Overlay for two axes plot

Question

I have these two plots that I want to merge in order to create a plot with two axes. I just want to translate the second plot in order for them precisely coincide. However, it seems that the Translate command does not work for plots. How can I make the plots coincide?

Thanks!

lambda=18.0;

dataIL={{0*lambda,-7.919},{10*lambda,-8.274},{50*lambda,-9.381},{100*lambda,-11.193},{200*lambda,-14.969}};

fitIL=Transpose[{Table[x,{x,0,200*lambda,lambda}],Table[-7.810743628185908`-0.001957142262202232` x,{x,0,200*lambda,lambda}]}];

dataGD={{0*lambda,0.03849},{10*lambda,0.05877},{50*lambda,0.1597},{100*lambda,0.2843},{200*lambda,0.5677}};

fitGD=Transpose[{Table[x,{x,0,200*lambda,lambda}],Table[0.03100392803598201` +0.00014721301849075468` x,{x,0,200*lambda,lambda}]}];

a=ListPlot[{dataIL,fitIL},PlotRange->{All,All},Joined->{False,True},PlotStyle->{{Thickness[0.0060],PointSize[0.007],Darker[Opacity[1,Blue],0.5]},{Thickness[0.0060],PointSize[0.007],Darker[Opacity[1,Red],0.15]}},PlotLegends->Placed[LineLegend[{Style["Experimental",Black,40,FontFamily->"Arial"],Style["Fitted",Black,40,FontFamily->"Arial"]},LegendLabel->None,LegendFunction->Framed,LegendMargins->{{5,5},{1,1}},LegendMarkerSize->{35,5}],{Right,Top}],Frame->True,FrameStyle->Directive[Thickness[0.0015]],FrameTicks->{{{-15,-14,-13,-12,-11,-10,-9,-8},None},{{0,1000,2000,3000,4000},None}},FrameLabel->{Style["Transmitter-Receiver Gap, lDL (μm)",Black,48,FontFamily->"Arial"],Style["Transmission, Mag(S21) (dB)",Black,48,FontFamily->"Arial"]},LabelStyle->{Black,48,FontFamily->"Arial"},ImagePadding->{{150,10},{130,50}},ImageMargins->{{10,10},{10,10}},Axes->False,ImageSize->1000]

b=ListPlot[{dataGD,fitGD},PlotRange->{All,All},Joined->{False,True},PlotStyle->{{Thickness[0.0060],PointSize[0.007],Darker[Opacity[1,Blue],0.5]},{Thickness[0.0060],PointSize[0.007],Darker[Opacity[1,Red],0.15]}},PlotLegends->Placed[LineLegend[{Style["Experimental",Black,40,FontFamily->"Arial"],Style["Fitted",Black,40,FontFamily->"Arial"]},LegendLabel->None,LegendFunction->Framed,LegendMargins->{{5,5},{1,1}},LegendMarkerSize->{35,5}],{Right,Bottom}],Frame->True,FrameStyle->Directive[Thickness[0.0015]],FrameTicks->{{None,{0,0.25,0.5,0.75,1}},{{0,1000,2000,3000,4000},None}},FrameLabel->{{None,Style["Group Delay, τ21 (μs)",Black,48,FontFamily->"Arial"]},{Style["Transmitter-Receiver Gap, lDL (μm)",Black,48,FontFamily->"Arial"],None}},LabelStyle->{Black,48,FontFamily->"Arial"},ImagePadding->{{10,150},{130,50}},ImageMargins->{{10,10},{10,10}},Axes->False,ImageSize->1000]

Overlay[{a,b}]

Answer 1

A starting point:

lambda=18.0;
dataIL={{0*lambda,-7.919},{10*lambda,-8.274},{50*lambda,-9.381},{100*lambda,-11.193},{200*lambda,-14.969}};
fitIL=Transpose[{Table[x,{x,0,200*lambda,lambda}],Table[-7.810743628185908`-0.001957142262202232` x,{x,0,200*lambda,lambda}]}];
dataGD={{0*lambda,0.03849},{10*lambda,0.05877},{50*lambda,0.1597},{100*lambda,0.2843},{200*lambda,0.5677}};
fitGD=Transpose[{Table[x,{x,0,200*lambda,lambda}],Table[0.03100392803598201` +0.00014721301849075468` x,{x,0,200*lambda,lambda}]}];
a=ListPlot[{dataIL,fitIL},PlotRange->All,Frame->{{True,False},{True,True}},FrameTicks -> {{All, None}, {All,None}},ImagePadding ->20];
b=ListPlot[{dataGD,fitGD},PlotRange->All,Frame->{{False,True},{False,False}},FrameTicks -> {{None, All}, {None, None}},ImagePadding ->20];
Overlay[{a,b}]

Output: