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Refractive index for Silicon – 2D vs 3D Simulations

    • Joel Sved


      I was wondering why under certain conditions (presumably isotropic media etc) the refractive index of Silicon in 2-D environment is approx. 2.8 wheras for 3-D it is approx 3.48?

      The WDM design in LumOpt seemed to use a RI of 2.8 for Si in their optimisation (while SiO2 seems to remain at 1.44 for both 2-D and 3-D).

      Please let me know if I have got this wrong, or indeed why this may be the case. 



    • Guilin Sun
      Ansys Employee

      Good question!

      The example article does not mention anything regarding to this. But it should be from the fact that, such waveguide has limited 3rd dimension. Therefore, its effective or equivalent refractive index becomes smaller, with weak mode confinement in 2D. You can refer to varFDTD physics to get some insight on how to calculate the equivalent refractive index from 3D to 2D: MODE - 2.5D varFDTD solver introduction – Ansys Optics 

      For SiO2, since it is the environment, it is approximate. Using the above method one may get smaller data or sometimes unphysical value, such as smaller than 1.


      Anyway, such 2D example is simply an illustration for such initial design with topology optimization. The final design should be verified with 3D FDTD, and you may use 3D FDTD for further optimization. However it will be much slower than 2D. 


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