> On Nov 2, 2020, at 11:49 AM, Mandy Xia <m...@cornell.edu> wrote:
> Thank you so much Steven for this step-by-step explanation! It makes much
> more sense to me now.
>
> Regarding the actual field calculation, I noticed that green3d uses the point
> source field computation from a dielectric dipole moment (adopted from
> SCUFF-EM with some modification that changes eclectic dipole moment to
> current). I was wondering when we use the point source formula
> (http://homerreid.github.io/scuff-em-documentation/reference/IncidentFields/
> <http://homerreid.github.io/scuff-em-documentation/reference/IncidentFields/>)
> for near to far field calculation, whether we can drop the higher-order
> terms since we are in the far field (MEEP still keeps them).
You're right that, far enough away, only the leading-order 1/r terms will
matter. However, technically the "near-to-farfield" transformation can be
evaluated anywhere in space, not just in the far field, thanks to the
Equivalence Principle. So, we keep all of the terms just in case someone
evaluates a point close enough for their contributions to matter.
In the future, a possible optimization would be to preprocess the far-field
points and check that they are far enough away to drop the higher-order terms,
and if so call a simplified Green's function. But I'm not sure how much this
would actually matter in practice.
> Also, I wonder if there is a reference I could look up the derivation of this
> point source formula. I'm trying to understand whether it is equivalent to
> the other from shown in other references, e.g.
> https://en.wikipedia.org/wiki/Electric_dipole_moment#Potential_and_field_of_an_electric_dipole
>
> <https://en.wikipedia.org/wiki/Electric_dipole_moment#Potential_and_field_of_an_electric_dipole>.
That Wikipedia article is for the electrostatic field, which is different from
the field of an oscillating dipole (also called a "dipole antenna").
You can find lots of references for the field of a dipole antenna; e.g.
Jackson's Classical Electrodynamics book covers the topic.
> This question might be too much of detail, but I'm trying to implement a near
> to far field calculation for a periodic structure that uses the spectral
> representation of the periodic green's function to avoid the slow convergence
> when summing spatially so I want to make sure I understand all the details.
SCUFF-EM implements a Ewald summation for this case; see:
https://github.com/HomerReid/scuff-em/blob/324bfd2c88a663b062f547184c666752075f9128/doc/docs/tex/EwaldTake1.tex
<https://github.com/HomerReid/scuff-em/blob/324bfd2c88a663b062f547184c666752075f9128/doc/docs/tex/EwaldTake1.tex>
https://github.com/HomerReid/scuff-em/blob/324bfd2c88a663b062f547184c666752075f9128/libs/libscuff/GBarVDEwald.cc
<https://github.com/HomerReid/scuff-em/blob/324bfd2c88a663b062f547184c666752075f9128/libs/libscuff/GBarVDEwald.cc>
We discussed porting it to Meep (https://github.com/NanoComp/meep/pull/769
<https://github.com/NanoComp/meep/pull/769>) but haven't worked on it yet._______________________________________________
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