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Calculation of the T-matrix using the DDA
It is possibly to calculate T-matrix using the DDA, which can be used for
repeated simulation of different particle orientations. Originally it was
proposed by Dan Mackowski in 2002 - http://dx.doi.org/10.1364/JOSAA.19.000881 .
However, the procedure was quiet cumbersome.
Recently, Dan showed that it can be significantly simplified by using
plane-wave spectrum instead of spherical harmonics. Details can be found at ELS
12 proceedings http://www.helsinki.fi/els/articles/38/ . It probably will also
be published in special JQSRT issue after this conference.
So that is an interesting idea to implement. However, it is still not trivial.
To perform such calculation efficiently, significant changes of the code
internals are required. Moreover, in many cases T-matrix is not really needed.
For example, if one wants to perform orientation averaging it is probably
faster to do it directly by a quadrature than to calculate T-matrix and use
analytical formulae. The most viable application for T-matrix calculation seems
to be databases. Complete information about the particle can be stored in a
relatively small T-matrix, which can be further used to obtain any light
scattering patterns for any particle orientation.
Original issue reported on code.google.com by yurkin on 12 Jul 2010 at 5:41
- Blocked on: #138
This may be especially useful for metallic nanoparticles, when order of the
T-matrix is relatively small, while Niter can be up to a few thousands. Then
calculating T-matrix and performing analytical orientation averaging may be
faster than doing straightforward orientation averaging by multiple DDA
simulations.
Original comment by yurkin on 6 Jan 2011 at 7:23
Spherical-harmonics expansion of the scattered field can help.
Original comment by yurkin on 4 Jul 2013 at 9:58
- Now blocked on: #138
Another related idea is compressive sensing, see e.g. Carin L., Liu D., Lin W., and Guo B. Compressive sensing for multi-static scattering analysis, J. Comput. Phys. 228, 3464–3477 (2009).
Such calculation with ADDA (using plane-wave excitation) has been performed in Stilgoe A.B., Nieminen T.A., and Rubinsztein-Dunlop H. Controlled transfer of transverse orbital angular momentum to optically trapped birefringent microparticles, Nat. Photon., 1–6 (2022).