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Expanding scattered field into series of spherical harmonics
Currently ADDA calculates the scattered intensity for a set of scattering
angles. In certain applications, scattering function is described as a series
of spherical harmonics. Thus, simulation method should provide the
corresponding coefficients. The straightforward way is to calculate the
scattering intensity for a large set of scattering angles and then obtain
coefficients by simple numerical integration.
However, a more direct approach is also possible. Radiation of each dipole is a
trivial spherical harmonics itself. Hence, the problem transforms into
translation of spherical-harmonics expansion to a different origin. For this
problem, efficient algorithms have already been developed for multiple-sphere
T-matrix codes.
Solution of this issue may also help with issue 103.
Original issue reported on code.google.com by yurkin on 21 Dec 2011 at 9:41
- Blocking: #154, #103, #22, #51, #11
This may also provide a solution for issue 154.
Original comment by yurkin on 18 Sep 2012 at 3:44
Original comment by yurkin on 4 Jul 2013 at 9:46
- Now blocking: #154
Original comment by yurkin on 4 Jul 2013 at 9:58
- Now blocking: #103
Original comment by yurkin on 4 Jul 2013 at 10:00
- Now blocking: #22
Original comment by yurkin on 6 Jul 2013 at 10:41
- Now blocking: #51
Original comment by yurkin on 6 Jul 2013 at 10:44
- Now blocking: #11
The following paper describes another approach to calculate first several
multipoles by direct formula:
Evlyukhin A.B., Reinhardt C., and Chichkov B.N. Multipole light scattering by
nonspherical nanoparticles in the discrete dipole approximation, Phys. Rev. B
84, 235429 (2011). http://dx.doi.org/10.1103/PhysRevB.84.235429
However, an approach based on spherical-harmonics translation seems to be more
efficient.
Original comment by yurkin on 7 Jul 2013 at 9:57
Original comment by yurkin on 7 Jul 2013 at 9:57
- Added labels: Maintainability, Priority-High
- Removed labels: Priority-Medium
Actually, the above describes approaches to obtain _spherical_ and _Cartesian_
multipoles. Each of them is probably relevant for different applications.
It is interesting, whether a fast method to calculate many Cartesian multipoles
is available (similar to fast methods for translation of spherical harmonics).
Original comment by yurkin on 19 Mar 2014 at 10:54
This paper is also relevant. It uses fast-multipole method for near-to-far-field transformation in the FDTD and ray tracing. G. Tang et al., “Enhancement of the computational efficiency of the near-to-far field mapping in the finite-difference method and ray-by-ray method with the fast multi-pole plane wave expansion approach,” J. Quant. Spectrosc. Radiat. Transfer 176, 70–81 (2016) http://dx.doi.org/10.1016/j.jqsrt.2016.02.027
This can probably be done with fast spherical Fourier transform, but this assumes that we have only scattered fields already in far-field. But, in reality, we start with dipole fields (and FFT-reminding transformation to the far-field, so some other approach from the family of non-equidistant FFTs may be even more efficient.
Transformation of dipole polarizations into spherical harmonics expansion coefficients is performed in https://gitlab.com/k.czajkowski/addatmatrix/