File:Phased-antenna-array-principle.webm

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Original file ‎(WebM audio/video file, VP9, length 30 s, 719 × 720 pixels, 1.2 Mbps overall, file size: 4.24 MB)

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Summary

[edit]
Description
English: If you can control the relative phase of a number of point emitters, you can control the shape of your propagating wave.
Date
Source https://twitter.com/j_bertolotti/status/1252635852867547137
Author Jacopo Bertolotti
Permission
(Reusing this file)		 https://twitter.com/j_bertolotti/status/1030470604418428929

Mathematica 12.0 code

[edit]
\[Lambda] = 1;
k0 = (2 \[Pi])/\[Lambda];
\[Alpha] = (4 I)/k0^2;
\[Sigma] = (k0^3 Norm[\[Alpha]]^2)/4;
G[r_] := N[I/4 HankelH1[0, k0 Norm[r] ]];
ReMapC[x_] := RGBColor[(Cos[2 \[Pi] x] + 1)/2 UnitStep[x - 0.5], 0, (Cos[2 \[Pi] x] + 1)/2 UnitStep[0.5 - x]];

pos = Riffle[Range[0, 10, \[Lambda]/2], 
   Reverse@Range[-10, -\[Lambda]/2, \[Lambda]/2] ];
dim = Dimensions[pos][[1]]
p0 = Table[
   \[Theta] = Table[0, {j, 1, dim}];
   source = 
    Sum[G[{x - pos[[j]], y} ] E^(I \[Theta][[j]]), {j, 1, nsources}];
   DensityPlot[
    Re[source], {x, -10, 10}, {y, -\[Lambda]/2, 20 - \[Lambda]/2}, 
    PlotPoints -> 60, ColorFunction -> ReMapC, Frame -> False, 
    PlotRange -> {-0.25, 0.25}, Exclusions -> None,
    Epilog -> {White, 
      Table[Disk[{pos[[j]], 0}, \[Lambda]/4], {j, 1, nsources}], 
      Black, Table[
       Circle[{pos[[j]], 0}, \[Lambda]/4], {j, 1, nsources}],
      Table[
       Line[{{pos[[j]], 
          0}, {pos[[j]], 0} + \[Lambda]/
           4 {Sin[\[Theta][[j]] ], Cos[\[Theta][[j]] ]}}], {j, 1, 
        nsources}]}
    ]
   , {nsources, 1, dim, 1}];

pos = Range[-10, 10, \[Lambda]/2];
dim = Dimensions[pos][[1]]
p1 = Table[
   \[Theta] = (1 - Cos[ \[Pi] t])/2*
     Table[2 \[Pi] pos[[j]]/20, {j, 1, dim}];
   source = 
    Sum[G[{x - pos[[j]], y} ] E^(I \[Theta][[j]]), {j, 1, dim}];
   DensityPlot[Re[source], {x, -10, 10}, {y, -\[Lambda]/2, 20}, 
    PlotPoints -> 60, ColorFunction -> ReMapC, Frame -> False, 
    PlotRange -> {-0.25, 0.25}, Exclusions -> None,
    Epilog -> {White, 
      Table[Disk[{pos[[j]], 0}, \[Lambda]/4], {j, 1, dim}], Black, 
      Table[Circle[{pos[[j]], 0}, \[Lambda]/4], {j, 1, dim}],
      Table[
       Line[{{pos[[j]], 
          0}, {pos[[j]], 0} + \[Lambda]/
           4 {Sin[\[Theta][[j]] ], Cos[\[Theta][[j]] ]}}], {j, 1, 
        dim}]}
    ]
   , {t, 0, 1, 0.05}];

p3 = Table[
   \[Theta] = (1 - Cos[ \[Pi] t])/2*
     Table[-2 \[Pi] pos[[j]]^2/30, {j, 1, dim}];
   source = 
    Sum[G[{x - pos[[j]], y} ] E^(I \[Theta][[j]]), {j, 1, dim}];
   DensityPlot[Re[source], {x, -10, 10}, {y, -\[Lambda]/2, 20}, 
    PlotPoints -> 60, ColorFunction -> ReMapC, Frame -> False, 
    PlotRange -> {-0.25, 0.25}, Exclusions -> None, 
    ClippingStyle -> {Blue, Red},
    Epilog -> {White, 
      Table[Disk[{pos[[j]], 0}, \[Lambda]/4], {j, 1, dim}], Black, 
      Table[Circle[{pos[[j]], 0}, \[Lambda]/4], {j, 1, dim}],
      Table[
       Line[{{pos[[j]], 
          0}, {pos[[j]], 0} + \[Lambda]/
           4 {Sin[\[Theta][[j]] ], Cos[\[Theta][[j]] ]}}], {j, 1, 
        dim}]}]
   , {t, 0, 1, 0.05}];

p4 = Table[
   \[Theta] = 
    Table[-2 \[Pi] pos[[j]]^2/30 + (1 - Cos[ \[Pi] t])/
       2*2 \[Pi] pos[[j]]/10, {j, 1, dim}];
   source = 
    Sum[G[{x - pos[[j]], y} ] E^(I \[Theta][[j]]), {j, 1, dim}];
   DensityPlot[Re[source], {x, -10, 10}, {y, -\[Lambda]/2, 20}, 
    PlotPoints -> 60, ColorFunction -> ReMapC, Frame -> False, 
    PlotRange -> {-0.25, 0.25}, Exclusions -> None, 
    ClippingStyle -> {Blue, Red},
    Epilog -> {White, 
      Table[Disk[{pos[[j]], 0}, \[Lambda]/4], {j, 1, dim}], Black, 
      Table[Circle[{pos[[j]], 0}, \[Lambda]/4], {j, 1, dim}],
      Table[
       Line[{{pos[[j]], 
          0}, {pos[[j]], 0} + \[Lambda]/
           4 {Sin[\[Theta][[j]] ], Cos[\[Theta][[j]] ]}}], {j, 1, 
        dim}]}]
   , {t, 0, 1, 0.05}];

p5 = Table[
   \[Theta] = (1 - Cos[ \[Pi] t])/2*
     Table[-2 \[Pi] pos[[j]]^3/300, {j, 1, dim}];
   source = 
    Sum[G[{x - pos[[j]], y} ] E^(I \[Theta][[j]]), {j, 1, dim}];
   DensityPlot[Re[source], {x, -10, 10}, {y, -\[Lambda]/2, 20}, 
    PlotPoints -> 60, ColorFunction -> ReMapC, Frame -> False, 
    PlotRange -> {-0.25, 0.25}, Exclusions -> None, 
    ClippingStyle -> {Blue, Red},
    Epilog -> {White, 
      Table[Disk[{pos[[j]], 0}, \[Lambda]/4], {j, 1, dim}], Black, 
      Table[Circle[{pos[[j]], 0}, \[Lambda]/4], {j, 1, dim}],
      Table[
       Line[{{pos[[j]], 
          0}, {pos[[j]], 0} + \[Lambda]/
           4 {Sin[\[Theta][[j]] ], Cos[\[Theta][[j]] ]}}], {j, 1, 
        dim}]}]
   , {t, 0, 1, 0.05}];

p6 = Table[
   \[Theta] = (1 - Cos[ \[Pi] t])/2*
     Table[-2 \[Pi] Abs[pos[[j]] ]/3, {j, 1, dim}];
   source = 
    Sum[G[{x - pos[[j]], y} ] E^(I \[Theta][[j]]), {j, 1, dim}];
   DensityPlot[Re[source], {x, -10, 10}, {y, -\[Lambda]/2, 20}, 
    PlotPoints -> 60, ColorFunction -> ReMapC, Frame -> False, 
    PlotRange -> {-0.25, 0.25}, Exclusions -> None, 
    ClippingStyle -> {Blue, Red},
    Epilog -> {White, 
      Table[Disk[{pos[[j]], 0}, \[Lambda]/4], {j, 1, dim}], Black, 
      Table[Circle[{pos[[j]], 0}, \[Lambda]/4], {j, 1, dim}],
      Table[
       Line[{{pos[[j]], 
          0}, {pos[[j]], 0} + \[Lambda]/
           4 {Sin[\[Theta][[j]] ], Cos[\[Theta][[j]] ]}}], {j, 1, 
        dim}]}]
   , {t, 0, 1, 0.05}];

ListAnimate[
Join[Table[p0[[1]], {5}], p0, p1, Reverse[p1], p3, p4, Reverse[p4], 
 Reverse[p3], p5, Reverse[p5], p6, Reverse[p6], Reverse[p0] ]
]

Licensing

[edit]
I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero 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.

This file, which was originally posted to https://twitter.com/j_bertolotti/status/1252635852867547137, was reviewed on 6 July 2020 by reviewer GRuban, who confirmed that it was available there under the stated license on that date.

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Date/TimeThumbnailDimensionsUserComment
current15:37, 22 April 202030 s, 719 × 720 (4.24 MB)Berto (talk | contribs)Imported media from uploads:deae05fa-84ac-11ea-8457-162e1bb092a6

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WebM 360P 515 kbps Completed 15:37, 22 April 2020 11 s
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