\[Lambda] = 1;
\[Sigma] = 0.3 \[Lambda];
k0 = (2 \[Pi])/\[Lambda];
zR = \[Sigma]^2 k0;
w0 = Sqrt[(\[Lambda] zR)/\[Pi]];
w[z_] := w0 Sqrt[1 + z^2/zR^2];
R[z_] := (zR^2 + z^2)/z;
E2[x_, y_, z_] := w0/w[z] E^(I ArcTan[zR, z]) E^-((x^2 + y^2)/(w[z])^2) E^(I k0 (z + (x^2 + y^2)/(2 R[z])));
f = E2[x, y, z];
psi = f;
S = Abs[E2[x, y, z]]^2 Grad[ArcTan[zR, z] + k0 (z + (x^2 + y^2)/(2 R[z])), {x, y, z}];
p0 = Table[
   abs = DensityPlot[Evaluate[Abs[psi]^2 /. {z -> z1}], {x, -2, 2}, {y, -2, 2}, PlotRange -> All, Frame -> False, ImagePadding -> None, ColorFunction -> "SunsetColors"];
   arg = DensityPlot[Evaluate[Arg[psi] /. {z -> z1}], {x, -2, 2}, {y, -2, 2}, PlotRange -> All, Frame -> False, ImagePadding -> None, ColorFunction -> Hue];
   Grid[{{
      Graphics3D[{
        Texture[abs], 
        Polygon[{{-1, -1, z1}, {1, -1, z1}, {1, 1, z1}, {-1, 1, z1}}, VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1, 1}, {0, 1}}]
        , Orange,
        Table[
         If[Norm[Re@S /. {x -> x1, y -> y1, z -> z1}] > 0.1, 
          Arrow[{{x1, y1, z1}, {x1, y1, z1} + (Re[S /. {x -> x1, y -> y1, z -> z1}])/5}] ], {x1, -1, 1, 0.2}, {y1, -1, 1, 0.2}]
        }, Lighting -> "Neutral", PlotRange -> {{-1, 1}, {-1, 1}, {-2, 2.2}}]
      ,
      Graphics3D[{
        Texture[arg], 
        Polygon[{{-1, -1, z1}, {1, -1, z1}, {1, 1, z1}, {-1, 1, z1}}, VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1, 1}, {0, 1}}]
        , Black,
        Table[
         If[Norm[Re@S /. {x -> x1, y -> y1, z -> z1}] > 0.1, Arrow[{{x1, y1, z1}, {x1, y1, z1} + (Re[S /. {x -> x1, y -> y1, z -> z1}])/5}] ], {x1, -1, 1, 0.2}, {y1, -1, 1, 0.2}]
        }, Lighting -> "Neutral", 
       PlotRange -> {{-1, 1}, {-1, 1}, {-2, 2.2}}]
      }}]
   , {z1, -2.0005, 2., 0.01}];
ListAnimate[p0]