SetDirectory[NotebookDirectory[]]

lu=Import["Delta-u.dat"];
ld=Import["Delta-d.dat"];
ListPlot[{lu,ld},PlotRange->All,Joined->True]

fu=Interpolation[lu];
fd=Interpolation[ld];

ωs= Table[1/1.01^n,{n,0,1500}];
Last[ωs]
eps=10^-8;
ωs=Join[ωs,{eps}];
ωs=N[Sort[Join[ωs,-ωs]]];

l=Map[{#,{{fu[#],0},{0,fd[#]}}}&,ωs];

l11=Map[{#[[1]],Re@#[[2,1,1]]}&,l];
ListPlot[l11,Joined->True,PlotRange->All]

(*Flatten2[{x_,{{a_,b_},{c_,d_}}}]:={x,Re[a],Im[a],Re[b],Im[b],Re[c],Im[c],Re[d],Im[d]};*)
Flatten2[{x_,{{a_,b_},{c_,d_}}}]:={x,Re[a],Re[b],Re[c],Re[d]};
lfl=Map[Flatten2,l];
(* real vs. complex is indicated by the FILENAME !! *)
Export["Delta.dat",lfl]