File:Poynting vector Gaussian beam focus.gif
Summary
| Description |
English: The Poynting vector describes the direction of the local flow of energy, so it points inward before the focus and outward after the focus.
At the focus all the energy is flowing in the same direction, so a "collimated beam" is effectively a very long focus. (Left: modulus squared. Right: phase) |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1281605546592874497 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
| GIF development |
Mathematica 12.1 code
\[Lambda] = 1;
\[Sigma] = 0.3 \[Lambda];
k0 = (2 \[Pi])/\[Lambda];
zR = \[Sigma]^2 k0;
w0 = Sqrt[(\[Lambda] zR)/\[Pi]];
w[z_] := w0 Sqrt[1 + z^2/zR^2];
R[z_] := (zR^2 + z^2)/z;
E2[x_, y_, z_] := w0/w[z] E^(I ArcTan[zR, z]) E^-((x^2 + y^2)/(w[z])^2) E^(I k0 (z + (x^2 + y^2)/(2 R[z])));
f = E2[x, y, z];
psi = f;
S = Abs[E2[x, y, z]]^2 Grad[ArcTan[zR, z] + k0 (z + (x^2 + y^2)/(2 R[z])), {x, y, z}];
p0 = Table[
abs = DensityPlot[Evaluate[Abs[psi]^2 /. {z -> z1}], {x, -2, 2}, {y, -2, 2}, PlotRange -> All, Frame -> False, ImagePadding -> None, ColorFunction -> "SunsetColors"];
arg = DensityPlot[Evaluate[Arg[psi] /. {z -> z1}], {x, -2, 2}, {y, -2, 2}, PlotRange -> All, Frame -> False, ImagePadding -> None, ColorFunction -> Hue];
Grid[{{
Graphics3D[{
Texture[abs],
Polygon[{{-1, -1, z1}, {1, -1, z1}, {1, 1, z1}, {-1, 1, z1}}, VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1, 1}, {0, 1}}]
, Orange,
Table[
If[Norm[Re@S /. {x -> x1, y -> y1, z -> z1}] > 0.1,
Arrow[{{x1, y1, z1}, {x1, y1, z1} + (Re[S /. {x -> x1, y -> y1, z -> z1}])/5}] ], {x1, -1, 1, 0.2}, {y1, -1, 1, 0.2}]
}, Lighting -> "Neutral", PlotRange -> {{-1, 1}, {-1, 1}, {-2, 2.2}}]
,
Graphics3D[{
Texture[arg],
Polygon[{{-1, -1, z1}, {1, -1, z1}, {1, 1, z1}, {-1, 1, z1}}, VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1, 1}, {0, 1}}]
, Black,
Table[
If[Norm[Re@S /. {x -> x1, y -> y1, z -> z1}] > 0.1, Arrow[{{x1, y1, z1}, {x1, y1, z1} + (Re[S /. {x -> x1, y -> y1, z -> z1}])/5}] ], {x1, -1, 1, 0.2}, {y1, -1, 1, 0.2}]
}, Lighting -> "Neutral",
PlotRange -> {{-1, 1}, {-1, 1}, {-2, 2.2}}]
}}]
, {z1, -2.0005, 2., 0.01}];
ListAnimate[p0]
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
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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.
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