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--- docs:become [2020/04/14 14:18]
pklapetek
+++ docs:become [2020/04/14 14:24]
pklapetek
@@ Line 9: / Line 9: @@
 ===== 2D calculation =====
-Calculations in 2D are performed using the GSvit2D solver which is an almost unused extension of GSvit to 2D calculations. As this was very outdated, most of the algorithms had to be implemented, incuding near-to-far field calculation and various materials treatment including dispersive metal treatment via PLRC algorithm. To test the correctness of the newly implemented code we compared a simple transmission grating diffraction pattern to the analytically known solution.
+Calculations in 2D are performed using the GSvit2D solver which is an almost unused extension of GSvit to 2D calculations. As this was very outdated, most of the algorithms had to be implemented, incuding near-to-far field calculation and various materials treatment including dispersive metal treatment via PLRC algorithm.
+----
+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.
 In most of the graphs here we show complete diffraction pattern.
@@ Line 25: / Line 31: @@
 {{:docs:methods_explanation_humanized.png?600|}}
-//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
+//Technical remarks: To calculate single aperture or three apertures in one computational domain 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.
+However, using periodic boundary conditions and virtual repetitions are valid only if we sum many virtual repetitions for far field calculation, at least about 7.
-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?).
+Using this approach for only few apertures (e.g. 3) leads to wrong result (even if it still looks fine at the diffraction order angle, is it only 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
+On the other hand, summing virtual repetitions without periodic BCs does not lead to anything reasonable - we have to use periodic BCs, to get the
-correct fields.
+correct fields in the near field.
-When higher orders are evaluated, 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),
 however it is still unclear if this is the only effect.//
+----
-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 **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.

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