Q1. I need help understanding why this structure basically has resonance at this specific wavelength.
A1. As is mentioned in the paper, the resonance here refers to a sharp dip in the transmission spectrum, which is a result of the waveguide mode better coupling to the plasmonic mode at that specific wavelength. If you look at the hybrid modes in the detection zone, you will see the modes having multiple peaks due to the coupling of waveguide mode to the surface plasmonic mode.
Q2. I can’t find the first 2 modes at 700 nm as reported in the paper. I only find the third mode. (True this is the mode that has the largest overlap with the input but still I am curious to know where the other modes are).
A2. It is difficult to tell why this is the case without looking at your simulation settings. But it would be worth checking whether you have fine enough meshes over the gold layer.
Q3. I am not an expert with EME simulations so are there any suggestions to improve the simulation, please?
A3. Again, it would be difficult to say how you can improve your simulation without seeing what your current simulation setting is. You might want to consider uploading your simulation file for us to better understand what your simulation settings are and how it compare with the settings mentioned in the reference.
Note that the paper does not provide much information about the index profile of the waveguide as a result of the ion-exchange. You might need to make sure that you are using the same index profile as in the paper to obtain a result reasonably comparable to that of the reference.