Dear Meep users and Dear Prof. Johnson,
I'd like to check the attenuation and phase shift of a plane wave to
understand if I'm setting the material parameters correctly.
My unit is a=1e-2 and my central frequency is 6Ghz, hence 0.2 in Meep units.
My material epsilon=100 and sigma=4 [S/m].
In Meep this means epsilon=100 and
d-conductivity=a/c*4/100/epsilon_0=0.0094 (right?)
I'm using this code to create the plane wave:
==== code start ====
(define-param sxc 40) ; the x size of the computational cell, not including PML
(define-param syc 50) ; the x size of the computational cell, not including PML
(define-param dpml 1) ; thickness of PML layers
(define sx (+ sxc (* 2 dpml))) ; cell size, including PML
(define sy (+ syc (* 2 dpml))) ; cell size, including PML
(set! geometry-lattice (make lattice (size sx sy no-size)))
(set! default-material (make dielectric (epsilon 100)
(D-conductivity 0.0094)
(mu 1)
))
(set! pml-layers (list (make pml (thickness dpml))))
(set-param! resolution 15)
(define-param fcen 0.2) ; pulse center frequency
(define-param df 0.1) ; turn-on bandwidth
(set! sources
(list
(make source
(src (make continuous-src (frequency fcen) (fwidth df)))
(component Ez) (center -19 0) (size 0 sy)
)
)
)
(define-param T 250) ; run time
(run-until T
(at-end output-efield-z)
(to-appended "src" (at-every 0.2 (in-point (vector3 -19 0)
output-efield-z)))
(to-appended "tgt-1" (at-every 0.2 (in-point (vector3 -14 0)
output-efield-z)))
(to-appended "tgt-2" (at-every 0.2 (in-point (vector3 -9 0)
output-efield-z)))
)
==== code stop ====
as you can see the source is at -19cm, and the 2 points where I'm
looking at at -14cm and -9cm. the distance between this 2 points is
5cm.
from Pozar, I calculated the complex propagation factor as:
k = j * 2 * pi * f * sqrt( mu0 * (er * e0 - j * sigma / (2 * pi * f) ) )
the expected attenuation is -2.04dB and I get -2.24dB
given the peak of the wave at 9cm, I expect that peak to be in the
wave at 14cm t=imag(k)/omega * 5cm = 1.6674e-9. however there is no
peak at that point
what s happening? why I cant verify mathematically what Im looking for?
is the way I'm generating the plane wave good enought to do this calculation?
Thanks to everybody who can help me!
Matteo
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