From a theoretical point of view, regarding a vertical incidence on a metal-insulator-metal periodic structure, its sum-frequency signals should be zero if only zero-order diffraction is allowed. Here, the metal has centro-symmetric atomic lattice. The insulator is Al203 without nonlinear effect. The unit cell has centro-symmetric geometry.
Experimentally, it should not be expected to get signals for transmittance or reflectance at the sum frequency. However, we found that it not the case. We tried to explain the experimental effect by bulk contribution from high-order modes. It still needs to be examined and understood. Your comments or views are highly welcomed.
Below is our work:
Chip-Scale Plasmonic Sum Frequency Generation
https://doi.org/10.1109/JPHOT.2017.2705061
There could a couple of origins of your sum frequency signal.
First of all, your structure is not centro-symmetric. The bottom is made from a continuous gold film, while the top is a patterned gold film. Therefore inverting the unit cell in the vertical direction does not give you the same structure back. I also assume that the thickness of the bottom and top films differs.
The second reason could be surface effects. The surface layer of a centro-symmetric material is not centro-symmetric and can therefore lead to SFG.
Dear Sebastian:
Thanks for your answer.
For point 1, yes, there is a net nonlinear polarization along the vertical z direction. But for the periodic structure, only x and y polarized fields at sum frequency can be observed at far field. Only zero-order diffraction is allowed by the geometry configuration. It is also confirmed by experiments.
For point 2, except for gold materials, Al203 layer has no nonlinear signals. For 5-nm-thick Cr adhesion layer, I am not sure that Cr is centro symmetric or not.
I am studying the problem more carefully by solving the Maxwell-hydrodynamic model, starting from a centro-symmetric gold slab excited at a low order or high order plasmonic mode.
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