File:Anderson localization 1D vs number of layers.webm
Anderson_localization_1D_vs_number_of_layers.webm (WebM audio/video file, VP9, length 1 min 55 s, 414 × 462 pixels, 213 kbps overall, file size: 2.91 MB)
Captions
Summary
[edit]DescriptionAnderson localization 1D vs number of layers.webm |
English: If instead of in a periodic fashion, you start staking dielectric layers randomly, there will be no passband or stop-gap. What you will get are discrete exponentially localized modes inside the structure (Anderson localization). |
Date | |
Source | https://twitter.com/j_bertolotti/status/1267064606524149760 |
Author | Jacopo Bertolotti |
Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 12.0 code
[edit]c = 3 10^8; (*speed of light*) M[n_, k_, d_] := {{Cos[n k d], I c/n Sin[n k d]}, {I n/c Sin[n k d], Cos[n k d]}}; (*transfer matrix*) Mi[n_, k_, d_] := {{Cos[d k n], -((I c Sin[d k n])/n)}, {-((I n Sin[d k n])/c), Cos[d k n]}}; (*Inverse of a transfer matrix*) t[m_, n0_, n2_] := (2 n0/c)/(n2/c m[[1, 1]] - (n0 n2)/c^2 m[[1, 2]] - m[[2, 1]] + n0/c m[[2, 2]]); (*transmission coefficient*) d = 0.4 10^-6; (*layer thickness in m*) nstep = 1500; \[Omega]min = 405. 10^12; \[Omega]max = 790. 10^12; dimmax = 200; (*number of layers in the Bragg mirror*) nlayermax = dimmax - 10; randn = RandomReal[{1.5, 2.5}, nlayermax]; p0 = Reap[For[nlayers = 0, nlayers <= nlayermax, nlayers++, s = Join[Table[1., 10], Table[randn[[j]], {j, 1, nlayers}], Table[1., dimmax - nlayers - 10]];(*Reflective indices of each layer (including some space to show the pulse arrive*) dim = Dimensions[s][[1]]; trasm = Reap[For[\[Omega] = \[Omega]min, \[Omega] <= \[Omega]max, \[Omega] = \[Omega] + (\[Omega]max - \[Omega]min)/nstep, tm = Apply[Dot, Table[M[s[[j]], \[Omega]/c, d], {j, 1, dim}]]; Sow[N[t[tm, 1, 1]] ]; ];][[2, 1]]; field = trasm; (*Field at the last interface*) sexpand = 1; (*increase spatial resolution*) s2 = Flatten@Table[Table[s[[j]], sexpand], {j, 1, dim}]; freq = Table[j, {j, \[Omega]min, \[Omega]max, (\[Omega]max - \[Omega]min)/nstep}]; fn = Transpose[{field, field/c}]; tmp0 = fn; ssm = Reap[For[i = dim*sexpand, i > 0, i--, tmp = Table[((Mi[s2[[i]], freq/c, d/sexpand])[[All, All, j]].tmp0[[j]]), {j, 1, nstep}]; Sow[tmp[[All, 1]]]; tmp0 = tmp; ];][[2, 1]]; Sow@Grid[{ {ListPlot[Abs[trasm]^2, Joined -> True, DataRange -> {\[Omega]min, \[Omega]max}, AspectRatio -> 1/2, ImagePadding -> {{40, 10}, {5, 0}}, ImageSize -> {250, UpTo[250]}, PlotStyle -> {Thick, Black}, Axes -> False, Frame -> True, FrameTicks -> {{{0, 0.5, 1}, None}, {None, None}}, FrameStyle -> {Directive[Thick, Gray]}, FrameLabel -> {None, "T"}, Ticks -> {None, Automatic}, LabelStyle -> {Black, Bold}, PlotRange -> {0, 1.05}] , "" }, { ArrayPlot[Abs[ssm]/1.5, AspectRatio -> 1, ColorFunction -> "SunsetColors", ColorFunctionScaling -> False, Frame -> True, FrameTicks -> {{None, None}, {Automatic, None}}, DataRange -> {{\[Omega]min, \[Omega]max}, {0, d*Dimensions[s][[1]]}}, ImagePadding -> {{40, 10}, {35, 0}}, ImageSize -> 250, FrameLabel -> {None, "\[Omega]"}, LabelStyle -> {Black, Bold}] , BarLegend[{"SunsetColors", {0, 1}}, LegendLabel -> Placed["|E|", Right], LegendMargins -> 0, Ticks -> None, LabelStyle -> Directive[Bold]] } }, Alignment -> Top] ];][[2, 1]]; ListAnimate[p0]
Licensing
[edit]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 |
This file, which was originally posted to
https://twitter.com/j_bertolotti/status/1267064606524149760, was reviewed on 12 June 2020 by reviewer Didym, who confirmed that it was available there under the stated license on that date.
|
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 12:15, 31 May 2020 | 1 min 55 s, 414 × 462 (2.91 MB) | Berto (talk | contribs) | Imported media from uploads:60b50406-a337-11ea-b460-421279eada85 |
You cannot overwrite this file.
File usage on Commons
There are no pages that use this file.
Transcode status
Update transcode statusMetadata
This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.
Software used |
---|