Learning Forum

[Nayem Hosen]

Can anyone help me regarding phase delay spectrum of metasurfaces with varying radius vs wavelength.

Here is the figure I attached for you reference:

Which simulation method should I use, fdtd or rcwa or others?

[Amrita Pati]

Hi Nayem,

I apologize for the delay in response. In metalens/metasurfaces there is usually a target phase and the metalens is designed such that the total phase imparted by it is as close to the target phase. The approach that we follow in our metalens example is that we first simulate the unit cell of the metasurface. This can be done using either FDTD or RCWA, but RCWA will be much faster. We calculate what would be the phase change for different radii by using the sweep tool (one simulation per radius). This will help us create a library of phase vs radius (similar to the screenshot you have attached).

Next, we create the full metalens geometry (which consists a certain distribution of elements of different radii) by mapping the target phase back to the radius using the library we created in the first step. For example, if the target phase is 0.5 rad at a certain position, we will map it back to the radius that will produce that phase. Then we create an element of that radius at that position. And in this way we design the full metalens geometry. The full metalens usually consists of elements of different radii (non-periodic), so we can not use RCWA. In that case we can either use FDTD or a field-stictching method to calculate the total phase imparted by the overall metalens geometry. Then this is compared to the target phase profile. 

The screenshot that you have attached tells me that this is most likely the unit cell simulation of elements of different radii. Feel free to correct me if I am wrong. If that is the case you can use either FDTD or RCWA, but as I mentioned RCWA will be faster. You can also look at the (Step-2) of the linked article on exact details. I will recommend you to have a look at the article and let me know if you have any further questions.

Regards,
Amrita

[Nayem Hosen]

Thank you for your response.

Actually, I am stuck with the phase delay spectrum (Figure 7b).

Also, this paper worked on the unit cell, and I got the unit cell phase plot before.

If I take the radius of 235–270 nm from the above phase graph, the figure looks like:

I don't think it is a phase delay spectrum. How can I get the exact figure 7b? Could you please give me a suggestion regarding this?

[Amrita Pati]

Hi Nasem,

Thanks for sharing the screenshot! I believe they are using a wider range of wavelength than you are, is that correct? Secondly, for their figure the x-axis is radius and the y-axis is wavelength. For yours, it's the opposite. Are you intentionally running the simulation for a shorter wavelength range? Also, would you be able to reverse the axes and share a screenshot?

Regards,
Amrita

[Nayem Hosen]

Yes, this is the figure, with a with a radius of 235–270 nm (y axis) and a wavelength of 1300–1600 nm (x axis)...I took a screenshot directly from lumerical and did not process it in Matlab. I just want to show that I think it is not the phase delay spectrum. 

here is the paper for your reference: http://www.koenderink.info/reading/Deckerhuygens.pdf