The increase in EFR as a function of slot width or height might be due to the shifting of the mode towards its cutoff. Due to the finite computational domain and reflecting boundary condition, the power which is supposed to be leak into the substrate gets reflected back and the software can't differentiate between the reflected power with the real power and include this in the calculation of EFR.

To ensure that this is due to the above effect, you can try to observe the value of the effective index along with EFR, you will probably find that the effective index is either approaching towards the refractive index of the substrate or below it. You can also look at the modal profile to see whether the mode decays completely when you keep on increasing either the slot width or height.

Nikhil Dhingra

Thanks for your comments.

my structure includes silver in both rails which surronds the gap and they are located on the silicon nitride layer as substrate. in order to confine the mode into the slot (gap) region, I used mode analysis study performing in Comsol and in the mode search around, I defined the refractive index of silicon nitride. The mode can be confined into the slot region, although some part of it leaks to the caldding and substrate naturally. Did I select the proper refractive index or I have to define the refractive indx of silver instead of that of silicon nitride?

what do you mean by observing the value of effective index along with EFR??

what is your suggestion to optimize the slot waveguide parameters like slot width and heigh and also rail width?

Dear Parviz Saeidi

The refractive index of silicon nitride in the mode search is fine as the effective index of your slot mode is gonna be a little bit higher that the refractive index of the silicon nitride. Hence, it shouldn't be a problem for the software to find a mode around it.

Next, you need to make sure that your substrate height should be atleast 2 um and the space on the left of your left Ag rail and the on the right of your right Ag rail should be atleast 1.5 um. The cover height of 1.5 is okay. These values ensure that the computational domain is big enough.

If for any set of S, W and H, your modal field doesn't decay till the computational boundaries, then the value of EFR, which you are going to get, is not correct. In such case you can leave those parameter as your mode is no longer guided for those set of parameters.

Note: based on your structure the required substrate height, cover height, and left and right space of your Ag rails might needs to be changed. The values I have given above works for the SOI slot waveguide. As starting point you can use these value and if you find the need to increase those, you can.

Dear Nikhil Dhingra

The effective mode index I obtained is a bit lower than the refractive index of silicon nitride. based on your comments, then the mode I got is incorrect, yes?

if I want to search modes around the refractive index of silver, how should I enter it into the comsol sfotware? As you know, it has both real part and imaginary part.

Should I only enter the real part of it or both part?

The mode is not incorrect; it is just no longer guided. Maybe the dimensions you are using are not appropriate. The effective index of the guided mode can never be around the refractive index of Ag. So you don't need to enter the refractive index of Ag in the mode search around. Tell me the dimensions (W, S, H) which you are using. I will check if there exists a guided mode corresponding to that set of dimensions.

Actually, with silicon nitride substrate and air cladding, it is hard to get a guided slot mode. As your structure involves a very high vertical asymmetry, it is probably not going to support a slot mode with air cladding.

Just change the whole cladding (substrate as well as cover) to SiN and you will get your slot mode.