Is s-parameter calculation still valid when multiple periods are included in the unit cell?

s-parameters

#1

Hi Skim,

Thank you for your reply. Sorry for the confusion I made in the last post. By looking at the E result of the reflection monitor, and taking the x-axis component. The angle operation should tell you the phase of the field, however I just found out that this is not a valid method of looking at the phase in a periodic structure as it accounts for the evanescent coupling of the other structures around the unit cell.


Here is the plot I am referring to.

My next question is with regards to designing the 4 disk case. Is the analysis group still a valid way of looking at the phase relationship with regards to the wavelength?


Position of reflection monitor in the s-parameter analysis group
#2

In principle, including multiple periods of the structure in the unit cell, hence making the unit cell bigger, would not change the phase vs. wavelength relationship.
However, this will inevitably increase the number of diffraction orders supported by the grating. The additional orders have near-zero strength, though. As a result, the total number of meaningful orders will stay the same.
I do not think you gain anything by Including multiple periods in the unit cell. It results in increase in memory requirement and simulation time. The results also include unnecessary zero-strength orders.
As to the phase of the unit cell, the results will be the same if you do some convergence test on both cases.

Here are examples of a grating with a single period and three periods:

To produce the above results, open the simulation file [ 30966_2.fsp (276.3 KB) ] and run the script [ 30966_2.lsf (692 Bytes) ].

If you are interested in the phase of the nearfield for the entire metalens, you cannot use the grating projection. Instead, you will need to use the nearfield result over the surface of the metalens. If the period of the unit cell is subwavelength, the injected will propagate mostly like a planewave. In such case, the phase directly from the nearfield would be close to the phase calculated from the grating projection.


#3

Hi Skim,

Thank you for reply once again. This clarifies things a bit more for me. So as long as my unit cell period within the subwavelength regime (<1000nm), then the grating projection phase response should provide me with an accurate phase value or close enough to the actual phase of the structure. Otherwise I would need to take the angle(Ex) or angle(Ey) depending of what direction I’m interested in? My idea is that I’m looking at a bigger unit cell (just like the file I posted a couple of days ago), where the period is around 1.7um, where the unit cell consists of 4 or more pillars that deffer in refractive index and/or radius, so that I would be able to obtain a total phase and amplitude difference from that unit cell.

What I’m also confused about is that you look at the value of the E in the monitor, while using periodic boundaries? I’ve thought this would implicitly be affected by the evanescent field coupling? Even not, what simulation strategy would you recommend in the case of simulating a unit cell of a non-subwavelength period (periodic boundaries?, S-Parameters grating projection? angle(Ex), Angle(Ey)?)


#4
  1. This clarifies things a bit more for me. So as long as my unit cell period within the subwavelength regime (<1000nm), then the grating projection phase response should provide me with an accurate phase value or close enough to the actual phase of the structure. Otherwise I would need to take the angle(Ex) or angle(Ey) depending of what direction I’m interested in?
    –>That is correct. If you move away from the subwavelength regime towards larger periods, the phase from grating projection might be different from the phase from the nearfield.

  2. My idea is that I’m looking at a bigger unit cell (just like the file I posted a couple of days ago), where the period is around 1.7um, where the unit cell consists of 4 or more pillars that deffer in refractive index and/or radius, so that I would be able to obtain a total phase and amplitude difference from that unit cell.
    –> This is something that reguires your own test to see how it behaves. The answer I provided in A1 is based on identical structures.

  3. What I’m also confused about is that you look at the value of the E in the monitor, while using periodic boundaries? I’ve thought this would implicitly be affected by the evanescent field coupling?
    –> Your original question was about the validity of the phase calculation when multiple periods are included in a unit cell. The purpose then was to see the local phase over a specific period are the same for a single period and multiple periods simulation. If the near fields for both cases are the same, it is obvious their phase from grating projection should be the same. Hence, the plots for the nearfield will suffice for the verification of the argument.

  4. Even not, what simulation strategy would you recommend in the case of simulating a unit cell of a non-subwavelength period (periodic boundaries?, S-Parameters grating projection? angle(Ex), Angle(Ey)?)
    –> This could be something beyond the scope of our technical support. This could be about developing methodology for a scientific research and has no direct relevance to the functionality of our product. If you come up with a certain methodology and then need some help to implement the methodology using the functionalities available from our products, then we are happy to provide further help on this.
    Having said that, one thing seems to be clear:
    For a non-subwavelength unit cell, you will most likely need to use the grating projection (s-parameter analysis group) to obtain correct phase vs. geometry parameters relations. I am not sure whether you already know about it, but we have an updated page for the metalens example here.