Plotting 3D data in (Fr, Fθ, Fz) cylindrical coordinates

My understanding is, that you have a vector field, given in cylindrical coordinates, that only depends on the radius r (Note r should be >0 in cylindrical coordinates). And you want to plot the vectors in a slice with z==0.

Toward this aim we first define the coordinate functions r[r], [Theta][r] and z[r] that give the cylindrical coordinates.

Then we need the three cylinder base vectors in cartesian coordinates for our plot. This is done with the the function cylbas[x,y]

Next, as the vectors depend only on r, we define a function vec0[r] that gives the cartesian components of the searched for vectors in the y==z==0 plane.

Then we rotate the vectors in the plane y==z==0 around the z-axis. This gives a table of vector called: vecs

Finally we feed vecs to Graphics3D, where we change the vectors to Arrows. Here is the code:

[Lambda] = 633*10^(-9);
[Omega] = 2*[Pi]*3*10^8/[Lambda];
k0 = 2 [Pi]/[Lambda];
kr = 1.05*k0;
kz = Sqrt[kr^2 - k0^2];

r[r_] = 0.8*kz*kr^2/(2*[Omega])*1/r*BesselJ[1, kr*r]^2/(4.96*10^11);
[Theta][r_] = 
  0.2*kz*kr^2/(2*[Omega])*1/r*BesselJ[1, kr*r]^2/(4.96*10^11);
z[r_] = kr^3/(2*[Omega])*1/r*
   BesselJ[1, 
    kr*r]*(BesselJ[0, kr*r] - BesselJ[2, kr*r])/2/(4.96*10^11);

cylbase[x_, 
   y_] = {{Cos[ph], Sin[ph], 0}, 
    Sqrt[x^2 + y^2] {- Sin[ph], Cos[ph], 0 }, {0, 0, 1}} /. 
   ph -> ArcTan[x, y];

vec0[r_] = 
  Arrow[{{r, 0, 
     0}, {r, 0, 
      0} + {r[r [Lambda]], [Theta][r [Lambda]], 
       z[r [Lambda]]}.cylbase[r, 0 ]}];

vecs = Table[
   Rotate[Table[vec0[r ], {r, Table[i, {i, 0.2, 1, 0.05}]}], 
    ph, {0, 0, 1}], {ph, 0, 2 Pi, Pi/5}];

Graphics3D[{Thickness[0.005], 
  Arrowheads[Medium, Appearance -> "Projected"], vecs, Opacity[0.3], 
  Cylinder[{{0, 0, 0}, {0, 0, 0.005}}, 1]}, 
 PlotRange -> {{-1., 1.}, {-1., 1.}, {-.2, 0.4}}, ImageSize -> 400, 
 Axes -> True, BoxRatios -> {1, 1, 1}]