File:Wave guiding.gif
Wave_guiding.gif (300 × 300 pixels, file size: 5 MB, MIME type: image/gif, looped, 68 frames, 6.8 s)
Captions
Captions
Summary
[edit]DescriptionWave guiding.gif |
English: You can guide light with a waveguide. You can also couple the waveguide with a ring resonator, where the light will circulate. And if you attach a second waveguide to the ring resonator you can effectively move the light from one waveguide to the other. |
Date | |
Source | https://twitter.com/j_bertolotti/status/1448566344702730245 |
Author | Jacopo Bertolotti |
Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 12.0 code
[edit]\[Lambda]0 = 1.; k0 = N[(2 \[Pi])/\[Lambda]0]; (*The wavelength in vacuum is set to 1, so all lengths are now in units of wavelengths*)
\[Delta] = \[Lambda]0/20; \[CapitalDelta] = 50*\[Lambda]0; (*Parameters for the grid*) \[Sigma] = 10 \[Lambda]0; (*width of the gaussian beam*)
sourcef[x_, y_] :=E^(-((x + \[CapitalDelta]/8)^2 + (y + \[CapitalDelta]/3)^2)/(2 (\[Lambda]0/5)^2));
\[Phi]in = Table[Chop[sourcef[x, y]], {x, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}, {y, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}]; (*Discretized source*)
d = \[Lambda]0/2; (*typical scale of the absorbing layer*)
imn = Table[
Chop[5 (E^-((x + \[CapitalDelta]/2)/d) + E^((x - \[CapitalDelta]/2)/d) + E^-((y + \[CapitalDelta]/2)/d) + E^((y - \[CapitalDelta]/2)/d))], {x, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}, {y, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}]; (*Imaginary part of the refractive index (used to emulate absorbing boundaries)*)
dim = Dimensions[\[Phi]in][[1]];
L = -1/\[Delta]^2*KirchhoffMatrix[GridGraph[{dim, dim}]]; (*Discretized Laplacian*)
ReMapC[x_] := RGBColor[(2 x - 1) UnitStep[x - 0.5], 0, (1 - 2 x) UnitStep[0.5 - x]];
frames1 = Table[
ren = Clip[
Table[If[-\[Lambda]0 - \[CapitalDelta]/8 < x < \[Lambda]0 - \[CapitalDelta]/8, \[Alpha], 1], {x, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}, {y, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}], {1, 2}];
n = ren + I imn;
b = -(Flatten[n]^2 - 1) k0^2 Flatten[\[Phi]in]; (*Right-hand side of the equation we want to solve*)
M = L + DiagonalMatrix[
SparseArray[Flatten[n]^2 k0^2]]; (*Operator on the left-
hand side of the equation we want to solve*)
\[Phi]s = Partition[LinearSolve[M, b], dim]; (*Solve the linear system*)
ImageAdd[
MatrixPlot[Transpose[(Re[(\[Phi]in + \[Phi]s)]/Max[Abs@Re[\[Phi]in + \[Phi]s][[(4 d)/\[Delta] ;; (-4 d)/\[Delta], (4 d)/\[Delta] ;; (-4 d)/\[Delta]]]])][[(4 d)/\[Delta] ;; (-4 d)/\[Delta], (4 d)/\[Delta] ;; (-4 d)/\[Delta]]], ColorFunction -> ReMapC, DataReversed -> True, Frame -> False, PlotRange -> {-1, 1}]
,
ArrayPlot[Transpose[Re[(n - 1)/5]] [[(4 d)/\[Delta] ;; (-4 d)/\[Delta], (4 d)/\[Delta] ;; (-4 d)/\[Delta]]], DataReversed -> True , ColorFunctionScaling -> False, ColorFunction -> GrayLevel, Frame -> False]
]
, {\[Alpha], 1, 2, 1/10}]
frames2 =
Table[ren = Clip[Table[If[-\[Lambda]0 - \[CapitalDelta]/8 < x < \[Lambda]0 - \[CapitalDelta]/8, 2, 1], {x, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}, {y, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}] + Table[If[\[CapitalDelta]/2 - 6*\[Lambda]0 < (x - \[CapitalDelta]/8 - \[Lambda]0/4 + \[CapitalDelta]/8 + (-(\[CapitalDelta]/1.7) (t - 1)^4))^2 + (y)^2 < \[CapitalDelta]/2 + 6*\[Lambda]0, 1, 0], {x, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}, {y, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}], {1, 2}];
n = ren + I imn;
b = -(Flatten[n]^2 - 1) k0^2 Flatten[\[Phi]in]; (*Right-hand side of the equation we want to solve*)
M = L + DiagonalMatrix[SparseArray[Flatten[n]^2 k0^2]]; (*Operator on the left-hand side of the equation we want to solve*)
\[Phi]s = Partition[LinearSolve[M, b], dim]; (*Solve the linear system*)
ImageAdd[
MatrixPlot[Transpose[(Re[(\[Phi]in + \[Phi]s)]/Max[Abs@Re[\[Phi]in + \[Phi]s][[(4 d)/\[Delta] ;; (-4 d)/\[Delta], (4 d)/\[Delta] ;; (-4 d)/\[Delta]]]])][[(4 d)/\[Delta] ;; (-4 d)/\[Delta], (4 d)/\[Delta] ;; (-4 d)/\[Delta]]], ColorFunction -> ReMapC, DataReversed -> True, Frame -> False, PlotRange -> {-1, 1}]
,
ArrayPlot[Transpose[Re[(n - 1)/5]] [[(4 d)/\[Delta] ;; (-4 d)/\[Delta], (4 d)/\[Delta] ;; (-4 d)/\[Delta]]], DataReversed -> True , ColorFunctionScaling -> False, ColorFunction -> GrayLevel, Frame -> False]
]
, {t, 0, 1, 1/10}]
frames3 =
Table[ren = Clip[Table[If[-\[Lambda]0 - \[CapitalDelta]/8 < x < \[Lambda]0 - \[CapitalDelta]/8, 2, 1], {x, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}, {y, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}] + Table[If[\[CapitalDelta]/2 - 6*\[Lambda]0 < (x - \[CapitalDelta]/8 - \[Lambda]0/4 + \[CapitalDelta]/8)^2 + (y)^2 < \[CapitalDelta]/2 + 6*\[Lambda]0, 1, 0], {x, -\[CapitalDelta]/2, \[CapitalDelta]/ 2, \[Delta]}, {y, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}] + Table[If[-\[Lambda]0 + \[CapitalDelta]/4 + \[Lambda]0/2 - \[CapitalDelta]/8 + (\[CapitalDelta]/1.7 (t - 1)^4) < x < \[Lambda]0 + \[CapitalDelta]/4 + \[Lambda]0/2 - \[CapitalDelta]/8 + (\[CapitalDelta]/1.7 (t - 1)^4), 1, 0], {x, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}, {y, -\[CapitalDelta]/2, \[CapitalDelta]/2, \[Delta]}], {1, 2}];
n = ren + I imn;
b = -(Flatten[n]^2 - 1) k0^2 Flatten[\[Phi]in]; (*Right-hand side of the equation we want to solve*)
M = L + DiagonalMatrix[SparseArray[Flatten[n]^2 k0^2]]; (*Operator on the left-hand side of the equation we want to solve*)
\[Phi]s = Partition[LinearSolve[M, b], dim]; (*Solve the linear system*)
ImageAdd[
MatrixPlot[Transpose[(Re[(\[Phi]in + \[Phi]s)]/Max[Abs@Re[\[Phi]in + \[Phi]s][[(4 d)/\[Delta] ;; (-4 d)/\[Delta], (4 d)/\[Delta] ;; (-4 d)/\[Delta]]]])][[(4 d)/\[Delta] ;; (-4 d)/\[Delta], (4 d)/\[Delta] ;; (-4 d)/\[Delta]]], ColorFunction -> ReMapC, DataReversed -> True, Frame -> False, PlotRange -> {-1, 1}]
,
ArrayPlot[Transpose[Re[(n - 1)/5]] [[(4 d)/\[Delta] ;; (-4 d)/\[Delta], (4 d)/\[Delta] ;; (-4 d)/\[Delta]]], DataReversed -> True , ColorFunctionScaling -> False, ColorFunction -> GrayLevel, Frame -> False]
]
, {t, 0, 1, 1/10}]
ListAnimate[Join[
Table[frames1[[1]], {5}], frames1,
Table[frames2[[1]], {5}], frames2,
Table[frames3[[1]], {5}], frames3, Table[frames3[[-1]], {20}]
], ImageSize -> Medium]
Licensing
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
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current | 14:42, 15 October 2021 | ![]() | 300 × 300 (5 MB) | Berto (talk | contribs) | Uploaded own work with UploadWizard |
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