LDR coefficients for arbitrary lattice

[myurkin]

As a continuation of the work on rectangular dipoles #196, it is desirable to calculate LDR coefficients (for point-dipole formulation) for any dipole ratios. This can replace even the standard LDR coefficients for cubic dipoles.

All formulae (lattice sums) are in Appendix B of Smunev D.A., Chaumet P.C., and Yurkin M.A. Rectangular dipoles in the discrete dipole approximation, J. Quant. Spectrosc. Radiat. Transfer 156, 67–79 (2015). (PDF) see R0(mu) and R3(mu,nu)

[myurkin]

Proof-of-principle is available at https://github.com/VadimBelkin/adda/tree/DraineCoefficients

[myurkin]

I have managed to compute the original LDR coefficients (b1,b2,b3) with arbitrary precision. In particular, ADDA now contains them up to 35 significant digits (887a63c)

[myurkin]

This seems to be related to the lattice sums in Rahmani A., Chaumet P.C., and Bryant G.W. Local-field correction for an interstitial impurity in a crystal, Opt. Lett. 27, 430–432 (2002). Those are important when a point source is placed inside a particle, leading to a position-dependent correction factor. The latter may also need to be calculated in ADDA, and the paper refers to a few works, which may guide the efficient evaluation.