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app:diffraction_grating
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app:diffraction_grating [2018/01/30 12:41] pklapetek |
app:diffraction_grating [2018/01/30 12:58] pklapetek |
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| ==== Transmission through single aperture ==== | ==== Transmission through single aperture ==== | ||
| + | {{:app:aperture.png?200 |}} | ||
| First, consider a single hole in an opaque screen - rectangular aperture. If a light is illuminating the screen on the other side a diffraction pattern is formed behind it (and can be seen on the screen located behind). With smaller ratio between aperture size and wavelength this effect becomes more pronouced and angular spacing between diffraction maxima is larger. | First, consider a single hole in an opaque screen - rectangular aperture. If a light is illuminating the screen on the other side a diffraction pattern is formed behind it (and can be seen on the screen located behind). With smaller ratio between aperture size and wavelength this effect becomes more pronouced and angular spacing between diffraction maxima is larger. | ||
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| If we consider x and y as axes on the screen where diffraction pattern is seen, the intensity space distribution varies as | If we consider x and y as axes on the screen where diffraction pattern is seen, the intensity space distribution varies as | ||
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| + | {{ :app:eq_aperture.png?300 |}} | ||
| 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|}} | ||
| 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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| 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, both in normal and logarithmic scale (note that in contrast to aperture simulation results now the θ axis is the horizontal one). | ||
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| + | Analytically this can be written for diffraction angles θ1 (in the x direction) and θ2 (in the y direction) as | ||
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| + | 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) | ||
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app/diffraction_grating.txt · Last modified: 2018/08/29 12:25 by pklapetek
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