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TMM_module.jl
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TMM_module.jl
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module TMM
# The following packages are required in this module.
using Pkg
#Pkg.add("Plots")
#Pkg.add("NPZ")
#Pkg.add("LinearAlgebra")
#Pkg.add("Distributions")
#Pkg.add("PythonPlot") # Due to the SSL certificate issue, it cannot be used in LG INNOTEK.
#Pkg.add("PlotlyJS")
#Pkg.add("PlotlyBase")
#Pkg.add("UnicodePlots")
using Base
using Distributions
using NPZ
using Printf
using Plots
import LinearAlgebra as la
# Choose the backends of the Plots package.
gr()
# pythonplot()
# plotlyjs()
# unicodeplots()
export _get_Amatrix, _get_Bmatrix
export _get_HxHy, _get_Ez, _get_Hz
export _make_WhVh, _make_WpVp, _make_WmVm
export get_eigenvectors
export get_the_left_to_right_operators
export get_the_right_to_left_operators
export left_to_right_field_visualization
export right_to_left_field_visualization
export get_scc_of_a_block
export get_scc_of_each_n_blocks
export redheffer
export redheffer_n_blocks
export redheffer_two_blocks
export redheffer_combine_all_blocks
export multiblock_visualization_left_to_right
export multiblock_visualization_right_to_left
# Calculate corresponding Ez, Hx, Hy and Hz for the given Ex and Ey.
function _get_Amatrix(
kx_bar::Number,
ky_bar::Number,
mur::Number,
epsr::Number
)
A = zeros(ComplexF64, 2, 2)
murx = mur
mury = mur
murz = mur
epsrx = epsr
epsry = epsr
epsrz = epsr
A[1,1] = ky_bar * kx_bar / epsrz
A[1,2] = murx - ky_bar * ky_bar / epsrz
A[2,1] =-mury + kx_bar * kx_bar / epsrz
A[2,2] =-A[1,1]
return A
end
function _get_Bmatrix(
kx_bar::Number,
ky_bar::Number,
mur::Number,
epsr::Number
)
B = zeros(ComplexF64, 2, 2)
murx = mur
mury = mur
murz = mur
epsrx = epsr
epsry = epsr
epsrz = epsr
B[1,1] = ky_bar * kx_bar / murz
B[1,2] = epsrx - ky_bar * ky_bar / murz
B[2,1] =-epsry + kx_bar * kx_bar / murz
B[2,2] =-B[1,1]
return B
end
function _get_HxHy(
k0::Number,
kzn::Number,
A::AbstractMatrix,
input::AbstractVector,
impedance::Number)
H11 = (1im .* kzn./k0) .* (inv(A) * input)
Hy = H11[1]
Hx = H11[2]
Hx *= (1im / impedance)
Hy *= (1im / impedance)
return Hx, Hy
end
function _get_Ez(ky_bar, kx_bar, Hy, Hx, epsr, impedence)
Hy *= (impedence / 1im)
Hx *= (impedence / 1im)
Ez = 1im.*(ky_bar.*Hx .- kx_bar.*Hy) ./ epsr
return Ez
end
function _get_Hz(ky_bar, kx_bar, Ey, Ex, mur, impedance)
Hz = 1im.*(ky_bar.*Ex .- kx_bar.*Ey) ./ mur
Hz*= (1im / impedance)
return Hz
end
# Obtain the eigen vectors and eigenvalues in a medium.
function get_eigenvectors(k0, kx0, ky0, mur, epsr)
μ_0 = 4*π*10^-7
ε_0 = 8.8541878128e-12
impedance = sqrt(μ_0 /ε_0)
kx_bar = kx0 / k0 # it is equal to sin(θ) cos(ϕ)
ky_bar = ky0 / k0 # it is equal to sin(θ) sin(ϕ)
murx = mur
mury = mur
murz = mur
epsrx = epsr
epsry = epsr
epsrz = epsr
A = _get_Amatrix(kx_bar, ky_bar, mur, epsr)
B = _get_Bmatrix(kx_bar, ky_bar, mur, epsr)
C = (k0^2) .* (A * B)
eigvals, EyEx_eigvecs = la.eigen(C)
kzTEp = sqrt(-eigvals[1]) # Left-to-right, TE mode.
kzTEm =-sqrt(-eigvals[1]) # Right-to-left, TE mode.
kzTMp = sqrt(-eigvals[2]) # Left-to-right, TM mode.
kzTMm =-sqrt(-eigvals[2]) # Right-to-left, TM mode.
EyTE = EyEx_eigvecs[1,1] # Ey, TE mode.
ExTE = EyEx_eigvecs[2,1] # Ex, TE mode.
EyTM = EyEx_eigvecs[1,2] # Ey, TM mode.
ExTM = EyEx_eigvecs[2,2] # Ex, TM mode.
# Note that H field (magnetic induction vector) is scaled by 1im * sqrt(ε_0/μ_0) for convenience,
# i.e., H_hat = 1im * sqrt(ε_0/μ_0) * H_bar, and we are calculating H_hat.
# Also, the order of the eigenvector is reversed, i.e., H11 = [Hy, Hx], not [Hx, Hy].
HxTEp, HyTEp = _get_HxHy(k0, kzTEp, A, [EyTE, ExTE], impedance)
HxTEm, HyTEm = _get_HxHy(k0, kzTEm, A, [EyTE, ExTE], impedance)
HxTMp, HyTMp = _get_HxHy(k0, kzTMp, A, [EyTM, ExTM], impedance)
HxTMm, HyTMm = _get_HxHy(k0, kzTMm, A, [EyTM, ExTM], impedance)
EzTEp = _get_Ez(ky_bar, kx_bar, HyTEp, HxTEp, epsrz, impedance)
EzTEm = _get_Ez(ky_bar, kx_bar, HyTEm, HxTEm, epsrz, impedance)
EzTMp = _get_Ez(ky_bar, kx_bar, HyTMp, HxTMp, epsrz, impedance)
EzTMm = _get_Ez(ky_bar, kx_bar, HyTMm, HxTMm, epsrz, impedance)
HzTE = _get_Hz(ky_bar, kx_bar, EyTE, ExTE, murz, impedance)
HzTM = _get_Hz(ky_bar, kx_bar, EyTM, ExTM, murz, impedance)
eigenvec1 = [ExTE, EyTE, EzTEp, HxTEp, HyTEp, HzTE] # Left-to-right, TE mode.
eigenvec2 = [ExTE, EyTE, EzTEm, HxTEm, HyTEm, HzTE] # Right-to-left, TE mode.
eigenvec3 = [ExTM, EyTM, EzTMp, HxTMp, HyTMp, HzTM] # Left-to-right, TM mode.
eigenvec4 = [ExTM, EyTM, EzTMm, HxTMm, HyTMm, HzTM] # Right-to-left, TM mode.
eigvalues = [kzTEp, kzTEm, kzTMp, kzTMm]
eigenvecs = hcat(eigenvec1, eigenvec2, eigenvec3, eigenvec4)
return eigvalues, eigenvecs
end
"""
_make_WhVh(ω, kx, ky, kz, eigvecs, z)
Make Wh and Vh matrices.
# Arguments
- 'ω::Real': angular frequency of the input wave.
- 'kx::Real': kx in free space.
- 'ky::Real': ky in free space.
- 'kz::Real': kz in free space.
# Returns
- 'Wh::AbstractMatrix': 2x2 identity matrix.
- 'Vh::AbstractMatrix': 2x2 matrix.
# Examples
'''julia
julia>
'''
# Notes
"""
function _make_WhVh(ω::Real, kx::Real, ky::Real, kz::Real)
μ_0 = 4*π*10^-7
Wh = la.I # The most Julianic way of expressing the identity matrix.
Vh = zeros(ComplexF64, 2, 2)
Vh[1,1] = kx * ky / kz / ω / μ_0
Vh[1,2] = (kx^2 + kz^2) / kz / ω / μ_0
Vh[2,1] =-(ky^2 + kz^2) / kz / ω / μ_0
Vh[2,2] =-kx * ky / kz / ω / μ_0
return Wh, Vh
end
"""
_make_WpVp(eigvecs, z)
Make some matrices and calculate the coupling coeffient matrix operators.
# Arguments
# Returns
# Examples
```julia
julia>
```
# Notes
"""
function _make_WpVp(
eigvalues::AbstractVector,
eigvecs::AbstractMatrix,
z::Real
)
kz1p = eigvalues[1]
kz1m = eigvalues[2]
kz2p = eigvalues[3]
kz2m = eigvalues[4]
ExTEp = eigvecs[1,1]
ExTEm = eigvecs[1,2]
ExTMp = eigvecs[1,3]
ExTMm = eigvecs[1,4]
EyTEp = eigvecs[2,1]
EyTEm = eigvecs[2,2]
EyTMp = eigvecs[2,3]
EyTMm = eigvecs[2,4]
EzTEp = eigvecs[3,1]
EzTEm = eigvecs[3,2]
EzTMp = eigvecs[3,3]
EzTMm = eigvecs[3,4]
HxTEp = eigvecs[4,1]
HxTEm = eigvecs[4,2]
HxTMp = eigvecs[4,3]
HxTMm = eigvecs[4,4]
HyTEp = eigvecs[5,1]
HyTEm = eigvecs[5,2]
HyTMp = eigvecs[5,3]
HyTMm = eigvecs[5,4]
HzTEp = eigvecs[6,1]
HzTEm = eigvecs[6,2]
HzTMp = eigvecs[6,3]
HzTMm = eigvecs[6,4]
Wp = zeros(ComplexF64, 2, 2)
Vp = zeros(ComplexF64, 2, 2)
Wp[1,1] = EyTEp * exp(1im*kz1p*z)
Wp[1,2] = EyTMp * exp(1im*kz2p*z)
Wp[2,1] = ExTEp * exp(1im*kz1p*z)
Wp[2,2] = ExTMp * exp(1im*kz2p*z)
Vp[1,1] = HyTEp * exp(1im*kz1p*z)
Vp[1,2] = HyTMp * exp(1im*kz2p*z)
Vp[2,1] = HxTEp * exp(1im*kz1p*z)
Vp[2,2] = HxTMp * exp(1im*kz2p*z)
return Wp, Vp
end
function _make_WmVm(
eigvalues::AbstractVector,
eigvecs::AbstractMatrix,
z::Real
)
kz1p = eigvalues[1]
kz1m = eigvalues[2]
kz2p = eigvalues[3]
kz2m = eigvalues[4]
ExTEp = eigvecs[1,1]
ExTEm = eigvecs[1,2]
ExTMp = eigvecs[1,3]
ExTMm = eigvecs[1,4]
EyTEp = eigvecs[2,1]
EyTEm = eigvecs[2,2]
EyTMp = eigvecs[2,3]
EyTMm = eigvecs[2,4]
EzTEp = eigvecs[3,1]
EzTEm = eigvecs[3,2]
EzTMp = eigvecs[3,3]
EzTMm = eigvecs[3,4]
HxTEp = eigvecs[4,1]
HxTEm = eigvecs[4,2]
HxTMp = eigvecs[4,3]
HxTMm = eigvecs[4,4]
HyTEp = eigvecs[5,1]
HyTEm = eigvecs[5,2]
HyTMp = eigvecs[5,3]
HyTMm = eigvecs[5,4]
HzTEp = eigvecs[6,1]
HzTEm = eigvecs[6,2]
HzTMp = eigvecs[6,3]
HzTMm = eigvecs[6,4]
Wm = zeros(ComplexF64, 2, 2)
Vm = zeros(ComplexF64, 2, 2)
Wm[1,1] = EyTEm * exp(1im*kz1m*z)
Wm[1,2] = EyTMm * exp(1im*kz2m*z)
Wm[2,1] = ExTEm * exp(1im*kz1m*z)
Wm[2,2] = ExTMm * exp(1im*kz2m*z)
Vm[1,1] = HyTEm * exp(1im*kz1m*z)
Vm[1,2] = HyTMm * exp(1im*kz2m*z)
Vm[2,1] = HxTEm * exp(1im*kz1m*z)
Vm[2,2] = HxTMm * exp(1im*kz2m*z)
return Wm, Vm
end
function get_the_left_to_right_operators(
ω::Number,
kx0::Number,
ky0::Number,
kz0::Number,
eigvalues::AbstractVector,
eigvectors::AbstractMatrix,
zm::Real,
zp::Real
)
Wh, Vh = _make_WhVh(ω, kx0, ky0, kz0)
Wp0, Vp0 = _make_WpVp(eigvalues, eigvectors, 0.)
Wpp, Vpp = _make_WpVp(eigvalues, eigvectors, zp-zm)
Wm0, Vm0 = _make_WmVm(eigvalues, eigvectors, 0)
Wmm, Vmm = _make_WmVm(eigvalues, eigvectors, zm-zp)
A = inv(Wh)*Wp0 + inv(Vh)*Vp0
B = inv(Wh)*Wmm + inv(Vh)*Vmm
C = inv(Wh)*Wpp - inv(Vh)*Vpp
D = inv(Wh)*Wm0 - inv(Vh)*Vm0
E = zeros(ComplexF64, 4, 4)
E[1:2,1:2] = A
E[1:2,3:4] = B
E[3:4,1:2] = C
E[3:4,3:4] = D
u = zeros(Float64, 4, 2)
u[1,1] = 2
u[2,2] = 2
ca = inv(E) * u
cap = ca[1:2,1:2]
cam = ca[3:4,1:2]
R = inv(Wh) * (Wp0*cap + Wmm*cam - Wh*la.I)
T = inv(Wh) * (Wpp*cap + Wm0*cam)
return cap, cam, R, T
end
function get_the_right_to_left_operators(
ω::Number,
kx0::Number,
ky0::Number,
kz0::Number,
eigvalues::AbstractVector,
eigvectors::AbstractMatrix,
zm::Real,
zp::Real
)
Wh, Vh = _make_WhVh(ω, kx0, ky0, kz0)
Wp0, Vp0 = _make_WpVp(eigvalues, eigvectors, 0.)
Wpp, Vpp = _make_WpVp(eigvalues, eigvectors, zp-zm)
Wm0, Vm0 = _make_WmVm(eigvalues, eigvectors, 0)
Wmm, Vmm = _make_WmVm(eigvalues, eigvectors, zm-zp)
A = inv(Wh)*Wp0 + inv(Vh)*Vp0
B = inv(Wh)*Wmm + inv(Vh)*Vmm
C = inv(Wh)*Wpp - inv(Vh)*Vpp
D = inv(Wh)*Wm0 - inv(Vh)*Vm0
E = zeros(ComplexF64, 4, 4)
E[1:2,1:2] = A
E[1:2,3:4] = B
E[3:4,1:2] = C
E[3:4,3:4] = D
u = zeros(Float64, 4, 2)
u[3,1] = 2
u[4,2] = 2
cb = inv(E) * u
cbp = cb[1:2,1:2]
cbm = cb[3:4,1:2]
R = inv(Wh) * (Wpp*cbp + Wm0*cbm - Wh*la.I)
T = inv(Wh) * (Wp0*cbp + Wmm*cbm)
return cbp, cbm, R, T
end
"""
plot_left_to_right_field(input::Tuple{Union{Float64, Int}, Union{Float64, Int}},
R1::Array{Float64, 2} where size(R1) == (2,2), T1::Array{Float64, 2} where size(R1) == (2,2))
Plot the field profile.
# Arguments
# Returns
# Examples
# Notes
"""
function left_to_right_field_visualization(dx, dz, Lx, Lz, λ, θ, ϕ, mur, epsr, zm, zp, input::AbstractVector)
c = 299792458 # m/s.
k0 = 2*π / λ # wavenumber in free space.
ω = c*k0
n = sqrt(mur*epsr)
μ_0 = 4*π*10^-7
ε_0 = 8.8541878128e-12
impedance = sqrt(μ_0 /ε_0)
# wave vector in free space.
# Note the the tangential component of the wavevector at the boundary
# is continuous, which means that they only differ in the refractive index.
kx0 = k0 * sin(θ) * cos(ϕ)
ky0 = k0 * sin(θ) * sin(ϕ)
kz0 = k0 * cos(θ)
# x = 1000*nm:-10*nm:0 # UnitRange object.
x = 0:dx:Lx # UnitRange object.
z = 0:dz:Lz # UnitRange object.
# x = range(1500, step=-500, stop=0) # StepRange object.
# z = range(0, step=500, stop=1500) # StepRange object.
y = 0
# X = repeat(x, 1, length(z))
# Z = repeat(z, length(x), 1)
# exit(0)
kzns, eigvectors = TMM.get_eigenvectors(k0, kx0, ky0, mur, epsr)
kzTEp = kzns[1]
kzTEm = kzns[2]
kzTMp = kzns[3]
kzTMm = kzns[4]
eigTEp = eigvectors[:,1]
eigTEm = eigvectors[:,2]
eigTMp = eigvectors[:,3]
eigTMm = eigvectors[:,4]
# @show eigTEp
# @show eigTEm
# @show eigTMp
# @show eigTMm
kx_bar = kx0 / k0
ky_bar = ky0 / k0
kzTEp_bar = kzTEp / k0
kzTEm_bar = kzTEm / k0
kzTMp_bar = kzTMp / k0
kzTMm_bar = kzTMm / k0
norm_mag = sqrt(kx_bar^2 + ky_bar^2 + kzTEp_bar^2)
# @printf("normalized kx in a single block: %.3f\n", kx_bar)
# @printf("normalized ky in a single block: %.3f\n", ky_bar)
# @printf("normalized kz of TEp in a single block: %.3f\n", kzTEp_bar)
# @printf("normalized kz of TEm in a single block: %.3f\n", kzTEm_bar)
# @printf("normalized kz of TMp in a single block: %.3f\n", kzTMp_bar)
# @printf("normalized kz of TMm in a single block: %.3f\n", kzTMm_bar)
# @printf("normalized magnitude of the wavevector in a single block: %.3f\n", norm_mag)
cap, cam, R1, T1 = TMM.get_the_left_to_right_operators(ω, kx0, ky0, kz0, kzns, eigvectors, zm, zp)
# @show cap
# @show cam
# @show R1
# @show T1
Eix = input[1]
Eiy = input[2]
Eiz =-(kx0*Eix + ky0*Eiy) / kz0
Hix = (ky0*Eiz - kz0*Eiy) / ω / μ_0 # Not H_bar field.
Hiy = (kz0*Eix - kx0*Eiz) / ω / μ_0
Hiz = (ky0*Eix - kx0*Eiy) / ω / μ_0
Erx = la.dot(R1[2,:], [Eiy, Eix])
Ery = la.dot(R1[1,:], [Eiy, Eix])
Erz = (kx0*Erx + ky0*Ery) / kz0
Hrx = (ky0*Erz + kz0*Ery) / ω / μ_0
Hry =-(kz0*Erx + kx0*Erz) / ω / μ_0
Hrz = (ky0*Erx - kx0*Ery) / ω / μ_0
Etx = la.dot(T1[2,:], [Eiy, Eix])
Ety = la.dot(T1[1,:], [Eiy, Eix])
Etz =-(kx0*Etx + ky0*Ety) / kz0
Htx = (ky0*Etz - kz0*Ety) / ω / μ_0
Hty = (kz0*Etx - kx0*Etz) / ω / μ_0
Htz = (ky0*Etx - kx0*Ety) / ω / μ_0
inputE = la.norm([Eix,Eiy,Eiz])^2
outputE = la.norm([Erx, Ery, Erz])^2 + la.norm([Etx, Ety, Etz])^2
energy_conservation = outputE - inputE
@printf("input energy: %g\n", inputE)
@printf("output energy: %g\n", outputE)
@printf("Difference between the input and output energy: %g\n", energy_conservation)
caTEp = cap[1,:]' * [Eiy, Eix] # The coupling coefficient for left-to-right, TE mode.
caTMp = cap[2,:]' * [Eiy, Eix] # The coupling coefficient for left-to-right, TM mode.
caTEm = cam[1,:]' * [Eiy, Eix] # The coupling coefficient for right-to-left, TE mode.
caTMm = cam[2,:]' * [Eiy, Eix] # The coupling coefficient for right-to-left, TM mode.
coeff = [caTEp, caTEm, caTMp, caTMm]
# @show caTEp
# @show caTMp
# @show caTEm
# @show caTMm
leftregion = (z .< zm)
middleregion = (zm .<= z .< zp)
rightregion = (zp .<= z)
Ex_tot = zeros(ComplexF64, length(x), length(z))
Ey_tot = zeros(ComplexF64, length(x), length(z))
Ez_tot = zeros(ComplexF64, length(x), length(z))
Hx_tot = zeros(ComplexF64, length(x), length(z))
Hy_tot = zeros(ComplexF64, length(x), length(z))
Hz_tot = zeros(ComplexF64, length(x), length(z))
Ex_inc = zeros(ComplexF64, length(x), length(z))
Ey_inc = zeros(ComplexF64, length(x), length(z))
Ez_inc = zeros(ComplexF64, length(x), length(z))
Hx_inc = zeros(ComplexF64, length(x), length(z))
Hy_inc = zeros(ComplexF64, length(x), length(z))
Hz_inc = zeros(ComplexF64, length(x), length(z))
Ex_ref = zeros(ComplexF64, length(x), length(z))
Ey_ref = zeros(ComplexF64, length(x), length(z))
Ez_ref = zeros(ComplexF64, length(x), length(z))
Hx_ref = zeros(ComplexF64, length(x), length(z))
Hy_ref = zeros(ComplexF64, length(x), length(z))
Hz_ref = zeros(ComplexF64, length(x), length(z))
Ex_trs = zeros(ComplexF64, length(x), length(z))
Ey_trs = zeros(ComplexF64, length(x), length(z))
Ez_trs = zeros(ComplexF64, length(x), length(z))
Hx_trs = zeros(ComplexF64, length(x), length(z))
Hy_trs = zeros(ComplexF64, length(x), length(z))
Hz_trs = zeros(ComplexF64, length(x), length(z))
Ex_TEp = zeros(ComplexF64, length(x), length(z))
Ey_TEp = zeros(ComplexF64, length(x), length(z))
Ez_TEp = zeros(ComplexF64, length(x), length(z))
Hx_TEp = zeros(ComplexF64, length(x), length(z))
Hy_TEp = zeros(ComplexF64, length(x), length(z))
Hz_TEp = zeros(ComplexF64, length(x), length(z))
Ex_TMp = zeros(ComplexF64, length(x), length(z))
Ey_TMp = zeros(ComplexF64, length(x), length(z))
Ez_TMp = zeros(ComplexF64, length(x), length(z))
Hx_TMp = zeros(ComplexF64, length(x), length(z))
Hy_TMp = zeros(ComplexF64, length(x), length(z))
Hz_TMp = zeros(ComplexF64, length(x), length(z))
Ex_TEm = zeros(ComplexF64, length(x), length(z))
Ey_TEm = zeros(ComplexF64, length(x), length(z))
Ez_TEm = zeros(ComplexF64, length(x), length(z))
Hx_TEm = zeros(ComplexF64, length(x), length(z))
Hy_TEm = zeros(ComplexF64, length(x), length(z))
Hz_TEm = zeros(ComplexF64, length(x), length(z))
Ex_TMm = zeros(ComplexF64, length(x), length(z))
Ey_TMm = zeros(ComplexF64, length(x), length(z))
Ez_TMm = zeros(ComplexF64, length(x), length(z))
Hx_TMm = zeros(ComplexF64, length(x), length(z))
Hy_TMm = zeros(ComplexF64, length(x), length(z))
Hz_TMm = zeros(ComplexF64, length(x), length(z))
# For z < z-
phase_inc = ((kx0.*x) .+ (ky0.*y) .+ (kz0.*(z' .- zm)))[:,leftregion]
phase_ref = ((kx0.*x) .+ (ky0.*y) .- (kz0.*(z' .- zm)))[:,leftregion]
Ex_ref[:,leftregion] = (Erx .* exp.(1im .* phase_ref))
Ey_ref[:,leftregion] = (Ery .* exp.(1im .* phase_ref))
Ez_ref[:,leftregion] = (Erz .* exp.(1im .* phase_ref))
Hx_ref[:,leftregion] = (Hrx .* exp.(1im .* phase_ref))
Hy_ref[:,leftregion] = (Hry .* exp.(1im .* phase_ref))
Hz_ref[:,leftregion] = (Hrz .* exp.(1im .* phase_ref))
Ex_inc[:,leftregion] = (Eix .* exp.(1im .* phase_inc))
Ey_inc[:,leftregion] = (Eiy .* exp.(1im .* phase_inc))
Ez_inc[:,leftregion] = (Eiz .* exp.(1im .* phase_inc))
Hx_inc[:,leftregion] = (Hix .* exp.(1im .* phase_inc))
Hy_inc[:,leftregion] = (Hiy .* exp.(1im .* phase_inc))
Hz_inc[:,leftregion] = (Hiz .* exp.(1im .* phase_inc))
# For z- <= z < z+
phase_TEp = ((kx0.*x) .+ (ky0.*y) .+ (kzTEp.*(z' .- zm)))[:,middleregion]
phase_TMp = ((kx0.*x) .+ (ky0.*y) .+ (kzTMp.*(z' .- zm)))[:,middleregion]
phase_TEm = ((kx0.*x) .+ (ky0.*y) .+ (kzTEm.*(z' .- zp)))[:,middleregion]
phase_TMm = ((kx0.*x) .+ (ky0.*y) .+ (kzTMm.*(z' .- zp)))[:,middleregion]
Ex_TEp[:,middleregion] = (caTEp .* (eigTEp[1] .* exp.(1im .* phase_TEp)))
Ex_TEm[:,middleregion] = (caTEm .* (eigTEm[1] .* exp.(1im .* phase_TEm)))
Ex_TMp[:,middleregion] = (caTMp .* (eigTMp[1] .* exp.(1im .* phase_TMp)))
Ex_TMm[:,middleregion] = (caTMm .* (eigTMm[1] .* exp.(1im .* phase_TMm)))
Ey_TEp[:,middleregion] = (caTEp .* (eigTEp[2] .* exp.(1im .* phase_TEp)))
Ey_TEm[:,middleregion] = (caTEm .* (eigTEm[2] .* exp.(1im .* phase_TEm)))
Ey_TMp[:,middleregion] = (caTMp .* (eigTMp[2] .* exp.(1im .* phase_TMp)))
Ey_TMm[:,middleregion] = (caTMm .* (eigTMm[2] .* exp.(1im .* phase_TMm)))
Ez_TEp[:,middleregion] = (caTEp .* (eigTEp[3] .* exp.(1im .* phase_TEp)))
Ez_TEm[:,middleregion] = (caTEm .* (eigTEm[3] .* exp.(1im .* phase_TEm)))
Ez_TMp[:,middleregion] = (caTMp .* (eigTMp[3] .* exp.(1im .* phase_TMp)))
Ez_TMm[:,middleregion] = (caTMm .* (eigTMm[3] .* exp.(1im .* phase_TMm)))
Hx_TEp[:,middleregion] = (caTEp .* (eigTEp[4] .* exp.(1im .* phase_TEp)))
Hx_TEm[:,middleregion] = (caTEm .* (eigTEm[4] .* exp.(1im .* phase_TEm)))
Hx_TMp[:,middleregion] = (caTMp .* (eigTMp[4] .* exp.(1im .* phase_TMp)))
Hx_TMm[:,middleregion] = (caTMm .* (eigTMm[4] .* exp.(1im .* phase_TMm)))
Hy_TEp[:,middleregion] = (caTEp .* (eigTEp[5] .* exp.(1im .* phase_TEp)))
Hy_TEm[:,middleregion] = (caTEm .* (eigTEm[5] .* exp.(1im .* phase_TEm)))
Hy_TMp[:,middleregion] = (caTMp .* (eigTMp[5] .* exp.(1im .* phase_TMp)))
Hy_TMm[:,middleregion] = (caTMm .* (eigTMm[5] .* exp.(1im .* phase_TMm)))
Hz_TEp[:,middleregion] = (caTEp .* (eigTEp[6] .* exp.(1im .* phase_TEp)))
Hz_TEm[:,middleregion] = (caTEm .* (eigTEm[6] .* exp.(1im .* phase_TEm)))
Hz_TMp[:,middleregion] = (caTMp .* (eigTMp[6] .* exp.(1im .* phase_TMp)))
Hz_TMm[:,middleregion] = (caTMm .* (eigTMm[6] .* exp.(1im .* phase_TMm)))
# For z+ <= z
phase_trs = ((kx0.*x) .+ (ky0.*y) .+ (kz0.*(z' .- zp)))[:,rightregion]
Ex_trs[:,rightregion] = (Etx .* exp.(1im .* phase_trs))
Ey_trs[:,rightregion] = (Ety .* exp.(1im .* phase_trs))
Ez_trs[:,rightregion] = (Etz .* exp.(1im .* phase_trs))
Hx_trs[:,rightregion] = (Htx .* exp.(1im .* phase_trs))
Hy_trs[:,rightregion] = (Hty .* exp.(1im .* phase_trs))
Hz_trs[:,rightregion] = (Htz .* exp.(1im .* phase_trs))
# Add specific fields.
Ex_inc += Ex_TEp + Ex_TMp + Ex_trs
Ey_inc += Ey_TEp + Ey_TMp + Ey_trs
Ez_inc += Ez_TEp + Ez_TMp + Ez_trs
Hx_inc += Hx_TEp + Hx_TMp + Hx_trs
Hy_inc += Hy_TEp + Hy_TMp + Hy_trs
Hz_inc += Hz_TEp + Hz_TMp + Hz_trs
Ex_ref += Ex_TEm + Ex_TMm
Ey_ref += Ey_TEm + Ey_TMm
Ez_ref += Ez_TEm + Ez_TMm
Hx_ref += Hx_TEm + Hx_TMm
Hy_ref += Hy_TEm + Hy_TMm
Hz_ref += Hz_TEm + Hz_TMm
Ex_tot += Ex_inc + Ex_ref + Ex_TEp + Ex_TEm + Ex_TMp + Ex_TMm + Ex_trs
Ey_tot += Ey_inc + Ey_ref + Ey_TEp + Ey_TEm + Ey_TMp + Ey_TMm + Ey_trs
Ez_tot += Ez_inc + Ez_ref + Ez_TEp + Ez_TEm + Ez_TMp + Ez_TMm + Ez_trs
Hx_tot += Hx_inc + Hx_ref + Hx_TEp + Hx_TEm + Hx_TMp + Hx_TMm + Hx_trs
Hy_tot += Hy_inc + Hy_ref + Hy_TEp + Hy_TEm + Hy_TMp + Hy_TMm + Hy_trs
Hz_tot += Hz_inc + Hz_ref + Hz_TEp + Hz_TEm + Hz_TMp + Hz_TMm + Hz_trs
incfields = cat(real(Ex_inc), real(Hx_inc), real(Ey_inc), real(Hy_inc), real(Ez_inc), real(Hz_inc), dims=3)
reffields = cat(real(Ex_ref), real(Hx_ref), real(Ey_ref), real(Hy_ref), real(Ez_ref), real(Hz_ref), dims=3)
trsfields = cat(real(Ex_trs), real(Hx_trs), real(Ey_trs), real(Hy_trs), real(Ez_trs), real(Hz_trs), dims=3)
totfields = cat(real(Ex_tot), real(Hx_tot), real(Ey_tot), real(Hy_tot), real(Ez_tot), real(Hz_tot), dims=3)
title=["Ex", "Hx", "Ey", "Hy", "Ez", "Hz"]
cmins = []
cmaxs = []
ps_inc = []
ps_ref = []
ps_trs = []
ps_tot = []
l = @layout([a d; b e; c f;])
for (i, slice) in enumerate(eachslice(incfields, dims=3))
name = title[i]*"_inc"
cmax = maximum(abs, slice)
if isapprox(cmax, 0; atol=1e-10)
p = heatmap(slice, title=name, c=:bwr, clims=(-1,1))
else
p = heatmap(slice, title=name, c=:bwr, clims=(-cmax, cmax))
end
# gui(p)
push!(ps_inc, p)
filename = "./" * name * ".png"
# savefig(p, filename)
end
plot(ps_inc..., layout=l, plot_title="inc", size=(1200, 1000))
savefig("singleblock_LtoR_inc.png")
for (i, slice) in enumerate(eachslice(reffields, dims=3))
name = title[i]*"_ref"
cmax = maximum(abs, slice)
if isapprox(cmax, 0; atol=1e-10)
p = heatmap(slice, title=name, c=:bwr, clims=(-1,1))
else
p = heatmap(slice, title=name, c=:bwr, clims=(-cmax, cmax))
end
push!(ps_ref, p)
filename = name * ".png"
# savefig(filename)
end
plot(ps_ref..., layout=l, plot_title="ref", size=(1200, 1000))
savefig("singleblock_LtoR_ref.png")
for (i, slice) in enumerate(eachslice(trsfields, dims=3))
name = title[i]*"_trs"
cmax = maximum(abs, slice)
if isapprox(cmax, 0; atol=1e-10)
p = heatmap(slice, title=name, c=:bwr, clims=(-1,1))
else
p = heatmap(slice, title=name, c=:bwr, clims=(-cmax, cmax))
end
push!(ps_trs, p)
cmax = maximum(abs, slice)
push!(cmaxs, cmax)
filename = name * ".png"
# savefig(filename)
end
plot(ps_trs..., layout=l, plot_title="trs", size=(1200, 1000))
savefig("singleblock_LtoR_trs.png")
for (i, slice) in enumerate(eachslice(totfields, dims=3))
name = title[i]*"_tot"
if isapprox(cmaxs[i], 0; atol=1e-10)
p = heatmap(slice, title=name, c=:bwr, clims=(-1,1))
else
p = heatmap(slice, title=name, c=:bwr, clims=(-cmaxs[i], cmaxs[i]))
end
push!(ps_tot, p)
filename = name * ".png"
# savefig(filename)
end
plot(ps_tot..., layout=l, plot_title="tot", size=(1200, 1000))
savefig("singleblock_LtoR_tot.png")
# plot(ps..., layout=l, plot_title="trs", size=(1200, 1000), yformatter=:scientific)
return eigvectors, coeff
end
function right_to_left_field_visualization(dx, dz, Lx, Lz, λ, θ, ϕ, mur, epsr, zm, zp, input::AbstractVector)
c = 299792458 # m/s.
k0 = 2*π / λ # wavenumber in free space.
ω = c*k0
n = sqrt(mur*epsr)
μ_0 = 4*π*10^-7
ε_0 = 8.8541878128e-12
impedance = sqrt(μ_0 /ε_0)
# wave vector in free space.
kx0 = k0 * sin(θ) * cos(ϕ)
ky0 = k0 * sin(θ) * sin(ϕ)
kz0 = k0 * cos(θ)
# x = 1000*nm:-10*nm:0 # UnitRange object.
x = 0:dx:Lx # UnitRange object.
z = 0:dz:Lz # UnitRange object.
# x = range(1500, step=-500, stop=0) # StepRange object.
# z = range(0, step=500, stop=1500) # StepRange object.
y = 0
# X = repeat(x, 1, length(z))
# Z = repeat(z, length(x), 1)
# exit(0)
kzns, eigvectors = TMM.get_eigenvectors(k0, kx0, ky0, mur, epsr)
kzTEp = kzns[1]
kzTEm = kzns[2]
kzTMp = kzns[3]
kzTMm = kzns[4]
eigTEp = eigvectors[:,1]
eigTEm = eigvectors[:,2]
eigTMp = eigvectors[:,3]
eigTMm = eigvectors[:,4]
cbp, cbm, R, T = TMM.get_the_right_to_left_operators(ω, kx0, ky0, kz0, kzns, eigvectors, zm, zp)
Eix = input[1]
Eiy = input[2]
Eiz = (kx0*Eix + ky0*Eiy) / kz0
Hix = (ky0*Eiz + kz0*Eiy) / ω / μ_0 # Not H_bar field.
Hiy =-(kz0*Eix + kx0*Eiz) / ω / μ_0
Hiz = (ky0*Eix + kx0*Eiy) / ω / μ_0
Erx = la.dot(R[2,:], [Eiy, Eix])
Ery = la.dot(R[1,:], [Eiy, Eix])
Erz =-(kx0*Erx + ky0*Ery) / kz0
Hrx = (ky0*Erz - kz0*Ery) / ω / μ_0
Hry = (kz0*Erx - kx0*Erz) / ω / μ_0
Hrz = (ky0*Erx + kx0*Ery) / ω / μ_0
Etx = la.dot(T[2,:], [Eiy, Eix])
Ety = la.dot(T[1,:], [Eiy, Eix])
Etz =-(kx0*Etx + ky0*Ety) / kz0
Htx = (ky0*Etz + kz0*Ety) / ω / μ_0
Hty =-(kz0*Etx + kx0*Etz) / ω / μ_0
Htz = (ky0*Etx + kx0*Ety) / ω / μ_0
inputE = la.norm([Eix,Eiy,Eiz])^2
outputE = la.norm([Erx, Ery, Erz])^2 + la.norm([Etx, Ety, Etz])^2
energy_conservation = outputE - inputE
@printf("input energy: %g\n", inputE)
@printf("output energy: %g\n", outputE)
@printf("Difference between the input and output energy: %g\n", energy_conservation)
cbTEp = cbp[1,:]' * [Eiy, Eix] # The coupling coefficient for left-to-right, TE mode.
cbTMp = cbp[2,:]' * [Eiy, Eix] # The coupling coefficient for left-to-right, TM mode.
cbTEm = cbm[1,:]' * [Eiy, Eix] # The coupling coefficient for right-to-left, TE mode.
cbTMm = cbm[2,:]' * [Eiy, Eix] # The coupling coefficient for right-to-left, TM mode.
coeff = [cbTEp, cbTEm, cbTMp, cbTMm]
leftregion = (z .< zm)
middleregion = (zm .<= z .< zp)
rightregion = (zp .<= z)
Ex_tot = zeros(ComplexF64, length(x), length(z))
Ey_tot = zeros(ComplexF64, length(x), length(z))
Ez_tot = zeros(ComplexF64, length(x), length(z))
Hx_tot = zeros(ComplexF64, length(x), length(z))
Hy_tot = zeros(ComplexF64, length(x), length(z))
Hz_tot = zeros(ComplexF64, length(x), length(z))
Ex_inc = zeros(ComplexF64, length(x), length(z))
Ey_inc = zeros(ComplexF64, length(x), length(z))
Ez_inc = zeros(ComplexF64, length(x), length(z))
Hx_inc = zeros(ComplexF64, length(x), length(z))
Hy_inc = zeros(ComplexF64, length(x), length(z))
Hz_inc = zeros(ComplexF64, length(x), length(z))
Ex_ref = zeros(ComplexF64, length(x), length(z))
Ey_ref = zeros(ComplexF64, length(x), length(z))
Ez_ref = zeros(ComplexF64, length(x), length(z))
Hx_ref = zeros(ComplexF64, length(x), length(z))
Hy_ref = zeros(ComplexF64, length(x), length(z))
Hz_ref = zeros(ComplexF64, length(x), length(z))
Ex_trs = zeros(ComplexF64, length(x), length(z))
Ey_trs = zeros(ComplexF64, length(x), length(z))
Ez_trs = zeros(ComplexF64, length(x), length(z))
Hx_trs = zeros(ComplexF64, length(x), length(z))
Hy_trs = zeros(ComplexF64, length(x), length(z))
Hz_trs = zeros(ComplexF64, length(x), length(z))
Ex_TEp = zeros(ComplexF64, length(x), length(z))
Ey_TEp = zeros(ComplexF64, length(x), length(z))
Ez_TEp = zeros(ComplexF64, length(x), length(z))
Hx_TEp = zeros(ComplexF64, length(x), length(z))
Hy_TEp = zeros(ComplexF64, length(x), length(z))
Hz_TEp = zeros(ComplexF64, length(x), length(z))
Ex_TMp = zeros(ComplexF64, length(x), length(z))
Ey_TMp = zeros(ComplexF64, length(x), length(z))
Ez_TMp = zeros(ComplexF64, length(x), length(z))
Hx_TMp = zeros(ComplexF64, length(x), length(z))
Hy_TMp = zeros(ComplexF64, length(x), length(z))
Hz_TMp = zeros(ComplexF64, length(x), length(z))
Ex_TEm = zeros(ComplexF64, length(x), length(z))
Ey_TEm = zeros(ComplexF64, length(x), length(z))
Ez_TEm = zeros(ComplexF64, length(x), length(z))
Hx_TEm = zeros(ComplexF64, length(x), length(z))
Hy_TEm = zeros(ComplexF64, length(x), length(z))
Hz_TEm = zeros(ComplexF64, length(x), length(z))
Ex_TMm = zeros(ComplexF64, length(x), length(z))
Ey_TMm = zeros(ComplexF64, length(x), length(z))
Ez_TMm = zeros(ComplexF64, length(x), length(z))
Hx_TMm = zeros(ComplexF64, length(x), length(z))
Hy_TMm = zeros(ComplexF64, length(x), length(z))
Hz_TMm = zeros(ComplexF64, length(x), length(z))
# For z < z-
phase_trs = ((kx0.*x) .+ (ky0.*y) .- (kz0.*(z' .- zm)))[:,leftregion]
Ex_trs[:,leftregion] = (Etx .* exp.(1im .* phase_trs))
Ey_trs[:,leftregion] = (Ety .* exp.(1im .* phase_trs))
Ez_trs[:,leftregion] = (Etz .* exp.(1im .* phase_trs))
Hx_trs[:,leftregion] = (Htx .* exp.(1im .* phase_trs))
Hy_trs[:,leftregion] = (Hty .* exp.(1im .* phase_trs))
Hz_trs[:,leftregion] = (Htz .* exp.(1im .* phase_trs))
# For z- <= z < z+
phase_TEp = ((kx0.*x) .+ (ky0.*y) .+ (kzTEp.*(z' .- zm)))[:,middleregion]
phase_TMp = ((kx0.*x) .+ (ky0.*y) .+ (kzTMp.*(z' .- zm)))[:,middleregion]
phase_TEm = ((kx0.*x) .+ (ky0.*y) .+ (kzTEm.*(z' .- zp)))[:,middleregion]
phase_TMm = ((kx0.*x) .+ (ky0.*y) .+ (kzTMm.*(z' .- zp)))[:,middleregion]
Ex_TEp[:,middleregion] = (cbTEp .* (eigTEp[1] .* exp.(1im .* phase_TEp)))
Ex_TEm[:,middleregion] = (cbTEm .* (eigTEm[1] .* exp.(1im .* phase_TEm)))
Ex_TMp[:,middleregion] = (cbTMp .* (eigTMp[1] .* exp.(1im .* phase_TMp)))
Ex_TMm[:,middleregion] = (cbTMm .* (eigTMm[1] .* exp.(1im .* phase_TMm)))
Ey_TEp[:,middleregion] = (cbTEp .* (eigTEp[2] .* exp.(1im .* phase_TEp)))
Ey_TEm[:,middleregion] = (cbTEm .* (eigTEm[2] .* exp.(1im .* phase_TEm)))
Ey_TMp[:,middleregion] = (cbTMp .* (eigTMp[2] .* exp.(1im .* phase_TMp)))
Ey_TMm[:,middleregion] = (cbTMm .* (eigTMm[2] .* exp.(1im .* phase_TMm)))
Ez_TEp[:,middleregion] = (cbTEp .* (eigTEp[3] .* exp.(1im .* phase_TEp)))
Ez_TEm[:,middleregion] = (cbTEm .* (eigTEm[3] .* exp.(1im .* phase_TEm)))
Ez_TMp[:,middleregion] = (cbTMp .* (eigTMp[3] .* exp.(1im .* phase_TMp)))
Ez_TMm[:,middleregion] = (cbTMm .* (eigTMm[3] .* exp.(1im .* phase_TMm)))
Hx_TEp[:,middleregion] = (cbTEp .* (eigTEp[4] .* exp.(1im .* phase_TEp)))
Hx_TEm[:,middleregion] = (cbTEm .* (eigTEm[4] .* exp.(1im .* phase_TEm)))
Hx_TMp[:,middleregion] = (cbTMp .* (eigTMp[4] .* exp.(1im .* phase_TMp)))
Hx_TMm[:,middleregion] = (cbTMm .* (eigTMm[4] .* exp.(1im .* phase_TMm)))
Hy_TEp[:,middleregion] = (cbTEp .* (eigTEp[5] .* exp.(1im .* phase_TEp)))
Hy_TEm[:,middleregion] = (cbTEm .* (eigTEm[5] .* exp.(1im .* phase_TEm)))
Hy_TMp[:,middleregion] = (cbTMp .* (eigTMp[5] .* exp.(1im .* phase_TMp)))
Hy_TMm[:,middleregion] = (cbTMm .* (eigTMm[5] .* exp.(1im .* phase_TMm)))
Hz_TEp[:,middleregion] = (cbTEp .* (eigTEp[6] .* exp.(1im .* phase_TEp)))
Hz_TEm[:,middleregion] = (cbTEm .* (eigTEm[6] .* exp.(1im .* phase_TEm)))
Hz_TMp[:,middleregion] = (cbTMp .* (eigTMp[6] .* exp.(1im .* phase_TMp)))
Hz_TMm[:,middleregion] = (cbTMm .* (eigTMm[6] .* exp.(1im .* phase_TMm)))
# For z+ <= z
phase_inc = ((kx0.*x) .+ (ky0.*y) .- (kz0.*(z' .- zp)))[:,rightregion]
phase_ref = ((kx0.*x) .+ (ky0.*y) .+ (kz0.*(z' .- zp)))[:,rightregion]
Ex_inc[:,rightregion] = (Eix .* exp.(1im .* phase_inc))
Ey_inc[:,rightregion] = (Eiy .* exp.(1im .* phase_inc))
Ez_inc[:,rightregion] = (Eiz .* exp.(1im .* phase_inc))
Hx_inc[:,rightregion] = (Hix .* exp.(1im .* phase_inc))
Hy_inc[:,rightregion] = (Hiy .* exp.(1im .* phase_inc))
Hz_inc[:,rightregion] = (Hiz .* exp.(1im .* phase_inc))
Ex_ref[:,rightregion] = (Erx .* exp.(1im .* phase_ref))
Ey_ref[:,rightregion] = (Ery .* exp.(1im .* phase_ref))
Ez_ref[:,rightregion] = (Erz .* exp.(1im .* phase_ref))
Hx_ref[:,rightregion] = (Hrx .* exp.(1im .* phase_ref))
Hy_ref[:,rightregion] = (Hry .* exp.(1im .* phase_ref))
Hz_ref[:,rightregion] = (Hrz .* exp.(1im .* phase_ref))
# Add specific fields.
Ex_inc += Ex_TEm + Ex_TMm + Ex_trs
Ey_inc += Ey_TEm + Ey_TMm + Ey_trs
Ez_inc += Ez_TEm + Ez_TMm + Ez_trs
Hx_inc += Hx_TEm + Hx_TMm + Hx_trs
Hy_inc += Hy_TEm + Hy_TMm + Hy_trs
Hz_inc += Hz_TEm + Hz_TMm + Hz_trs
Ex_ref += Ex_TEp + Ex_TMp
Ey_ref += Ey_TEp + Ey_TMp
Ez_ref += Ez_TEp + Ez_TMp
Hx_ref += Hx_TEp + Hx_TMp
Hy_ref += Hy_TEp + Hy_TMp
Hz_ref += Hz_TEp + Hz_TMp
Ex_tot += Ex_inc + Ex_ref + Ex_TEp + Ex_TEm + Ex_TMp + Ex_TMm + Ex_trs