LDOS of an emitter in subpixel averaged index

[msanch23]

Hi!

I've been calculating the Purcell enhancement of my cavity using MEEP by calculating the LDOS of my point source in the cavity and normalizing it by the LDOS of the emitter in free-space with an index equal to the dielectric material.
Recently I wanted to see what adding a slot would do to the Purcell enhancement of the cavity, which means my emitter is now in air. I wanted to do a study of different slot widths, but a question came up that I can't seem to figure out or convince myself of.

When the slot is very small, say 10 nm wide, subpixel-averaging makes it so that the index in the slot and where my emitter is located equal to n, where n_air < n < n_dielectric. This, of course, is determined by my resolution. The resolution required so that with subpixel averaging the emitter is in n=1 is high enough that it isn't trivial to simulate (and my fields are blowing up, but that's a separate issue).

I've found that my results start to converge around a resolution of 100 pixels/um, but the resolution at 100 pixels/um leave only 1 pixel to represent the slot width.

My questions:

1. If my emitter is in this sub-pixel averaged slot index, should I be normalizing using an emitter in air or in the averaged slot index?
2. Can I trust my results are accurate since my resonance, Q, V, LDOS all converge even though I can't necessarily resolve my small feature? Or should I consider using some other software with non uniform meshing to get enough pixels in the slot?

Thank you!

(I just want to say that I appreciate MEEP for being an open-source and free software package, I've been doing all my simulation work for my PhD thesis in it)