ECE 695 Numerical Simulations Lecture 31 - Purdue...
Transcript of ECE 695 Numerical Simulations Lecture 31 - Purdue...
ECE 695Numerical Simulations
Lecture 31: Finite-Difference Time Domain Band Structures
Prof. Peter Bermel
April 3, 2017
Recap from Friday: MEEPPV Graphical User Interfacehttps://nanohub.org/tools/meeppv
Click here to select 2D/3D solar cell for simulation
You will be directed to
this page if the
graphical user
interface (first option)
is selected.
Users can input
parameters that
describe the solar cell
features as well as the
simulation domain.
2
Outline
• Photonic Crystal Waveguides:
– Photonic Bandstructure
– Defect Resonant Modes
– Waveguide Transmission
• Inverse Opal Photonic Crystals:
– Photonic Band structures
– Photonic Crystal Phosphors
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Photonic Bandstructure(define-param eps 13) ; dielectric constant of waveguide(define-param w 1.2) ; width of waveguide(define-param r 0.36) ; radius of holes (define-param sy 12) ; size of cell in y direction (perp. to wvg.)(define-param dpml 1) ; PML thickness (y direction only!)(set! geometry-lattice (make lattice (size 1 sy no-size)))(set! geometry (list (make block (center 0 0)
(size infinity w infinity)(material (make dielectric (epsilon eps))))
(make cylinder (center 0 0) (radius r)(height infinity) (material air))))
(set-param! resolution 20)(set! pml-layers (list (make pml (direction Y) (thickness dpml))))
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Our 1x12 unit cell
𝑤 2𝑟
𝑑𝑝𝑚𝑙
4
Photonic Bandstructure(define-param fcen 0.25) ; pulse center frequency(define-param df 1.5) ; pulse frequency width(set! sources (list (make source (src
(make gaussian-src (frequency fcen)(fwidth df))) (component Hz) (center 0.1234 0))))
(set! symmetries (list (make mirror-sym (direction Y) (phase -1))))(set-param! k-point (vector3 0.4 0))(run-sources+ 300 (after-sources (harminv Hz (vector3 0.1234) fcen df)))(define-param k-interp 19)(run-k-points 300 (interpolate k-interp (list (vector3 0) (vector3 0.5))))
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Photonic Bandstructure
• Output frequencies at each 𝑘𝑥 – for example:freqs:, 14, 0.325, 0.0, 0.0, 0.171671252741341, 0.319717964514696,
0.323470450791478freqs-im:, 14, 0.325, 0.0, 0.0, -8.74808991364674e-8, 1.82230861728163e-4, 0.00144227925408331 • Extract frequency lines via grep:unix% meep holey-wvg-bands.ctl | tee holey-wvg-bands.outunix% grep freqs: holey-wvg-bands.out > fre.datunix% grep freqs-im: holey-wvg-bands.out > fim.dat
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Defect Resonant Modes
N holes on each side surround a defect cavity of size d (in units of a)
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Defect Resonant Modes(define-param eps 13) ; dielectric constant of waveguide(define-param w 1.2) ; width of waveguide(define-param r 0.36) ; radius of holes(define-param d 1.4) ; defect spacing (ordinary spacing = 1)(define-param N 3) ; number of holes on either side of defect(define-param sy 6) ; size of cell in y direction (perpendicular to wvg.)(define-param pad 2) ; padding between last hole and PML edge(define-param dpml 1) ; PML thickness(define sx (+ (* 2 (+ pad dpml N)) d -1)) ; size of cell in x direction(set! geometry-lattice (make lattice (size sx sy no-size)))(set! geometry (append ; combine lists of objects:
(list (make block (center 0 0) (size infinity w infinity)(material (make dielectric (epsilon eps)))))
(geometric-object-duplicates (vector3 1 0) 0 (- N 1) (make cylinder(center (/ d 2) 0) (radius r) (height infinity) (material air)))
(geometric-object-duplicates (vector3 -1 0) 0 (- N 1) (make cylinder(center (/ d -2) 0) (radius r) (height infinity) (material air)))))
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Defect Resonant Modes
(set! pml-layers (list (make pml (thickness dpml))))(set-param! resolution 20) (define-param fcen 0.25) ; pulse center frequency(define-param df 0.2) ; pulse width (in frequency)(set! sources (list (make source (src (make gaussian-src (frequency fcen) (fwidth df))) (component Hz) (center 0 0)))) (set! symmetries (list (make mirror-sym (direction Y) (phase -1)) (make mirror-sym (direction X) (phase -1))))(run-sources+ 400 (at-beginning output-epsilon) (after-sources (harminv Hz (vector3 0) fcen df)))(run-until (/ 1 fcen) (at-every (/ 1 fcen 20) output-hfield-z))
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Defect Resonant Modes
• Create a movie of defect mode over time:
unix% h5topng -RZc dkbluered -C holey-wvg-cavity-eps-000000.00.h5 holey-wvg-cavity-hz-*.h5
unix% convert holey-wvg-cavity-hz-*.png holey-wvg-cavity-hz.gif
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Defect Resonant Modes
• Determine quality factor versus number of holes:unix% meep N=4 compute-mode?=true holey-wvg-cavity.ctl |grep harminvunix% meep N=5 compute-mode?=true holey-wvg-cavity.ctl |grep harminv...
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Defect Resonant Modes• For large N, a second mode is observed…harminv0:, frequency, imag. freq., Q, |amp|, amplitude, errorharminv0:, 0.235201161007777, -1.34327185513047e-5, 8754.78631184943, 9.83220617825986, 6.83285024080876-7.06996717944934i, 3.03237056700397e-9harminv0:, 0.328227374843021, -4.6405752015136e-4, 353.649451404175, 0.134284355228178, -0.131856646632894-0.0254187489419837i, 4.11557526694386e-7• Generate field profile in time for extended mode at band edge:unix% meep sy=12 fcen=0.3282 df=0.01 N=16 holey-wvg-cavity.ctl
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Waveguide Transmission
(define-param nfreq 500) ; num. frequencies at which to compute flux (set! sources (list (make source (src (make gaussian-src
(frequency fcen) (fwidth df))) (component Ey)(center (+ dpml (* -0.5 sx)) 0) (size 0 w))))
(set! symmetries (list (make mirror-sym (direction Y) (phase -1))))(define trans ; transmitted flux
(add-flux fcen df nfreq(make flux-region (center (- (* 0.5 sx) dpml 0.5) 0) (size 0 (* w 2)))))
(run-sources+ (stop-when-fields-decayed 50 Ey (vector3 (- (* 0.5 sx) dpml 0.5) 0) 1e-3)(at-beginning output-epsilon)(during-sources (in-volume (volume (center 0 0) (size sx 0)) (to-appended "hz-slice" (at-
every 0.4 output-hfield-z)))))(display-fluxes trans) ; print out the flux spectrum
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Waveguide Transmission
• View 𝐻𝑧 field over space and time:unix% meep holey-wvg-cavity.ctl | tee holey-wvg-cavity.outunix% h5topng holey-wvg-cavity-eps-000000.00.h5unix% h5topng -Zc dkbluered holey-wvg-cavity-hz-slice.h5
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𝑡
𝑥
14
Waveguide Transmission
• Transmission spectrum computed as ratio:unix% meep N=0 holey-wvg-cavity.ctl | tee holey-wvg-cavity.out0unix% grep flux1: holey-wvg-cavity.out > flux.datunix% grep flux1: holey-wvg-cavity.out0 > flux0.dat unix% divide2.pl flux0.dat flux.dat > flux-q.dat
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SiO2 Opal Films• Opal films are polycrystalline, 10 m thick, FCC films
with the (111) planes oriented parallel to the surface.
• For visible spectrum, lattice constant ~ 140 – 500 nm.
300 nm1 µm
E. Graugnard et al., Photonic Crystals at Georgia Tech, www.nanophotonics.gatech.edu/PCs_at_GaTech.ppt
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Inverse Opal:Fabrication
• Self-assembled silica opal template
– 10 μm thick FCC polycrystalline film, (111) oriented.
• Infiltration of opal with high index materials
– ZnS:Mn n~2.5 @ 425 nm (directional PBG)
– TiO2 (rutile) navg~ 3.08 @ 425 nm (omni-directional PBG)
Sintered Opal Infiltrated Opal Inverted Opal
Self Assembly ALD Etch
E. Graugnard et al., Photonic Crystals at Georgia Tech, www.nanophotonics.gatech.edu/PCs_at_GaTech.ppt
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ALD of TiO2 at 100ºC
433 nm opal infiltrated with TiO2
433 nm TiO2 inverse opal
(111)
• TiO2 infiltration at 100ºC produces very smooth and conformal
surface coatings with rms roughness ~2Å.
• Heat treatment (400C, 2 hrs.) of infiltrated opal converts it to
anatase TiO2, increasing the refractive index from 2.35 to 2.65,
with only a 2Å increase in the rms surface roughness.
Cross-sections
E. Graugnard et al., Photonic Crystals at Georgia Tech, www.nanophotonics.gatech.edu/PCs_at_GaTech.ppt
2 µm
433 nm TiO2 inverse opal
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Specular Reflectivity• Measurements: 15° from normal
• Probes changes in -L photonic band structure (111)
400 600 800 10000.0
0.2
0.4
0.6
0.8
1.0
Norm
aliz
ed R
eflectivity
Wavelength (nm)
(a) (c) (b)
330 nm opal
ZnS:Mn
200 nm opal
TiO2
200 300 400 500 600 700 800
(c)
No
rmaliz
ed R
eflectivity
Wavelength (nm)
(a)(b)
-L PPBGs -L PPBGsFlat band peaksFlat band peaks
sintered
as-infiltrated
inverse opals
E. Graugnard et al., Photonic Crystals at Georgia Tech, www.nanophotonics.gatech.edu/PCs_at_GaTech.ppt4/3/2017 ECE 695, Prof. Bermel 19
Photonic Crystal Band Diagramω vs. k as calculated from Finite-difference time domain (FDTD)
• Photonic band gaps (PBG)
• Pseudo-photonic band gaps (PPBG)
• Flat bands, low group velocity
• Superprism and giant refraction
Photonic Bands of inverted 3D Si-air PC
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
k-vector
No
rm
ali
zed
Freq
uen
cy
X U L W
mse6059
Source-->Exec.
metalpc.f90 --> metalpc
This file:
\My documents\GT project\PcP
project\FDTD\defect\band
diagram\band diagram air_Si.xls
# ixmax= 20
# iymax= 20
# izmax= 20
# dx=1
# ikmax= 16
# nmax =32768
# n_pts_store=16
# radius=0.5
# eps_b=11.9
# eps_s=1
# sig_b=0
# sig_s=0
FPBG ratio=3.5%
K
PPBG FCC Brillouin zone
UPBG
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Inverse Opal Reflectivity300
400
500
600
700
800
900
1000
1100
Wa
ve
len
gth
(n
m)
L
Normalized Reflectivity Band Diagram
2-3 PPBG
Fabry-Perot
fringes
Flat band peaks
400
500
600
700
800
900
1000
1100
Wa
ve
len
gth
(n
m)
L
Normalized Reflectivity Band Diagram
2-3 PPBG
Flat band
peaks
300
400
500
600
700
800
900
1000
10-11
PPBG's
Wa
ve
len
gth
(n
m)
Normalized Intensity
L
Band Diagram
2-3 PPBG
5-68-9
• TiO2 infiltration of 330 nm opal.• ~88% filling fraction• 2.65 Refractive Index
• Agreement: full index attained!
Sintered Opal
Infiltrated Opal
Inverse Opal
E. Graugnard et al., Photonic Crystals at Georgia Tech, www.nanophotonics.gatech.edu/PCs_at_GaTech.ppt4/3/2017 21
Opal Defect Engineering
Silica Opal with DefectInfiltrated Opal
Inverted Opal Structure
(With Defect – soon!)
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Inverse Opal Defect Mode Calculations for PhCPs• What is the main idea behind Photonic Crystal Phosphor (PhCP)?
– Combining a 3D inverse opal with nanophosphors as a local defect in the PhC lattice
10 20 30 40 50 60 70
10
20
30
40
50
60
70
Si-air Pc slice Luminescent nanocrystal
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• Specific frequencies in the Photonic Band-Gap of the inverse structure are inhibited except for the defect modes
• A broad luminescent material spectrum within this band-gap would be filtered by the resonant frequency and therefore tuned up
Photonic Band-Gap Analysis
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0 0.5 1 1.5 2
Defect
mode
Fre
quency
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Spectrum analysis forPhCPs
Regular spectrum of a green
phosphor
Both spectrum combine and
Emission Energy of phosphor is totally
quenched into the defect mode
Regular spectrum of a defect
mode
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Main Characteristics of PhcPs
• The cavity mode emission spectrum lies within the phosphor emission spectrum
• The position and peak cavity spectrum from the host statically controls the color, luminous intensity and decay time
• Ultimate tunability would be achieved by tunable materials like liquid-crystal, PLZT, etc. to change both the position and peak of cavity mode
PhCPs are candidates for High-Definition Display devices
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Next Class
• Next time: we will continue finite-difference time domain techniques
• Suggested reference: S. Obayya’sbook, Chapter 5, Sections 4-6
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