QPMS
Electromagnetic multiple scattering library and toolkit.

*** This tutorial is partly obsolete, the interpolators are no longer the first choice of getting the Tmatrices. ***
The main C API for finite systems is defined in scatsystem.h, and the most relevant parts are wrapped into python modules. The central data structure defining the system of scatterers is qpms_scatsys_t, which holds information about particle positions and their Tmatrices (provided by user) and about the symmetries of the system. Specifically, it keeps track about the symmetry group and how the particles transform under the symmetry operations.
Let's have look how thinks are done on a small python script. The following script is located in misc/201903_finiterectlat_AaroBEC.py
.
Let's have a look at the imports.
Particle
is a wrapper over the C structure qpms_particle_t
, containing information about particle position and Tmatrix.CTMatrix
is a wrapper over the C structure qpms_tmatrix_t
, containing a Tmatrix.BaseSpec
is a wrapper over the C structure qpms_vswf_set_spec_t
, defining with which subset of VSWFs we are working with and how their respective coefficients are ordered in memory. Typically, this just means having all electric and magnetic VSWFs up to a given multipole order lMax
in the "standard" ordering, but other ways are possible. Note that different Particle
s (or, more specifically, CTMatrix
es) can have different BaseSpec
s and happily coexist in the same ScatteringSystem
. This makes sense if the system contains particles with different sizes, where the larger particles need cutoff at higher multipole orders.FinitePointGroup
is a wrapper over the C structure qpms_finite_group_t
containing info about a 3D point group and its representation. Its contents are currently not generated using C code. Rather, it is populated using a SVWFPointGroupInfo
instance from the point_group_info
python dictionary, which uses sympy to generate the group and its representation from generators and some metadata.ScatteringSystem
is a wrapper over the C structure qpms_scatsys_t
, mentioned earlier, containing info about the whole structure.TMatrixInterpolator
in a wrapper over the C structure qpms_tmatrix_interpolator_t
which contains tabulated Tmatrices (calculated e.g. using scufftmatrix
) and generates frequencyinterpolated Tmatrices based on these.eV
, hbar
, c
are numerical constants with rather obvious meanings.Let's go on:
The D2h
choice indicates that our system will have mirror symmetries along the xy, xz and yz axes. Using the BaseSpec
with the standard constructor with lMax = 2
we declare that we include all the VSWFs up to quadrupole order. Next, we create a TMatrixInterpolator
based on a file created by scufftmatrix
. We force the symmetrisation of the Tmatrices with the same point group as the overall system symmetry in order to eliminate the possible asymmetries caused by the used mesh. The atol
parameter just says that if the absolute value of a given Tmatrix element is smaller than the atol
value, it is set to zero.
This chunk sets the light frequency and array size based on a command line argument. Then it generates a list of particles covering a quarter of a rectangular array. Finally, these particles are used to generate the final scattering system – the rest of the particles is generated automatically to satisfy the specified system symmetry.
The last part iterates over the irreducible representations of the systems. It generates scattering problem LHS (TODO ref) matrix reduced (projected) onto each irrep, and performs SVD on that reduced matrix, and saving the lowest singular values (or all singular values smaller than sv_threshold
) together with their respective singular vectors to files.
The singular vectors corresponding to zero singular values represent the "modes" of the finite array.
TODO analyzing the resulting files.
Examples of how the data generated above can be analysed can be seen in the jupyter notebooks from the qpms_ipynotebooks repository in the AaroBEC
directory.