I have here a code. I have the density plot of a function with the parameters.
May I ask about correcting some errors. (This is a Gaussian Function)
The parameters
zr = (\[Pi]*w0^2)/\[Lambda]\
[Lambda] = 543*10^-7
wz = w0 Sqrt[1 + (z/zr)^2]
Rz = z[1 + (zr/z)^2]
theta = \[Lambda]/(\[Pi]*w0)
f = 50
w0 = 6.275*10^-1
r = sqrt[x^2 + y^2]
I (r, z) = exp[-2*[r/wz]^2]
DensityPlot[I[r, z], {x, -0.5, 0.5}, {y, -0.5, 0.5}, ColorFunction -> GrayLevel, MaxRecursion -> 5]
Color[z_] := RGBColor[0, z, 0]
Manipulate[DensityPlot[I[r, z]*(Cos[l*ArcTan[y/x]])^2, {x, -0.2, 0.2}, {y, -0.2, 0.2}, ColorFunction -> Color, MaxRecursion -> 5], {z, -50, 50}, {l, 1, 3}]