Hi,
I am using Maetzlers Mie Scattering Script from 2002 to calculate Phase Matrix entries. But under no conditions I am able to produce imaginary scattering amplitudes S1 and S2 which is kind of strange to me because in the phase matrix they produce the side entries. I know that some side entries vanish for spheres - or do they all actually?
So my question is basically: What are the conditions of imaginary scattering amplitudes.
Thank you and best regards
Thorsten Beuth
Thorsten,
If we speak of the first Mie coefficients a_1 and b_1, they corerspond to electric and magnetic dipole polarizabilities through a simple relation, respectively (\alpha_E = i a_1 times some factor whch I do not remember). Now, recall that for a passive system there always exists radiation correction, which causes the dipole polarizabilities to be not real valued (even for a lossless medium). Therefore, a_1 or b_1 can not be purely imaginary.
However, there may be an extreme case, when scattering by a spherical particle into a certain partial mode is completely suppressed, so that the corersponding Mie coefficient becomes zero [see Ref below], which is of course purely imaginary.
Article Nonradiating anapole modes in dielectric nanoparticles
Thank you very much, Dennis! I am going to have a look into the article in the weekend and have some thoughts about it.
Thorsten,
if you want to know more about specific constraints imposed on Mie coefficients, you might also want to look at the following very nice papers by A Alu:
Article Physical Bounds on Absorption and Scattering for Cloaked Sensors
Article Minimum-scattering superabsorbers
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