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app:diffraction_grating
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app:diffraction_grating [2018/01/30 13:03] pklapetek |
app:diffraction_grating [2018/08/29 12:25] (current) pklapetek |
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| where p and q are aperture dimensions, r is distance from aperture to screen center, A is related to incident field amplitude and k=2π/λ where λ is the incident light wavelength. | where p and q are aperture dimensions, r is distance from aperture to screen center, A is related to incident field amplitude and k=2π/λ where λ is the incident light wavelength. | ||
| - | {{ :app:a_grating_gratingmodel.png?300|}} | + | {{ :app:a_grating_gratingmodel.png?200|}} |
| Image on the right shows scheme of the computational volume used for the simulation (a cross-section). We use a parallelepiped bounded by simple absorbing boundary conditions. A plane wave source is established using Total/Scattered field approach (TSF), but only single plane is used to excite the plane wave (all the other faces are skipped). Grating material is introduced as vector material - by using one perfect electric conductor (PEC) parallelepiped to create thin non-transparent plate and one smaller vaccum parallelepiped to create a rectangular hole in it. | Image on the right shows scheme of the computational volume used for the simulation (a cross-section). We use a parallelepiped bounded by simple absorbing boundary conditions. A plane wave source is established using Total/Scattered field approach (TSF), but only single plane is used to excite the plane wave (all the other faces are skipped). Grating material is introduced as vector material - by using one perfect electric conductor (PEC) parallelepiped to create thin non-transparent plate and one smaller vaccum parallelepiped to create a rectangular hole in it. | ||
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| Comparison can be even better done on single profile across the direction of diffraction pattern as shown below. Note the effect of limited angular resolution of the calculation which can be one of reasons of small differences (besides limited NFFF integration area and other numerical errors). | Comparison can be even better done on single profile across the direction of diffraction pattern as shown below. Note the effect of limited angular resolution of the calculation which can be one of reasons of small differences (besides limited NFFF integration area and other numerical errors). | ||
| - | {{ :app:aperture_graphs.png?400 |}} | + | {{ :app:aperture_graphs.png?600 |}} |
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| To evaluate far field scattering pattern, a periodic NFFF computational boundary is used, which means that local fields on integration boundary are copied as many times as requested, simulating much larger periodic structure. | To evaluate far field scattering pattern, a periodic NFFF computational boundary is used, which means that local fields on integration boundary are copied as many times as requested, simulating much larger periodic structure. | ||
| - | The whole pattern as simulated for grating spacing to wavelength ratio of approx 10:1 and finite size of 13x13 holes is shown below, both in normal and logarithmic scale (note that in contrast to aperture simulation results now the θ axis is the horizontal one). | + | The whole pattern as simulated for grating spacing to wavelength ratio of approx 10:1 and finite size of 13x13 holes is shown below. |
| {{ :app:simulated_grating_1313.png?400 |}} | {{ :app:simulated_grating_1313.png?400 |}} | ||
| - | {{ :app:simulated_grating_1313_logscale.png?400 |}} | + | |
| Analytically this can be written for diffraction angles θ1 (in the x direction) and θ2 (in the y direction) as | Analytically this can be written for diffraction angles θ1 (in the x direction) and θ2 (in the y direction) as | ||
| + | |||
| + | {{ :app:eq_grating.png?600 |}} | ||
| where a1 and a2 are grating hole spacing in x,y direction and N1 and N2 are number of holes in these directions; the rest of symbols is same as in aperture equation. | where a1 and a2 are grating hole spacing in x,y direction and N1 and N2 are number of holes in these directions; the rest of symbols is same as in aperture equation. | ||
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| Even if it would be in principle possible to calculate the same images also using FDTD, the number of far field points with the same resolution would be around million which is already significantly slow in present version of GSvit. Therefore we had compared result only on a single profile in x direction again, similarily to how the aperture intensity graphs were obtained. Results are show below (x axis is in degrees) | Even if it would be in principle possible to calculate the same images also using FDTD, the number of far field points with the same resolution would be around million which is already significantly slow in present version of GSvit. Therefore we had compared result only on a single profile in x direction again, similarily to how the aperture intensity graphs were obtained. Results are show below (x axis is in degrees) | ||
| + | {{ :app:a_grating_results.png?600 |}} | ||
| + | |||
| + | |||
| + | ---- | ||
| + | // | ||
| + | {{ :app:img_grating.png?120|}} | ||
| + | Sample parameter file: {{app:grating.tar.gz|transmission grating}}. | ||
| + | \\ | ||
| + | A simulation of a transmission grating with large number of far field points evaluated across whole the half space behind the grating. The resulting diffraction pattern is the last channel in the output Gwyddion file. | ||
| + | // | ||
| + | ---- | ||
app/diffraction_grating.1517313816.txt.gz · Last modified: 2018/01/30 13:03 by pklapetek
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