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docs:become [2020/04/14 14:24] pklapetek |
docs:become [2020/04/19 15:42] pklapetek |
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| However, if we are interested in the maximum in some diffraction order direction, it is much simpler and it seems that this is the preferably used approach - we calculate the far field value only at the diffraction order maximum. Luckily enough, this value is dependent on the aperture only, which constructs the envelope for the diffraction pattern, so in this case one could work only with a single aperture. However, to construct the diffraction pattern is a good way how to debug the problem. | However, if we are interested in the maximum in some diffraction order direction, it is much simpler and it seems that this is the preferably used approach - we calculate the far field value only at the diffraction order maximum. Luckily enough, this value is dependent on the aperture only, which constructs the envelope for the diffraction pattern, so in this case one could work only with a single aperture. However, to construct the diffraction pattern is a good way how to debug the problem. | ||
| - | A comparison of the different evaluation methods is shown below. | + | A comparison of the different evaluation methods is shown below, also showing the first |
| + | diffraction order direction. | ||
| It shows a transmission grating that is evaluated different ways. First of all, analytical results for single aperture, for three apertures and nine apertures are shown. Results from | It shows a transmission grating that is evaluated different ways. First of all, analytical results for single aperture, for three apertures and nine apertures are shown. Results from | ||
| periodic calculation (based on a single motive) where the far field is evaluated from three | periodic calculation (based on a single motive) where the far field is evaluated from three | ||
| and nine virtual repetitions are then compared to the case where the calculation is not periodic | and nine virtual repetitions are then compared to the case where the calculation is not periodic | ||
| - | and three apertures are physically existing in the computational domain. | + | and three apertures are physically existing in the computational domain. The schematics of |
| + | the calculations is here: | ||
| + | |||
| + | {{:docs:schematics.png?600|}} | ||
| An important message is that | An important message is that | ||
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| When higher numbers of apertures are evaluated (e.g. 11), the values of the central maximum can drop and using a smaller time step helps to correct this effect. | When higher numbers of apertures are evaluated (e.g. 11), the values of the central maximum can drop and using a smaller time step helps to correct this effect. | ||
| This might be related to the far field integration (linear interpolation works better when signal is not changing so rapidly), | This might be related to the far field integration (linear interpolation works better when signal is not changing so rapidly), | ||
| - | however it is still unclear if this is the only effect.// | + | however it is still unclear if this is the only effect. The backup files for this calculation are {{ :docs:2d_transmission_aperture_backup_files.tar.gz |here}}.// |
| + | Accuracy aspects (evaluated on the single aperture transmission): | ||
| + | * effect of time step is small, prolonging it from dt=0.5 Courant limit to 0.25 does not change the shape of the curve in a detectable way. | ||
| + | * effect of absorbing boundary type smaller or distance to the boundary much smaller (mostly invisible, below percent?). The transmission around zero order is larger slightly when Liao condition is used instead of CPML. | ||
| + | * effect of NFFF box size is up to 6 percent for the maximum difference of intensities at the first diffraction order (NFFF box sizes from 100x20 to 340x130, when y size is evaluated from the aperture plane and even for maximum NFFF the boundary in x is about 200 voxels far). Smaller NFFF box seems to be better; when it is enlarged artefacts can be seen. There is always a difference between analytical model that does not go to zero for maximum angles, and numerical | ||
| + | model that goes to almost zero. | ||
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| * 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 of 0.178 | ||
| - | Dependence on problem size: | + | |
| + | 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). | ||
docs/become.txt · Last modified: 2020/04/24 12:27 by pklapetek
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