I managed to double the speed by simply moving some multiplications and divisions...

AbsoluteTiming[
  or2 = -2./Omegar^2.;
  oz2 = 2./Omegaz^2.;
  p = p^2.;
  Io*Table[
           Exp[(p[[i, t, 1]] + p[[i, t, 2]])*or2 - p[[i, t, 3]]*oz2],
           {t, 1, Deltat + 1}, {i, n}];
]

I managed to double the speed by simply moving some multiplications and divisions...

AbsoluteTiming[
  or2 = -2./Omegar^2.;
  oz2 = 2./Omegaz^2.;
  p = p^2.;
  Io*Table[
           Exp[(p[[i, t, 1]] + p[[i, t, 2]])*or2 - p[[i, t, 3]]*oz2],
           {t, 1, Deltat + 1}, {i, n}];
]

A dot product is 30 to 40% faster still.

AbsoluteTiming[
  or2 = -2./Omegar^2.;
  oz2 = 2./Omegaz^2.;
  v = {or2, or2, -oz2};
  p = p^2.;
  Io*Table[Exp[p[[i, t]].v],{t,1,Deltat+1},{i,n}];
]