I think your "actual" plot looks correct, honestly. It is roughly the same shape as the "desired" plot, and my guess is that zooming in to the +/-0.2 THz region will probably display the five peaks shown in the "desired" plot's inset. I think I can count these five peaks in your "actual" plot even though the quality of the image is not great.
The one thing you may be missing is the application of a window (hann, hamming, etc) prior to the fft. This was probably done with the "desired" plot and is commonly done in frequency analysis.
As for your example code, it's only zeros, so there's no way for me to verify that your data is actually correct.