\[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, 0, z];
psi = f;

p1 = Table[
   Show[
    RegionPlot[True, {z, -3, 3}, {x, -2, 2}, PlotPoints -> 200, ColorFunctionScaling -> False, ColorFunction -> Function[{z, x}, Hue[Arg[psi*E^(-I \[Phi])]/(2 Pi), 1, Abs[psi]^2]], Frame -> False]
    ,
    Plot[{w[z], -w[z]}, {z, -50, 50},  Background -> None, PlotStyle -> {White}]
    ]
   , {\[Phi], 0, 2 \[Pi], \[Pi]/10}];
ListAnimate[p1]