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MEEP: Export fluxes and DFT data

Fluxes, with flux objects

The function to save the dft data in human readable form (well, with the help of MATLAB) is called pretty-save-flux, and is called like

(pretty-save-flux "filename" fx)

where fx is a flux object. Also see the example [test ctl] file for an example how to use it and some output. The [test ctl] file contains a single dipole in vacuum, and 3 flux objects are created, one in each principal direction. After the simulation, the 3 flux objects are exported to disk and one can find 3 HDF5 files, each containing the appropriate E- and H-fields (real and imaginary parts) for each flux object, for just as many frequencies as are specified in the ctl file.

Quirks with flux export

1. When exporting fluxes to disk, the data is always exported such, that multiplying, in a point-wise fashion, the relevant e-field and h-field components and summing the resulting matrix over all rows and columns gives the flux. In MATLAB language: assume Ex and Ey are 2d
   matrices containing the x-component and y-component of the electric field, as exported from the computer memory to disk. Similarly, assume Hx and Hy to be the same for the H-field. Then the total flux is given by sum(sum(Ex.*Hy+Ey.*Hx)). Note the plus, and not a minus. This is due to MEEP, as it creates flux objects that internally weigh the 2nd electric field component with a negative factor.

2. Related to the above, the 2nd exported electric field component is exported with an additional -1 factor. Therefore, to get the actual electric field component, multiply that component with -1. These fields are:

   • Flux in x-direction: Ez
   • Flux in y-direction: Ex
   • Flux in z-direction: Ey

3. When exporting fluxes, the electric field component is exported with the necessary weights to include the surface area/volume.

4. when a flux plane is defined between grid points, MEEP will use 2 planes with DFT data, both located on grid points, and weigh them accordingly such that the fluxes shown with (display-fluxes ...) correspond with the flux at the requested position. When this data is saved by the function I've introduced, both DFT planes are exported including the proper weight factors. For a DFT on a plane, this means that 3D data is exported. Sum the data in this 3rd dimension to get the DFT on the desired plane. In the most extreme case, when the flux at a single point is requested, internally MEEP can up to 8 points. All 8 points will be exported.

5. Adding multiple flux regions to a single flux object, and then exporting it, is not supported!

6. Exporting flux objects when periodic boundary conditions are in use is not tested by me! However, I think it should work.

7. I haven't tested cylindrical coordinates.

8. Symmetry: in contrast to the normal output-Xfield functions, the exported data just contains the contents in memory. This means that if symmetry planes are used, you don't get the full solution on disk, but just the part that is actually calculated. You have to unfold the symmetry yourself. This is because I simply didn't get how in the source code the output-Xfield functions take care of the symmetry.

Quirks 2-4 are actually just because of the way MEEP sets up the flux
objects and the corresponding DFT objects. Nothing to worry about, but
something one should know.

DFTs, with DFT objects

Finally, it should be possible to directly add DFT objects instead of using flux objects with

(define mydft (meep-fields-add-dft Ez (volume (size ...) (center ...)) freqmin freqmax Nfreq false))

source: http://article.gmane.org/gmane.comp.science.electromagnetism.meep.general/2834/match=add_dft

But I got errors ("No matching method for generic function `meep_fields_add_dft'"). If anyone finds out how to to this, the dft should be exported to disk with

(pretty-save-dft "ez" mydft)

but I couldn't test this. The benefit of using DFT objects over flux objects is that you can simply specify the component you're interested in and save the memory and computational load for components that do not matter.

Update: it seems that the correct syntax for adding a DFT object is not to specify a volume, but a volume list. Not tested so far.

Hacking/Improving

Most of the modifications of MEEP are in dft.cpp, but some too in meep.hpp. Also, meep.scm and meep.scm.i are modified (I don't know if both are necessary to modify) to have a nice scheme function.