Photonics

Photonics

Inconsistent differences between lumerical fdtd and comsol FEM

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    • Jeroen Dekker
      Subscriber

      Hi ansys support,

      I want to validate my lumerical FDTD setup by reproducing two similair metasurfaces from two papers. One follows up research on the other so they use the same COMSOL finite element method and the second paper minorly edited this comsol file for the different geometry (which is important later).  
      I have a normally incident plane wave source in the band of 750-800nm, and a frequency monitor spanning the entire the simulation volume above the SiO2 layer region with 250 sampling points. My goal is to reproduce the surface lattice resonance found in the papers (links below). This resonace is due to the periodicity of the structure which can be tuned with by setting the x and y span of the unitcell roughly equal to the desired resonance wavelength. By looking at the maximum electric field enhancement per wavelength in the volume of the simulation, in the papers referred as maximum field enhancement, these resonances can be easiliy indentified by a fano-style peak in the frequency band.

      The structure of the first metasuface is given below in fig 1 where the pillars are Si and are positioned upon a small layer of SiO2 and a larger layer of gold.
      I was able to perfectly reproduce the resonance of the first metasurface by using the conformal variant 1 meshing method and stepwise refine the mesh by increasing the number of meshcells per wavelength up to 50. This gave a nice convergence of the maximum field enhancement of the resonance where it rises towards the value of 140 which was also found in the first paper using comsol FEM.

      The second metasurface has a slightly different geometry see fig 2 below, but the main difference is that the surrounding medium of the pillars is now water (in immersion). Due to the lower refractive index contrast this resonance is expected to be lower. Setting the background to water and further keeping all but a few geometric settings the same, yielded this time a significant difference in the resonance found in the two methods. In COMSOL an electric field enhancement of approx 90 was found, but in lumerical FDTD using conformal variant 1 the simulation yielded a resonance with an electric field enhancement of approx 50. Since the metric in my research is fully dependent on this resonance, because I investigate metasurfaces for SERS, this difference can not be ignored.

      Different meshing methods such as dielectric volume and yu-mittra 2 can yield higher resonance, but do not exhibit any convergent behavior when increasing meshing as seen for the first metasurface with the conformal variant 1 meshing. I am aware the staircasing of the cylinders could play some factor in this. As the resonances are very strong near the interface of the cylinders and only reside in a relatively small part of the volume of the simulation.

      I already elimated the use of different material databases and too short simulation time as a possible causes for this difference. What could be a possible reason for this difference?

      Kind regards,

      Jeroen Dekker

       

      Lattice Resonances and Local Field Enhancement in Array of Dielectric Dimers for Surface Enhanced Raman Spectroscopy | Scientific Reports (nature.com)

      Using the near field optical trapping effect of a dielectric metasurface to improve SERS enhancement for virus detection | Scientific Reports (nature.com)

      fig 1. Metasurface 1 two sillicon cylinders in air with small SiO2 spacer and reflective gold layer below.

      fig 2 metasurface 2 two sillicon cylinders in water with small SiO2 spacer and reflective gold layer below

       

    • Guilin Sun
      Ansys Employee

      Thank you for sharing the papers. To compare with any 3rd party tools, please be careful as you may not know the exact details of simulations. please refer this post: https://forum.ansys.com/forums/topic/ansys-insight-why-my-simulation-result-is-different-from-published-paper-or-experiment/

      For the 2nd case, there is a 10nm thin layer, and a 20nm gap. They might be important: how many meshes do they have? 50 cells per wavelength might not be enough, since the metal is lossy, and its skin depth is small. The mesh should well resolve the skin depth. For conformal variant 1 it works well for finer mesh. However we do not know how fine the mesh should be to get better result.  Please also do a convergence testing. Please note that when the mesh is fine, make sure the PML is thick enough to absorb em waves.

      One more question: is there any substrate below the 100nm Au ?  I believe experimentally it should have.

      Please force the mesh symmetric in the plane of the two circles.

       

      Happy New Year!

      • Jeroen Dekker
        Subscriber

        Thanks for your swift reply Guilin!

        -A while ago I did convergence testing for the PML and Z-boundary height (where the PMLs reside), in both cases their error was a few orders lower than that of the meshing. As a sanity check I increased the number of PML layers from 32 to 56 but this did made no difference.

        - I did convergence testing in the range of 10 to 50 meshcells per wavelength with steps of 1 with conformal variant 1 method, for metasurface 1 the refining it nicely converges to the expected value and at 50 meshcells per wavelength I declared that the resonance was fully reproduced. The original work had a resonance with an electric field enhancement of 140 and in lumerical this is 135. For metasurface 2 the resonance very quickly converges to 50 at 30 meshcells per wavelength while in comsol the same metasurface gives an electric field enhancement of 85 .

        - Since I do have acces to the original COMSOL files of the simulations I compared the meshing. The meshing seems to be as fine, if not finer, as their simulations.

        -I set the x and y symmetry setting on, but made no difference.

        - I looked at the points in this post you shared https://forum.ansys.com/forums/topic/ansys-insight-why-my-simulation-result-is-different-from-published-paper-or-experiment/.
        Only point 8 I can not answer with certainty (since I am not very familiar with COMSOL). But given that the second metasurface COMSOL file is based on the first COMSOL file I would assume they are exactly the same. If the settings were wrong this should most likely not give a reproduction for metasurface 1.  

        - There is a small empty region of background material below the gold layer, but testing gave virtually no difference for the resonance peak.

        Honestly I am out of ideas for finding the reason for the difference. It would have been easier to accept if I was not able to reproduce metasurface 1 too.

         

    • Guilin Sun
      Ansys Employee

      Comparing results with others is very challenge, as there are many factors that the customers cannot control.  I have listed some reference papers in that post so you can see that some difference indeed exists, if all the geomery and material parameters are identical. We could not comment on any 3rd party tool, but we are confident with Lumericla FDTD as there are countless publications and experimental verifications, as well as commercial products designed by it. Since the gap is only 20nm and the diameter is only 139nm, it might be challenge to mesh them neatly, as they do not have a small, common factor to have integer number of meshes. In addition, the conformal variant 1 needs small-enough mesh however we do know how fine the mesh should be when it is small enough. please refer https://optics.ansys.com/hc/en-us/articles/360034382614-Selecting-the-best-mesh-refinement-option-in-the-FDTD-simulation-object 

    • Jeroen Dekker
      Subscriber

      I just noticed from the auto shutoff conditions that the total power in the system sometimes goes a little bit up at lower values. Is this necessarily indicative of wrong PML settings?  

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