Plot complex level curves of a polar function?

Questions
,
1

Hello, I have a a polar function given by:

u[r_, phi_, n_] := 
 Piecewise[{{BesselJ[1.5 r, n]*Exp[I n phi], 
    0 < r < 1/2}, {(BesselJ[3 r, n] + BesselY[3 r, n])*Exp[I n phi], 
    1/2 < r < 1}, {HankelH1[r, n]*Exp[I n phi], r > 1}}]
u0[r_, phi_, k_] := Sum[I^(-n) BesselJ[n, r] Exp[I n phi], {k, -5, 5}];
u1[r_, phi_, n_] := 
 Sum[I^(-n) BesselJ[n, r] Exp[I n phi], {k, -5, 5}] + 
  Piecewise[{{BesselJ[1.5 r, n]*Exp[I n phi], 
     0 < r < 1/2}, {(BesselJ[3 r, n] + BesselY[3 r, n])*Exp[I n phi], 
     1/2 < r < 1}, {HankelH1[r, n]*Exp[I n phi], r > 1}}]

And I’d like to plot the level curves of the Real and Imaginary part in a Polar 3D system. How do I do this?

Thanks!

2

For example

ContourPlot[Im[u1[r, p, 3]], {r, 0, 3}, {p, 0, 2 Pi}, Contours -> 3]
3

Maybe something like this?

ParametricPlot3D[{r*Cos[phi], r*Sin[phi], Re[u1[r, phi, 3]]},
 {r, 0, 3}, {phi, 0, 2 Pi}, MeshFunctions -> {#3 &}]