Expanding scattered field into series of spherical harmonics

[GoogleCodeExporter]

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: Improve integration of Mueller matrix over phi (azimuthal angle) #154, Calculation of the T-matrix using the DDA #103, Optimize calculation of Csca and g  #22, Optimize scattered fields for large grid of angles #51, Enhance orientation averaging #11

[GoogleCodeExporter]

This may also provide a solution for issue 154.

Original comment by yurkin on 18 Sep 2012 at 3:44

[GoogleCodeExporter]

Original comment by yurkin on 4 Jul 2013 at 9:46

• Now blocking: Improve integration of Mueller matrix over phi (azimuthal angle) #154

[GoogleCodeExporter]

Original comment by yurkin on 4 Jul 2013 at 9:58

• Now blocking: Calculation of the T-matrix using the DDA #103

[GoogleCodeExporter]

Original comment by yurkin on 4 Jul 2013 at 10:00

• Now blocking: Optimize calculation of Csca and g  #22

[GoogleCodeExporter]

Original comment by yurkin on 6 Jul 2013 at 10:41

• Now blocking: Optimize scattered fields for large grid of angles #51

[GoogleCodeExporter]

Original comment by yurkin on 6 Jul 2013 at 10:44

• Now blocking: Enhance orientation averaging #11

[GoogleCodeExporter]

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

[GoogleCodeExporter]

Original comment by yurkin on 7 Jul 2013 at 9:57

• Added labels: Maintainability, Priority-High
• Removed labels: Priority-Medium

[GoogleCodeExporter]

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

[myurkin]

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

[myurkin]

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.

[myurkin]

Transformation of dipole polarizations into spherical harmonics expansion coefficients is performed in https://gitlab.com/k.czajkowski/addatmatrix/