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Light reflectivity and transmitivity of periodic surface structures

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Hello,
I am trying to simulate the reflectivity and transmitivity of different wavelengths of light on a periodic surface structure.

1) I am using a 2D simulation using the RF module to create a basic cell with two media air and silicon and am trying to repeat it for the entire structure (periodic condition on side walls). I plan to have a electromagnetic wave incident on it (first TE and TM then average it out).

2) I plan to input the refractive index of silicon for different wavelenghts and use this for the simulation over the entire wavelenght range using a parametric sweep. Refractive index is the only material property I have specified.

3) I have used two ports, one for the input of a plane wave (and reflectivity) and one after the silicon side to find the transmitivity.

Is this right approach? I am unable to get reliable results as the values of R and T are fluctuating rapidly (between 0 and 1) over the wavelenght range. Could someone please throw some light on the above problem. I have attached images of the geometry and my results below.

Thank you.


5 Replies Last Post Jun 27, 2015, 4:36 p.m. EDT
Robert Koslover Certified Consultant

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Posted: 9 years ago May 30, 2015, 4:02 p.m. EDT
1. Are you (and carefully!) using Floquet-type periodic boundary conditions? You probably should be. Or... are you instead using some other type of periodic condition(s)? If so, that's likely at least part of your problem.

2. A computationally brute-force alternative (avoiding the challenges of correctly setting up the Floquet conditions) is to model a much larger, but still finite structure (many cells) and hit it with a ~Gaussian (or other tapered) beam illuminating a bunch of the cells, then observe the resulting transmission and/or reflection (of the integrated power or whatever else is of interest to you). This may or may not be practical, depending on the nature of your problem and the capabilities of your computer.
1. Are you (and carefully!) using Floquet-type periodic boundary conditions? You probably should be. Or... are you instead using some other type of periodic condition(s)? If so, that's likely at least part of your problem. 2. A computationally brute-force alternative (avoiding the challenges of correctly setting up the Floquet conditions) is to model a much larger, but still finite structure (many cells) and hit it with a ~Gaussian (or other tapered) beam illuminating a bunch of the cells, then observe the resulting transmission and/or reflection (of the integrated power or whatever else is of interest to you). This may or may not be practical, depending on the nature of your problem and the capabilities of your computer.

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Posted: 9 years ago May 30, 2015, 6:22 p.m. EDT
1) As for the physics I have used the wave equation (EM frequency domain) with electric displacement field model: refractive index. I have used 2 periodic ports one for input from above and one for transmission below. I have used a Floquet periodicity condition on both sides of the geometry and the k-vector from periodic port. Is there anything I might need to check in the periodicity condition?

2) I will try the simulation with multiple channels instead of a single unit and see if it solves the problem.

3) In order to simulate over a broad band of wavelenghts, I have created a parametric sweep for lambdas and plotted them against abs(emw.S11)^2 and abs(emw.S21)^2 where 1 and 2 are the input and output ports respectively to get the reflectivity and transmittivity plots. Is this the right approach?

Thank you for your inputs.

Edit 1: I am getting accurate results for reflectivity of plain silicon i.e. without creating any features but when I add features (to obtain periodic surface structures) the results fluctuate and some of the reflectivity values at certain wavelenghts are even higher than that of the untextured surface.

Edit 2: I have tried using multiple channels and I am still getting highly oscillatory results. Do you have any more suggestions? Thank you.
1) As for the physics I have used the wave equation (EM frequency domain) with electric displacement field model: refractive index. I have used 2 periodic ports one for input from above and one for transmission below. I have used a Floquet periodicity condition on both sides of the geometry and the k-vector from periodic port. Is there anything I might need to check in the periodicity condition? 2) I will try the simulation with multiple channels instead of a single unit and see if it solves the problem. 3) In order to simulate over a broad band of wavelenghts, I have created a parametric sweep for lambdas and plotted them against abs(emw.S11)^2 and abs(emw.S21)^2 where 1 and 2 are the input and output ports respectively to get the reflectivity and transmittivity plots. Is this the right approach? Thank you for your inputs. Edit 1: I am getting accurate results for reflectivity of plain silicon i.e. without creating any features but when I add features (to obtain periodic surface structures) the results fluctuate and some of the reflectivity values at certain wavelenghts are even higher than that of the untextured surface. Edit 2: I have tried using multiple channels and I am still getting highly oscillatory results. Do you have any more suggestions? Thank you.

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Posted: 9 years ago Jun 22, 2015, 12:48 a.m. EDT
I am still not able to resolve the issue with the simulation. I have attached an image of the simulation results.
Also when I use a flat surface without any features, I am not getting the right reflactance values for higher angles of incidence but for normal incidence the values are correct. I am starting to wonder if that is the reason the simulation with features is incorrect as the values of reflectance for higher angles of incidence are incorrect.
Any comments on this would be appreciated. Thank you.
I am still not able to resolve the issue with the simulation. I have attached an image of the simulation results. Also when I use a flat surface without any features, I am not getting the right reflactance values for higher angles of incidence but for normal incidence the values are correct. I am starting to wonder if that is the reason the simulation with features is incorrect as the values of reflectance for higher angles of incidence are incorrect. Any comments on this would be appreciated. Thank you.


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Posted: 9 years ago Jun 22, 2015, 2:06 a.m. EDT

I am still not able to resolve the issue with the simulation. I have attached an image of the simulation results.
Also when I use a flat surface without any features, I am not getting the right reflactance values for higher angles of incidence but for normal incidence the values are correct. I am starting to wonder if that is the reason the simulation with features is incorrect as the values of reflectance for higher angles of incidence are incorrect.
Any comments on this would be appreciated. Thank you.


Could you share your model file.Then I can get an idea about what might be the problem.
[QUOTE] I am still not able to resolve the issue with the simulation. I have attached an image of the simulation results. Also when I use a flat surface without any features, I am not getting the right reflactance values for higher angles of incidence but for normal incidence the values are correct. I am starting to wonder if that is the reason the simulation with features is incorrect as the values of reflectance for higher angles of incidence are incorrect. Any comments on this would be appreciated. Thank you. [/QUOTE] Could you share your model file.Then I can get an idea about what might be the problem.

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Posted: 9 years ago Jun 27, 2015, 4:36 p.m. EDT
I have the same problem too. My transmission spectrum seems correct, because I checked it with Lumerical, however, it is oscillatory, whereas I expect a clear peak.
I have the same problem too. My transmission spectrum seems correct, because I checked it with Lumerical, however, it is oscillatory, whereas I expect a clear peak.

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