User Tools
docs:become
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision Next revision Both sides next revision | ||
|
docs:become [2020/04/22 15:28] pklapetek |
docs:become [2020/04/22 22:08] pklapetek |
||
|---|---|---|---|
| Line 60: | Line 60: | ||
| 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 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 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 | ||
| + | the far field point corresponding to surface normal direction. | ||
| Here, we don't have any analytical result to which | Here, we don't have any analytical result to which | ||
| Line 83: | Line 84: | ||
| The **Become benchmark grating** was setup the same way as the above test example. | The **Become benchmark grating** was setup the same way as the above test example. | ||
| - | The grating was now formed by silver, using the PLRC metal handling approach. | + | The grating was now formed by silver, using the PLRC metal handling approach. |
| + | All the other parameters we kept from the previous case. Normalization was again | ||
| + | done via reflection from a perfect electric conductor surface. | ||
| - | Periodic boundary conditions were used to introduce the grating periodicity. Total/scattered field approach was used to inject the plane wave normally to the surface. TE mode calculation was used for this 2D case, which should be the p-polarisation case as requested. Near-to-far field calculation domain was set up to be outside of the plane wave source region, so only reflected and scattered electric field was propagated to the far-field. Time domain far field calculation was used. Far field data were calculated for wide range of angles for debugging purposes (i.e. not only for the directions of the particular diffraction orders). | ||
| - | The model setup and a calculation snapshot of the periodic area are shown in the following figure. | ||
| - | The far field was evaluated from a fixed number of repetitions of the near-field values, the presented results therefore represent scattering by a finite size grating. The far field value in the direction of the maxima is however not affected by size of grating (number of repetitions), only its sharpness is affected. | ||
| - | {{:docs:model.png?600|}} | ||
| - | |||
| - | |||
| - | To get the data normalization to the incident wave intensity we used a similar model where the grating was replaced by a perfect electric conductor plane. The electric field intensity in | ||
| - | the far field point corresponding to surface normal direction was evaluated and used as a reference | ||
| - | in all the other calculations. | ||
| 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 0.178). 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. | ||
| Line 107: | Line 108: | ||
| 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. |
| - | 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). | + | Another suspect is the voxel spacing. However, at least for 5 nm and 10 nm voxel spacing the resulting diffraction maximum was nearly same (less than 0.5 percent difference). |
| ===== 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 ===== | ||
| Line 125: | Line 127: | ||
| 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
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Noncommercial 4.0 International
