Dear meep community,
I encounter a problem when using eigenmode-source:
The 3D simulation structure contains a waveguide along z direction which stops
at z=0 and extends to z=-infinity (pml is used at all the boundaries.) The
eigenmode source is a plane placed in the simulation region at some z < 0.
However, the Mpb does not give an eigenmode source and gives the following
error:
meep: Newton solver not converging -- need a better starting kpoint
However, when I simulate the same waveguide which extends from z=-infinity to
z=+infinity and place the planar source plane, Mpb gives the correct eigenmode
source. The initial k-points are same in thees two cases which are very close
to the k-point of the guided mode.
I am wondering about the reason of this problem. Is it related to how
eigenmode-source is built?
I would also appreciate if anyone could point out the error in my code.
Here are the ctl files for the semi-infinite waveguide and the infinite
waveguide.
ctl file for the semi-infite waveguide simulation:
(reset-meep)
(set-param! resolution 50) ;resolution is a pre-defined parameter
representing the resolution of simulation
(define-param dpml 0.4)
(define-param resol 50)
(define-param acone 0.2)
(define-param bcone 0.6)
(define-param eps_cone 12)
(define-param length-x 3)
(define-param length-y 3)
(define-param length-wg 1)
(define-param length-air 1)
(define-param length-z (+ length-wg length-air))
(define-param length-err (/ 1 resol))
(define-param lattice-x (+ length-x (* 2 dpml)))
(define-param lattice-y (+ length-y (* 2 dpml)))
(define-param lattice-z (+ length-z (* 2 dpml)))
(set! geometry-lattice (make lattice (size lattice-x lattice-y lattice-z)))
(set! pml-layers (list (make pml (thickness dpml))))
; parameters related to source
(define-param wvlen 2)
(define-param fcen (/ 1 wvlen)) ; wavelength 2um
(define-param df 0.05) ;delta_f of the gaussian beam, half width
(define-param src-cmpt Ey)
(define-param src-parity ODD-Y) ;TM
(define-param nfreq 11) ; number of frequencies to compute farfield
(define-param neff 1.9) ;effective refractive index of waveguide mode
(define-param wvg-kz (* neff (/ 1 wvlen))) ;define the k-point of the
guided mode in unit of 2*pi/a
(set! k-point (vector3 0 0 wvg-kz))
(define-param Hwg (+ length-wg dpml)) ;Height of waveguide including
the part in pml
(define list1 (list (make block (center 0 0 (/ (- Hwg lattice-z) 2))
; center of block 1/2*(Hwg - lattice-z)
(size acone bcone Hwg)
(material (make dielectric (epsilon
eps_cone))))))
(set! geometry list1)
; define the source
(set! sources (list
(make eigenmode-source
(src (make gaussian-src (frequency fcen)
(fwidth df))) ;(component src-cmpt) is comment, as the mode source contains J
and M in all directions
(center 0 0 (/ (- Hwg lattice-z) 2))
(size wvlen wvlen 0)
(component ALL-COMPONENTS)
(eig-kpoint k-point)
(eig-band 1)
(eig-match-freq? true)
(eig-parity src-parity)
(eig-lattice-size lattice-x lattice-y 0)
(eig-lattice-center 0 0 (/ (- Hwg lattice-z)
2))
) ))
(if (= src-cmpt Ex)
(set! symmetries (list (make mirror-sym (direction X)
(phase -1)) )))
(if (= src-cmpt Ey)
(set! symmetries (list (make mirror-sym (direction X)
(phase 1)) )))
; We also want to add a flux near the source
(define transmission (add-flux fcen df nfreq
(make flux-region (center 0 0 (- (* 4
length-err) (/ length-z 2)))
(size length-x length-y 0) )))
;; run the simulation
(define-param t0 (/ 5 df))
(run-sources+ (stop-when-fields-decayed 50 src-cmpt (vector3 0 0) 1e-8)
(at-beginning output-epsilon)
(if (= src-cmpt Ey)
(at-time t0 output-efield-y)
(at-time t0 output-efield-x)) )
; output the field at the time of the peak of gaussian pulse
(display-fluxes transmission)
; After simulation, use grep farfield: *.out > *.txt to extract farfield data
into file *.txt
-------------------------------------------------------
ctl file for the infinite waveguide simulation:
(reset-meep)
(set-param! resolution 50) ;resolution is a pre-defined parameter
representing the resolution of simulation
(define-param dpml 0.4)
(define-param resol 50)
(define-param acone 0.2)
(define-param bcone 0.6)
(define-param eps_cone 12)
(define-param length-err (/ 1 resol))
(define-param length-x 3)
(define-param length-y 3)
(define-param length-z (* 6 length-err))
(define-param lattice-x (+ length-x (* 2 dpml)))
(define-param lattice-z (+ length-z (* 2 dpml)))
(define-param lattice-y (+ length-y (* 2 dpml)))
(set! geometry-lattice (make lattice (size lattice-x lattice-y lattice-z)))
(set! pml-layers (list (make pml (thickness dpml))))
; parameters related to source
(define-param wvlen 2)
(define-param fcen (/ 1 wvlen)) ; wavelength 2um
(define-param df 0.05) ;delta_f of the gaussian beam, half width
(define-param src-cmpt Ey) ;source component, We still need it anyway!
(define-param src-parity ODD-Y) ;TM
(define-param nfreq 11) ; number of frequencies to compute farfield
(define-param neff 1.9) ;effective refractive index of waveguide mode
(define-param wvg-ky (* neff (/ 1 wvlen))) ;define the k-point of the
guided mode in unit of 2*pi/a
(set! k-point (vector3 0 0 wvg-ky))
(define list1 (list (make block (center 0 0 0) ; center of block
(size acone bcone lattice-z)
(material (make dielectric (epsilon
eps_cone))))))
(set! geometry list1)
(set! force-complex-fields? false)
; define the source
(set! sources (list
(make eigenmode-source
(src (make gaussian-src (frequency fcen)
(fwidth df))) ;(component src-cmpt) is comment, as the mode source contains J
and M in all directions
(center 0 0 (- 0 length-err))
(size wvlen wvlen 0)
(component ALL-COMPONENTS)
(eig-kpoint k-point)
(eig-match-freq? true)
(eig-parity src-parity)
(eig-lattice-size lattice-x lattice-y 0)
(eig-lattice-center 0 0 (- 0 length-err))
) ))
(if (= src-cmpt Ex)
(set! symmetries (list (make mirror-sym (direction X)
(phase -1)) )))
(if (= src-cmpt Ey)
(set! symmetries (list (make mirror-sym (direction X)
(phase 1)) )))
; We also want to add a flux near the source
(define transmission (add-flux fcen df nfreq
(make flux-region (center 0 0 length-err)
(size length-x length-y 0) )))
;; run the simulation
(define-param t0 (/ 5 df))
(run-sources+ (stop-when-fields-decayed 50 src-cmpt (vector3 0 0) 1e-8)
(at-beginning output-epsilon)
(if (= src-cmpt Ey)
(at-time t0 output-efield-y)
(at-time t0 output-efield-x))
(if (= src-cmpt Ey)
(at-time (+ t0 0.5) output-efield-y)
(at-time (+ t0 0.5) output-efield-x)) )
; output the field at the time of the peak of gaussian pulse
(display-fluxes transmission)
; After simulation, use grep flux1: *.out > *.txt to extract flux data into
file *.txt
---------------------------------------------------
Here are some of the outputs of MEEP:
Output of the semi-infinite waveguide simulation:
Using MPI version 3.0, 12 processes
-----------
Initializing structure...
Working in 3D dimensions.
Computational cell is 3.8 x 3.8 x 2.8 with resolution 50
block, center = (0,0,-0.7)
size (0.2,0.6,1.4)
axes (1,0,0), (0,1,0), (0,0,1)
dielectric constant epsilon diagonal = (12,12,12)
Halving computational cell along direction x
time for set_epsilon = 0.516129 s
-----------
Meep: using complex fields.
KPOINT: 0, 0, 0.95
near maximum in trace
linmin: converged after 7 iterations.
iteration 1: trace = 5.115624310137203 (198.778% change)
linmin: converged after 9 iterations.
iteration 2: trace = 1.301462483253573 (118.875% change)
linmin: converged after 6 iterations.
iteration 3: trace = 1.251212625843106 (3.93704% change)
linmin: converged after 9 iterations.
iteration 4: trace = 1.228494236027998 (1.83234% change)
linmin: converged after 6 iterations.
iteration 5: trace = 1.216128224414988 (1.01169% change)
linmin: converged after 6 iterations.
iteration 6: trace = 1.215825449143953 (0.0248998% change)
linmin: converged after 6 iterations.
iteration 7: trace = 1.215617748892674 (0.0170845% change)
linmin: converged after 12 iterations.
iteration 8: trace = 1.213850491414006 (0.145485% change)
linmin: converged after 6 iterations.
iteration 9: trace = 1.213796991469279 (0.00440755% change)
linmin: converged after 6 iterations.
iteration 10: trace = 1.213735308386204 (0.00508196% change)
linmin: converged after 6 iterations.
iteration 11: trace = 1.213661191327328 (0.00610671% change)
linmin: converged after 6 iterations.
iteration 12: trace = 1.213565335735766 (0.00789836% change)
linmin: converged after 6 iterations.
iteration 13: trace = 1.213419219406641 (0.012041% change)
linmin: converged after 10 iterations.
iteration 14: trace = 1.212962113896583 (0.037678% change)
linmin: converged after 6 iterations.
iteration 15: trace = 1.212690343386805 (0.022408% change)
linmin: converged after 7 iterations.
iteration 16: trace = 1.212341368325867 (0.0287811% change)
linmin: converged after 6 iterations.
iteration 17: trace = 1.212088318617335 (0.020875% change)
linmin: converged after 3 iterations.
iteration 18: trace = 1.212085791843462 (0.000208465% change)
linmin: converged after 3 iterations.
iteration 19: trace = 1.212085741540342 (4.15013e-06% change)
meep: Newton solver not converging -- need a better starting kpoint
--------------------------------------------------------------------------
MPI_ABORT was invoked on rank 3 in communicator MPI_COMM_WORLD
with errorcode 1.
————————————————
Output of the infinite waveguide simulation:
Using MPI version 3.0, 4 processes
-----------
Initializing structure...
Working in 3D dimensions.
Computational cell is 3.8 x 3.8 x 0.92 with resolution 50
block, center = (0,0,0)
size (0.2,0.6,0.92)
axes (1,0,0), (0,1,0), (0,0,1)
dielectric constant epsilon diagonal = (12,12,12)
Halving computational cell along direction x
time for set_epsilon = 0.649085 s
-----------
Meep: using complex fields.
KPOINT: 0, 0, 0.95
near maximum in trace
linmin: converged after 7 iterations.
iteration 1: trace = 3.874134575398054 (199.073% change)
linmin: converged after 9 iterations.
iteration 2: trace = 0.3371600882791002 (167.976% change)
linmin: converged after 4 iterations.
iteration 3: trace = 0.2725431147299467 (21.1962% change)
linmin: converged after 4 iterations.
iteration 4: trace = 0.260946907469141 (4.3473% change)
linmin: converged after 3 iterations.
iteration 5: trace = 0.2598623400796542 (0.416493% change)
linmin: converged after 3 iterations.
iteration 6: trace = 0.2596493636959499 (0.081991% change)
linmin: converged after 2 iterations.
iteration 7: trace = 0.2596191376889248 (0.0116418% change)
linmin: converged after 3 iterations.
iteration 8: trace = 0.2596124392241173 (0.00258015% change)
linmin: converged after 3 iterations.
iteration 9: trace = 0.2596112791941831 (0.000446832% change)
linmin: converged after 2 iterations.
iteration 10: trace = 0.2596111905348572 (3.41508e-05% change)
linmin: converged after 2 iterations.
iteration 11: trace = 0.2596111700800143 (7.87903e-06% change)
MPB solved for omega_1(0,0,0.95) = 0.509521 after 11 iters
Newton step: group velocity v=0.225609, kscale=0.95558
linmin: converged after 3 iterations.
iteration 1: trace = 0.250141844008388 (0.139838% change)
linmin: converged after 2 iterations.
iteration 2: trace = 0.2500453459669771 (0.0385848% change)
linmin: converged after 2 iterations.
iteration 3: trace = 0.2500400248923117 (0.00212807% change)
linmin: converged after 2 iterations.
iteration 4: trace = 0.250039253977889 (0.000308317% change)
linmin: converged after 2 iterations.
iteration 5: trace = 0.2500391834832076 (2.81934e-05% change)
linmin: converged after 2 iterations.
iteration 6: trace = 0.2500391738551966 (3.8506e-06% change)
MPB solved for omega_1(0,0,0.907801) = 0.500039 after 6 iters
Newton step: group velocity v=0.223761, kscale=0.955395
linmin: converged after 2 iterations.
iteration 1: trace = 0.2500000009975931 (3.11255e-06% change)
MPB solved for omega_1(0,0,0.907626) = 0.5 after 1 iters
Newton step: group velocity v=0.223728, kscale=0.955395
creating output file "./wg_3D_modesrc_meep_Si_Ey_kz-eps-000000.00.h5"...
on time step 17 (time=0.17), 0.236012 s/step
…
Thank you so much.
Best wishes,
Zhexin
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