# Disk Resonators Spectrum

#1

I am following the ring resonator model provided from Lumerical MODE Solutions, however, I want to simulate a waveguide coupling light into a disk (in place of a ring).

The simulation gives several higher order modes. How can I isolate the fundamental modes? Is there a place to put in azimuthal mode numbers?

Thanks!

#2

Hi @kar3

Can you please provide me the link for the KB example? Also, what you want to study?

I assume you are referring to fundamental modes of a microdisk, right? [quote=“kar3, post:1, topic:4365”]
Is there a place to put in azimuthal mode numbers?
[/quote]

Unfortunately not! If you know the frequency of the fundamental mode, you can select source bandwidth to exclude higher order modes.

You can calculate the whispering gallery modes of a microdisk in FDTD, and here is the link to the script that converts field component from Cartesian to cylindrical coordinates.

#3

Hi @kar3
For the microdisk resonator, the mode size supported by the adjacent waveguide must match the whispering-gallery-mode (WGM) width propagating in the disk. Proper mode matching will support single-mode behavior within the disk and optimize disk-to-waveguide coupling.

#4

Can you please provide me with the procedure of how you are doing this? This is what I expect to see, however, will be great if you can walk us through the steps.

Thanks

#5

Hi @bkhanaliloo
I start from the wave equation in cylindrical coordinate system. Then I apply conformal transformation to convert the structure into an equivalent planar parallel-piped waveguide, which preserve all the physical properties of the original structure. The propagation modes of the equivalent planar waveguide is solved with some simple approximations and periodic boundary conditions at each end to give analytical solutions. These solution can be easily transformed back to give the resonant modes of the microdisk.

#6

@konslekk, this is very interesting. Do you use a specific software for this? Or some matlab models?

@bkhanaliloo: I tried to do this using the Bent waveguide option in MODE solver. While it works quite well for the ring, I wasn’t able to set up the simulation for the disk case in order to get the modes. Is this possible at all?

#7

This is an interesting approach and I wasn’t aware of this technique before. It looks like you can use conformal transformation for microdisk as well where refractive index varies along the slab in transformed space. This is explained in this paper. Here is an screenshot from Optical Microring Resonators: Theory, Techniques, and Applications By Vien Van that verifies the technique used in the above mentioned paper:

Feel free to share you results for microring, and let me know if you are interested on working on the microdisk case.