I just posted this question yesterday, Color a phase and density of a density plot, and I was also curious how I can see this in 3D. I want to use the same equation,
LG[r_, \[Phi]_, p_, l_, w_] := (
Sqrt[(2 p!)/(\[Pi] (p + Abs[l])!)]
1/w E^(-r^2/w^2)
((r Sqrt[2])/w)^Abs[l]
LaguerreL[p, Abs[l], 2 r^2/w^2]
E^(I l \[Phi])
)
and plot it in 3D similar to this,
Plot3D[
Evaluate[
Arg@LG[
Sqrt[x^2 + y^2],
ArcTan[x, y],
2, 2, 1
]
]
, {x, -2, 2}
, {y, -2, 2}
, Mesh -> None
, PlotPoints -> 50
, PlotRange -> All
, ImageSize -> {400, 400}
]
The Arg takes the complex component and plots it on the z axis and this is good, but now I want to include along that path a density.
To further clarify, I'm interested in seeing a 3D density plot of Orbital Angular Momentum of light (OAM wiki page). The only image on that wiki page not only has a 3D representation of the phase (just as I have in the figure above), but it also has the density along that phase. I would like to take it one step further, (since the density is not limited to a cork screw plane) and show the 3D cork screw like density. (I'm not sure if it is frowned upon to copy an image over from that wiki page, so I won't.)
So I was trying to use DensityPlot3D, but I'm unsure how to proceed. So to recap the same as the first link above just in 3D (and there will be no need for the Hue for the phase since the phase will be shown in the $z$ direction). The final picture should just look like a spiral that has a density along that spiral (and obviously as you increase $p$ then you have additional spirals).
ColorFunction
? $\endgroup$ – Chip Hurst Jul 12 '18 at 22:20Exclusions -> {x^2 + y^2 == 1, x == 0, y == 0, x^2 + y^2 == 3}
will get rid of the artifacts at the discontinuities. $\endgroup$ – Chip Hurst Jul 12 '18 at 22:20