My question is how to calculate the flux spectrum in cylindrical coordinate.
For example I have a point dipole at origin:

(set! sources (list
                (make source
                (src (make gaussian-src (frequency fcen) (fwidth df)))
                (component Ez) (center 0 0 0) (size 0 0 0)))
)

Now I want to calculate the flux spectrum of it trough a 3d cylindrical box:

(define F1
(add-flux fcen df nfreq
(make flux-region (center 0.07 0 0) (size 0 (* 2 pi) 1.1) (direction R))))

(define F2
(add-flux fcen df nfreq
(make flux-region (center 0 0 0.55) (size 0.14 (* 2 pi) 0) (direction Z))))

(define F3
(add-flux fcen df nfreq
(make flux-region (center 0 0 -0.55) (size 0.14 (* 2 pi) 0) (direction Z))))

So basically I want to get the dipole radiation in the cylindrical
coordinate. The flux across the top and bottom sides (direction z) seem OK.
But the flux through the circular side wall has some issue. The spectrum is
partially positive and partially negative. I tried dividing the circular
wall into two half circles:

(define F1
(add-flux fcen df nfreq
(make flux-region (center 0.07 0 0) (size 0 (* 1 pi) 1.1) (direction R))))

(define F4
(add-flux fcen df nfreq
(make flux-region (center -0.07 0 0) (size 0 (* 1 pi) 1.1) (direction R))))

And tried to add them together. The flux spectrum is mostly positive now but
still has some negative region. Moreover, I set the area size along phi
direction to zero rather than pi or 2*pi, and got the same result. I'm
totally confused here. Any thoughts? Thanks.
 






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