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docs:become [2020/04/22 15:43] pklapetek |
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| - | The transition from transition geometry to reflection geometry was done first with perfect electric conductor as a grating material. The same motive as in the Become grating is used and also | + | The transition from transmission geometry to **reflection grating** geometry was done first with **perfect electric conductor** as a grating material. The same motive as in the Become grating is used and also |
| the same voxel spacing (5 nm), it is only from a different materials for calculation speed and simplicity. All the computational details were same as in the previous example. | the same voxel spacing (5 nm), it is only from a different materials for calculation speed and simplicity. All the computational details were same as in the previous example. | ||
| To get the data normalization to the incident wave intensity we used perfect electric conductor plane only (no grating motives) and evaluated the electric field intensity in | To get the data normalization to the incident wave intensity we used perfect electric conductor plane only (no grating motives) and evaluated the electric field intensity in | ||
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| The image below shows the normalized angular dependence of the diffraction from the (finite size) grating. | The image below shows the normalized angular dependence of the diffraction from the (finite size) grating. | ||
| - | {{:docs:become_grating_2d_normalised.png?600|}} | + | {{:docs:result_twomethods.png?800|}} |
| - | When inspected in detail, it can be seen that there is a slight asymmetry in the result which needs to be analyzed, probably due to wrong placement of far-field points. The average intensity of the s+1 and s-1 diffraction orders is 0.178 of the incident intensity for the default silver model (not the Become one). | + | When inspected in detail, it can be seen that there is a difference of about 3 percents between |
| + | the two methods output for the first diffraction maximum, similarly to the PEC case. | ||
| + | Again we expect that this difference is given by the difference in models - big single calculation | ||
| + | has to work with limited source size and repeated calculations work with infinitely periodic field | ||
| + | even if they are not infinitely periodic. | ||
| + | A bigger problem is that the diffracted intensity is about 0.147 of the incident intensity, | ||
| + | which is less than expected (the expected value is 0.186). Something has to be wrong. | ||
| + | The first suspect is the refractive index. | ||
| As we use the PLRC metal handling we can not enter the refractive index directly to the calculation. Instead we need to use some dispersive model, in our case based on two critical points. We have fitted part of the optical database data by the model to get closer to the prescribed values, however there are still small differences (unless we restrict the fitting spectral region much more, which would lead to quite unrealistic dispersive model). The correspondence of the fitted refractive index and database data is shown below. | As we use the PLRC metal handling we can not enter the refractive index directly to the calculation. Instead we need to use some dispersive model, in our case based on two critical points. We have fitted part of the optical database data by the model to get closer to the prescribed values, however there are still small differences (unless we restrict the fitting spectral region much more, which would lead to quite unrealistic dispersive model). The correspondence of the fitted refractive index and database data is shown below. | ||
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| To compare its impact on results, here is a list of different metal model settings and results: | To compare its impact on results, here is a list of different metal model settings and results: | ||
| - | * metal setting: 6 1.03583 0 1.37537e+16 1.25733e+14 2.1735 -0.504659 7.60514e+15 4.28131e+15 0.554478 -1.48944 6.13809e+15 6.62262e+14 means n=(0.129 + 3.87i) and leads to first order diffraction of 0.172 | + | * the fitted metal setting: 6 1.03583 0 1.37537e+16 1.25733e+14 2.1735 -0.504659 7.60514e+15 4.28131e+15 0.554478 -1.48944 6.13809e+15 6.62262e+14 means n=(0.129 + 3.87i) and leads to first order diffraction intensity of 0.147 |
| - | * default metal setting: 6 0.89583 0 13.8737e15 0.0207332e15 1.3735 -0.504659 7.59914e15 4.28431e15 0.304478 -1.48944 6.15009e15 0.659262e15 means n=(0.036 + 4.147i) and leads to first order diffraction of 0.178 | + | * default metal setting: 6 0.89583 0 13.8737e15 0.0207332e15 1.3735 -0.504659 7.59914e15 4.28431e15 0.304478 -1.48944 6.15009e15 0.659262e15 means n=(0.036 + 4.147i) and leads to first order diffraction intensity of 0.150. |
| + | The easiest way how to check the metal properties is to calculate the reflectance of a bulk. | ||
| + | This uses very similar geometry to our calculation (TSF source, periodic and CPML boundaries), | ||
| + | so we can expect that there are not many additional potential error sources when comparing to our calculation. | ||
| - | After improving nearly everything (CPML, periodic borders, source) the result is even worse, 0.148 for the fitted metal, spacing 10 nm. However, now the result is fully symmetric and does not depend on voxel size (0.147 for spacing 5 nm). | + | First of all, error in the reference value (PEC reflection) is below 0.001 percent. This certainly |
| + | cannot affect our results. | ||
| + | Reflectance of the default metal for this particular voxel spacing and other settings is 0.983 | ||
| + | Reflectanceof the fitted metal model is 0.9587. | ||
| + | Result from the Filmmetrics reflectance calculator is 0.9678, which is something in between. | ||
| + | This is probably also not the source of problem (however might be compared to reflectance | ||
| + | coming from FEM). | ||
| + | |||
| + | Another suspect is the voxel spacing. In the first tests for 5 nm and 10 nm voxel spacing the resulting diffraction maximum was nearly same when studied on PEC (less than 0.5 percent difference). In past we have however observed that the voxel spacing has an impact on the reflectance on real metals (not on PEC, which is ideal). | ||
| + | Too coarse mesh cannot treat the metal correctly, probably due to its small skin depth. | ||
| + | Here, in a quick check, for the fitted model we get reflectances of 0.959 for 10 nm voxel size, 0.962 for 5 nm voxel size and 0.958 for 2 nm voxel size, when roughly evaluated from the local fields. This means differences up to 1 percent. However, the difference between the expected value and the simulated value is about 20 percent. So, reflectance itself is probably also not the source of troubles. | ||
| + | |||
| + | The voxel size could impact the overall performance in more general way than only to wrong | ||
| + | reflectance. The very preliminary tests (with less accurate boundaries and other imperfections) however did not show large dependence on the voxel size, at least for reasonable voxel sizes, in the range of 3-12 nm. However, this could be still studied with the present setup. | ||
| ===== 3D calculation ===== | ===== 3D calculation ===== | ||
| - | The 3D calculation was a simple extension of the 2D case, so the voxel spacing was again 5 nm in every direction and computational domain size was 240x240x100 voxels. | + | To be completed after we are happy with the 2D case, should be simpler as 3D code is used for years already. |
| + | ===== Summary ===== | ||
| + | The sensitivity of 2D calculations results on the settings (computational domain size, time step, near-to-far field transformation, et.c) is in the order of few percent, the dominant effect of this uncertainty is the near-to-far field transformation. This does not affect the cases when these conditions are kept same in a series of calculations (so relative changes can be calculated with much higher accuracy), however it certainly affects the absolute values, e.g. when comparing a single calculation to completely different calculation or experimental data. | ||
| ===== TODO ===== | ===== TODO ===== | ||
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| The aspects that need further investigation or tuning: | The aspects that need further investigation or tuning: | ||
| * far-field calculation postprocessing speedup, now very slow, printing many debugging data. | * far-field calculation postprocessing speedup, now very slow, printing many debugging data. | ||
| - | * cross-check metal refractive index (now relying on pre-fitted database data, which is wrong) | + | * evaluate the voxel size vs. speed vs. accuracy for the benchmark, or anything else to benchmark |
| - | * there is still slight asymmetry | + | |
| - | * evaluate the voxel size vs. speed vs. accuracy for the benchmark. | + | |
docs/become.txt · Last modified: 2020/04/24 12:27 by pklapetek
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