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--- docs:become [2020/04/19 15:42]
pklapetek
+++ docs:become [2020/04/22 16:58]
pklapetek
@@ Line 16: / Line 16: @@
 To test the correctness of the newly implemented code we compared a simple **transmission grating** diffraction pattern to the analytically known solution.
-There are at least two possible ways how to treat the grating in FDTD calculation. First of all, we can setup the grating physically in the computation domain, as large as possible, run the calculation and evaluated the far field response. As we are usually interested in an infinite grating response, this would mean an infinite computational domain. Instead, we can use periodic boundary conditions, compute only one motive and evaluate the far field data. This still does not provide the results if the far field data are evaluated only from the single motive, we need to evaluate it from many virtual repetitions to get the impact of some number of motives.
+Total/scattered field approach was used to inject the plane wave normally to the plane containing the aperture or multiple apertures. TE mode calculation was used, which should mean 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 transmitted 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).
+There are at least two possible ways how to treat the grating in FDTD calculation. First of all, we can setup the grating physically in the computation domain, as large as possible, run the calculation and evaluated the far field response. As we are usually interested in an infinite grating response, this would mean an infinite computational domain. Instead, we can use periodic boundary conditions, compute only one motive and evaluate the far field data. This still does not provide the results if the far field data are evaluated only from the single motive, we need to evaluate it from many virtual repetitions to get the impact of some number of motives. We call this
+//periodic NFFF// in the next text.
 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. The schematics of
+the calculations is here:
+{{:docs:schematics.png?600|}}
 A comparison of the different evaluation methods is shown below, also showing the first
-diffraction order direction.
+diffraction order direction by a vertical line.
 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. The schematics of
+and three apertures are physically existing in the computational domain.
-the calculations is here:
-{{:docs:schematics.png?600|}}
 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).
+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. For large number of periodic approach repetitions we get results that are same as analytical results.
+If we manually extend the computational domain and include all the apertures, results agree with the analytical results also for small number of apertures. See the technical explanation listed below for our reference.
 {{:docs:methods_explanation_humanized.png?600|}}
@@ Line 53: / Line 58: @@
 ----
+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.
+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
+we could compare. We could therefore only compare the periodic calculation (using field from single motive with periodic boundary conditions and periodic NFFF) and the manual calculation (big model with all the motives).
+The two models that were compared are shown below.
+{{:docs:schematics_reflection_pec.png?600|}}
+The periodic calculation was done the same
+way as for the transmission grating, only the position of the NFFF integration area was changed. I
+For the large manual calculation, in contrast to the previous case, we could not use the simple plane wave to illuminate the grating as this would lead the source to cross the NFFF domain, which leads to wrong results (all sources must be inside to get physically valid result).  We have therefore truncated the plain wave at the edges with a Gaussian decay function, so whole
+source is now inside the NFFF domain. This leads to a diffraction effect due to finite source size, which is however small and has minor impact on the result.
+The results show that the correspondence between the 19 apertures manual model and the periodic model with evaluating 19 near-field repetitions for the far field calculation are comparable to about 4 percents. Better correspondence could be obtained if the manual domain would be further extended (as seen from the smaller domain calculations trends).
+{{:docs:validation.png?800|}}
+The backup files are {{ :docs:2d_reflection_cpml_backup_files.tar.gz |here}}.
+----
-The **Become benchmark grating** was setup with voxel spacing of 5 nm in every direction. The total computational domain size was 240x100 voxels. The grating was formed by silver, using the PLRC metal handling approach. 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|}}
+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.
+All the other parameters we kept from the previous case. Normalization was again
+done via reflection from a perfect electric conductor surface.
-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.
@@ Line 88: / Line 113: @@
+===== 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 =====

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