]

julia> using Plots julia> r=0:0.01:10 julia> plot(r,abs2.(computeField(m[1],r)),label="LP₀₁",xlabel="r (µm)",ylabel="|E|²") julia> plot!(r,abs2.(computeField(m[2],r)),label="LP₀₂",xlabel="r (µm)",ylabel="|E|²") ```

Finding leaky modes of a step-index fiber with a trench using the FEM mode solver with a PML

Let us consider a step-index fiber with a trench: - Core: radius 4 µm and refractive index 1.44 - Trench: thickness 16 µm and refractive index 1.41 - Cladding: refractive index 1.43

Computation of the guided modes $\ell=0$ without the cladding: julia julia> m=multi_step_fiber_modes(1.6,0,4,[1.44,1.41]) 2-element Vector{Mode}: [LP 0,1,1.4345691826486056,1.6,Nothing] [LP 0,2,1.4137165538840926,1.6,Nothing]

Computation of the guided modes $\ell=0$ with the cladding: julia julia> m2=multi_step_fiber_modes(1.6,0,[4,20],[1.44,1.41,1.43]) 1-element Vector{Mode}: [LP 0,1,1.4345691826495002,1.6,Nothing] The LP₀₂ becomes leaky when adding the cladding

To compute its losses, we have to use the FEM solver with a PML: julia julia> epsilon_trench=x->(1.44-0.03*(x[1]>=4)+0.02*(x[1]>20))^2; julia> model_trench = CartesianDiscreteModel((0,50),5000); julia> ms1D_trench=FEM1D(1.6,0,epsilon_trench,model_trench,field=true,dPML=5,approx_neff=m[2].neff) 1-element Vector{Mode{ScalarFieldFEM1D}}: [Mode LP n°1,1.4137165449018512 + 1.0825770569063048e-8im,1.6,ScalarFieldFEM1D] julia> losses(ms1D_trench[1])*1E6 369.26063441366387 Losses of the LP₀₂ mode are 369 dB/km.

Finding bend losses using the FEM mode solver with a PML

Let us consider the step_index fiber described below: - Core: radius 3.5 µm, refractive index 1.4457 - Cladding: refractive index 1.4378

Computation of the fundamental mode at $\lambda=1.55$ µm: julia julia> ms_straight=multi_step_fiber_modes(1.55,0,3.5,[1.4457,1.4378],field=true) 1-element Vector{Mode}: [LP 0,1,1.4414392004035022,1.55,Nothing]

To compute the funcamental mode when the fiber is bent, we need to use a 2D mesh generated with GMSH: julia julia> using GridapGmsh julia> model = GmshDiscreteModel("./models/example5.msh") Info : Reading './models/example5.msh'... Info : 10 entities Info : 14768 nodes Info : 29536 elements Info : Done reading './models/example5.msh' UnstructuredDiscreteModel() and define the relative permittivity for a straight fiber and for fiber bent with a radius of curvature of 10 mm: julia julia> epsilon2D=x->(1.4457-(1.4457-1.4378)*(hypot(x[1],x[2])>=3.5))^2; julia> epsilon2D_bent=x->epsilon2D(x)*(1+x[1]/10E3)^2; julia> ms2D_bent=FEM2D(1.55,epsilon2D_bent,model,field=true,neigs=1,dPML=3,approx_neff=ms_straight[1].neff) 1-element Vector{Mode{ScalarFieldFEM2D}}: [Mode LP n°1,1.4414582242320717 + 1.5096368959704397e-9im,1.55,ScalarFieldFEM2D] losses(ms2D_bent[1])*1E6 In this case, the bend losses are 53 dB/km

Credits

OpticalFibers.jl is maintained by Olivier Vanvincq (university of Lille, PhLAM laboratory).