# Starting a simulation for photonic crystal with a L3 cavity with a new material

#1

Hello,

I am interested in simulating a hexagonal photonic crystal with a L3 cavity for a new material.
I was wondering what the best strategy is to determine the right parameters (radius, lattice constant, thickness) to get the resonance of the cavity exactly at 1.56 um. A nested parameter sweep would be possible but the computation effort will be quite high for this.
I would be interested in how you tackled such a problem?

#2

Dear @voglerv

Indeed, nested parameter sweep and optimization tab will be useful for small tweaks in geometry and not for designing a cavity from scratch. The best approach will be to use literature to come up with the design theory.

In my best knowledge, a good approach is to focus on bandstructures and simulate periodic structure to find the bandgaps (in your case you want a large bandgap at ~1.56um). The periodic array section will act as the mirror part of PC. Then gradually tapering the hole size to build the cavity section. There should be plenty of papers and ideas on how you need to taper the hole size. For example, this paper was really good for designing 1D PC cavity (https://arxiv.org/abs/1108.2675) and you should be able to find similar papers that discusses the geometry for hexagonal PC cavities.

Please note that designing a high-Q PC cavity is generally challenging and will take time. Once you come up with some initial design, you can perform weep and use optimization tab to modify geometry to support high-Q devices. You also need to make sure that your devices is robust to fabrication imperfections if you are planning to measure their response experimentally.

#3

Dear bkjanaliloo,

thank you for your answer. I now finished the simulations. What I can recommend other users is to start with the values for a hexagonal photonic crystal from the paper of Yoshihiro Akahane and Susumu Noda “High-Q photonic nanocavity in a two-dimensional photonic crystal”. The only parameter that you have to determine in first place is the lattice constant (a). All other parameters are determined from the lattice constant. thickness of slab = 0.6a ; radii of air rods = 0.29a. Of course these values have to be optimized afterwards but they give a really good result in first place. If the refractive index of your material is lower than silicon, you have to increase the lattice constant. Also make sure that you have the right mode profile with the resonance you get. First, start with rough parameter sweeps and determine the approximate values. Then do more precise sweeps. In the end the Q-factor can be optimized by shifting the position of the innermost holes and their radii. I hope, somebody can profit from this.
Best,
Viola

#4

Dear @voglerv

Thank you very much for the updates and references. I am sure this will be quite useful for other users who want to obtain highQ L3 cavities.

Thanks again for the updates and best of luck in your studies.