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}];
    ]