Few beginner questions - sSNOM geometry: AFM tip illuminated with IR light

[jacekkozuch]

Dear all,

first of all: I'm new to electromagnetic simulations, so what will follow are pretty much beginner questions. The documentation was very informative, but now I'm reaching the point where I'm just missing experience. So, thanks in advance for all the input.

I would like to simulate the steady-state electric field of an AFM tip approached to a hBN sheet ontop of a Si substrate, as shown in the figure below; all set up in 2D. The goal is to visualize the nearfield electric field distribution (E^2) around the tip and through the hBN sheet as in this paper: https://doi.org/10.1364/OE.442305.

As seen in the figure, the tip apex radius is 10 nm, the hBN thickness 20 nm and my wavelength of interest 6 micrometers. So quite a mismatch in dimensions.

Here are things that I'm wondering about:

1. My current system is 500 nm x 500 nm sized and, therefore, much smaller that the wavelength. Is this acceptable given that I am concerned with the nearfield effects around the tip which decay within ~100 nm? Building a system on the scale of the wavelengths, but having nanometer-resolution around the tip are not quite compatible.
2. With the same argument (I'm interested in the nearfield around the tip), I've set the PML to 20 nm or so, which is far below the recommendation.
3. If I'm not mistaken, I should be careful when comparing Ex^2 with Ey^2 in terms of absolute values (x and y being the horizontal and vertical axes, respectively)? I planned to do a lower resolution 3D version for direct comparison with the 2D system. From there I should be able to extract scaling factors for Ex^2 with Ey^2 to correct for the choice of 2D?
4. Are the AFM tip, hBN and Si allowed to touch overlap with the PML? In the real experiment the dimensions are much larger, such that phonons/plasmons will propagate away anyways. Cutting my tip, hBN and Si seems to me like an equally wrong approximation as making the objects overlap with the PML, which will provide some quenching.

Thank you in advance for any thoughts and suggestions!
Best,
Jacek