I have the following code:
f[l_, p_, r_, \[Phi]_] := (r Sqrt[2])^Abs[l] E^(-r^2) LaguerreL[p, Abs[l],2r^2] E^(-I r^2/2) E^(I l \[Phi]);
L[oam1_, r_, \[Phi]_] := f[oam1, 0, r, \[Phi]] {1, I}/Sqrt[2];
R[oam2_, r_, \[Phi]_] := f[oam2, 0, r, \[Phi]] {1, -I}/Sqrt[2];
cl = 1/Sqrt[2];
cr = 1/Sqrt[2];(*1/Sqrt[2]*)
state[oam1_, \[Theta]_, oam2_, r_, \[Phi]_] := cr*R[oam1, r, \[Phi]] + E^(I \[Theta]) cl*L[oam2, r, \[Phi]];
vvpol = VectorPlot[Evaluate@Re[state[7, Pi, -7, Sqrt[x^2 + y^2], ArcTan[x, y]]], {x, -1.4,1.4}, {y, -1.4, 1.4},RegionFunction -> Function[{x, y, z}, 0.2 < x^2 + y^2 < 1.6],
VectorColorFunction -> (Hue[ArcTan[#, #2]/(2 \[Pi])] &), VectorColorFunctionScaling -> False,
Mesh -> None, PlotRange -> All, ImageSize -> 400, Frame -> True, VectorScale -> {0.03, 0.95, None}, VectorStyle -> {{Thickness[0.007], Black}}, VectorPoints -> 25]
Which produces the following image:
As you can see the Hue map varies circularly, independently on the vector directions. What I want to have is a Hue map that varies depending on the direction of the field.
For instance, all the arrows pointing north will be green and all those pointing south blue and, of course, different color shades from north to south and vice-versa.
Can someone help me?
Thanks in advance :)
