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| In most of the graphs here we show complete diffraction pattern. | In most of the graphs here we show complete diffraction pattern. | ||
| 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. | ||
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| + | A comparison of the different evaluation methods is shown below. | ||
| + | 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 | ||
| + | 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. | ||
| + | |||
| + | An important message is that | ||
| + | using the periodic approach for only a small number of repetitions does not work as it does not take into account the field on sides of the computational domain (see the technical explanation listed below for our reference). | ||
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| + | {{:docs:methods_explanation_humanized.png?600|}} | ||
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| + | //Technical remarks: To calculate single aperture correctly it is important to add the side boundaries. It is also crucial to use CPML throughout all the | ||
| + | calculations, otherwise we get everything dependent on the computational volume. | ||
| + | If we manually setup the few apertures grating, result corresponds to the theory. | ||
| + | However, using periodic boundary conditions and virtual repetitions are valid only if we sum many virtual repetitions for far field calculation. | ||
| + | Using this approach for only few apertures (e.g. 3) leads to wrong result (even if it looks fine at the diffraction order angle, by chance?). | ||
| + | On the other hand, summing virtual repetitions without periodic BCs does not lead to anything reasonable, we have to have them, to get the | ||
| + | correct fields. | ||
| + | When higher orders are evaluated, 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), | ||
| + | however it is still unclear if this is the only effect.// | ||
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docs/become.txt ยท Last modified: 2020/04/24 12:27 by pklapetek
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