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]))

Module[{l = 1, p = 0, xMax = 3, zMax}, zMax = 2 Pi ;
 DensityPlot3D[If[Cos[I( l [Phi] -I z)==0,
  Re[LG[Sqrt[x^2 + y^2], ArcTan[x, y], p, l, 1] Exp[-I z]]], {x, -xMax,
    xMax}, {y, -xMax, xMax}, {z, 0, zMax}, PlotPoints -> 60,
  AxesLabel -> {"x", "y", "z"}]]