Photonic band-gap formation and light localization in ... · Photonic band-gap formation and light...
Transcript of Photonic band-gap formation and light localization in ... · Photonic band-gap formation and light...
Photonic band-gap formation and light localization in photonic amorphous diamond
羽田野研セミナー 2011/5/25
K. Edagawa
Institute of Industrial Science, Univ. of Tokyo Co-workers: S. Imagawa (Edagawa’lab.) T. Niino (IIS, Univ. Tokyo) Y. Kagawa (RCAST, Univ. Tokyo) M. Notomi (NTT)
Outline
1. Background -- Research field of photonic crystals What are photonic crystals? How can they be useful? History of the field …
2. Discovery of photonic amorphous diamond (PAD) What is the PAD? What is new about it? PBG formation Light localization … 3. Microwave transmission experiments Fabrication of PAD Transmission spectra PBG formation Light localization …
4. Summary and future works
What is a photonic crsytal?
with a period comparable to light wavelength (~0.5μ m)
=Periodic structure of
low and high refractive-index materials
Crystalline Si (period0.5nm) (for reference) Photonic crystal
Electronic band structure in crystalline solid
electron in crys. photon in photonic crys.
field
eigenvalue eq.
Bloch’s law
operator
tiet )(),( rr tieHtH )(),( rr
EH HcH 2)/(
rkrr
iknkn eu )()( rk
rr i
knkn euH )()(
)(2
22
rVm
H
)(
1
r
=ck/n
fre
qu
en
cy
wavevector k O
fre
qu
en
cy
wavevector k
photonic band-gap
wavevector k
en
erg
y
E
electronic
band-gap
Electronic crystal vs. Photonic crystal
Photonic band structure in photonic crystal
Light controlling devices and IC using PBG
optical resonator
wav
egu
ide
micro-laser
Introduction
of defects Formation of defect levels
in PBG
Various types
of light control
light controlling devices
optical resonator
optical waveguide
laser
optical filter
optical switch
extr
em
ely
sm
all
siz
e
optical integrated circuit
realization of optical circuit
by one million times smaller in area
than conventional techniques
1987
1995
2000
2010
Evolution of the research field of photonic crystal
1987
1995
2000
2010
Proposal of 3D light confinement by PBG (Yablonobitch)
Fundamental studies on physics of 3D PC
・Photonic band theory
・Search for PC structures with 3D-PBG by computations
・Verification of 3D-PBG in microwave region
Fabrication of 3D PC
Fabrication of light-controlling
devices
・Fabrication in optical wave-
length region
・verification of 3D-PBG
・Trial manufacture of devices
Fundamental studies of 2D PC
・Propasal of concepts of
resonator and waveguide
・Proposal of concept of optical IC
・verification of 2D-PBG
in light-wave region
Fabrication of 2D devices and
progress of their performance
・high-Q resonator
・low-loss waveguide
・simple IC
Diamond crystal structure Inverse opal strcuture
The number of structures with sufficiently large PBG is
very limited.
3D structures with a sufficiently large PBG
2D and 3D photonic crystals
SiO2
2D photonic crystal slab 3D photonic crystal
Disadvantages
・A very limited number of
3D-PBG structures
・Difficulty in fabrication
Progress of performance of 2D light controlling devices
2000 2001 2002 2003 2004 2005 2006
100
101
102
103
NTT
IBM IBM
IBM
NTT
NTT
YNU
FESTA
Pro
paga
tion
Los
s (d
B/c
m)
Year2001 2002 2003 2004 2005 2006
103
104
105
106
KyotoKyoto
NTT
Kyoto
Kyoto
NTT
NTT
CALTECH
Kyoto
Qlo
ade
d (
mea
sure
d)
NTTCALTECH
CALTECH
KAIST
Year
Progress of Q-value of optical resonator Reduction of loss of optical waveguide
Outline
1. Background -- Research field of photonic crystals What are photonic crystals? How can they be useful? History of the field …
2. Discovery of photonic amorphous diamond (PAD) What is the PAD? What is new about it? PBG formation Light localization … 3. Microwave transmission experiments Fabrication of PAD Transmission spectra PBG formation Light localization …
4. Summary and future works
Discovery of photonic amorphous diamond structure
Contrary to common belief, a 3D-PBG has been found to be formed
in an amorphous structure in spite of complete lack of periodicity.
0.0 0.1 0.2 0.3 0.4 0.5
103
102
100
f d / c
a
Spec
tral
inte
nsi
ty (a
rb. unit
)
10
1
Band-gap formation mechanism
1. Nearly free electron approximation
E
k 0
k
E
a/2πa/2π 0
r
r
V
band gap
|k1>, |k2>, |k3>, …
Bragg scattering (i.e. long-range order) is
required.
Structure of photonic amorphous diamond
Photonic crystalline diamond
tetrahedral
configuration
(tetrapod)
periodically
connected
randomly
connected
Photonic amorphous diamond
model structure of the atomic arrangement of amorphous Si or Ge
(continuous random network (CRN))
・no trace of diamond-lattice periodicity
・definite short-range tetrahedral order
Bond-angle
distribution
Bond-length
distribution
Frequency distribution of photonic eigenstates
○ Computation procedures
photonic amorphous diamond photonic crystalline diamond
FDTD spectral method (C.T. Chan (1995))
・initial fields
random fields and like white noise
・calc. of time evolution of the fields by FDTD
B.C.
・Fourier transformation of the time evolution to frequency-domain
frequency distribution of eigenstates
)(rH)(rE
)()( rEprE i)()( rHprH i
supercell
11.5d
(d: bond length)
1000 nodes
supercell
5a=11.5d
(a: lattice const.)
1000 nodes
Principle of the method
...
...
supercell
5a×5a×5a
supercell
5a×5a×5a )()( rEprE
pk ii
i e
)()( rHprHpk ii
i e
)()( rHprH i
)()( rEprE i
0.0 0.1 0.2 0.3 0.4 0.5
103
102
101
Sp
ectr
al i
nte
nsi
ty
(a
rb.
un
it)
f d / c
b
100
dielectric contrast 13/1
air-fraction 78%
26%
C.T.Chan et al. (1995)
0.215
0.280
Photonic crystalline diamond (PCD)
Frequency distribution of photonic eigenstates (PCD)
0.0 0.1 0.2 0.3 0.4 0.5
103
102
100
f d / c
a
Spec
tral
inte
nsi
ty (a
rb. unit
)
101
Photonic amorphous diamond Photonic crystalline diamond
(PAD) (PCD)
0.0 0.1 0.2 0.3 0.4 0.5
103
102
101
Sp
ectr
al i
nte
nsi
ty
(a
rb.
un
it)
f d / c
b
100
dielectric contrast 13/1
air-fraction 78%
dielectric contrast 13/1
air-fraction 78%
18% 26%
Frequency distribution of photonic eigenstates
In PAD,
・the formation of PBG is confirmed.
・the PBG is as clean as that of PCD, with no trace of localized-state
formations in PBG.
1. Nearly free electron approximation
E
k 0
k
E
a/2πa/2π 0
r
r
V
2. Tight binding approximation
E
0
E
0 E
0
E
0
band gap
band gap
|k1>, |k1>, |k1>, …
Bragg scattering (i.e. long-range order) is
required.
t
r
t |r1> |r2> |r2> |r2>
t=<ri|H|ri+1>
t
t
r
t t
Band-gap formation mechanism
Bragg scattering (i.e. long-range order) is
not required.
Electronic band structures of crystalline and amorphous Si
Crystalline Si
E
Ele
ctro
nic
DO
S
extended
states
band-gap extended
states
Amorphous Si
band-gap
mobility-gap
localized state E
extended
states
extended
states E
lect
ron
ic D
OS
Localized photonic states in PAD
Inverse Participation Ratio
We find localized states at band-edges for PAD.
tot
V
VV
d
d
tot
tot
2
2
4
|)(|
|)(|IPR
rrE
rrEPAD PCD
Outline
1. Background -- Research field of photonic crystals What are photonic crystals? How can they be useful? History of the field …
2. Discovery of photonic amorphous diamond (PAD) What is the PAD? What is new about it? PBG formation Light localization … 3. Microwave transmission experiments Fabrication of PAD Transmission spectra PBG formation Light localization …
4. Summary and future works
Fabrication of PAD and PCD
material:Nylon+TiO2+ice
refractive index:3.0
rod length:d=3mm
rod radius: 0.26d
size:70×70×35mm3
air fraction:78%
Selective Laser Sintering method
Niino (IIS, Univ. Tokyo)
Microwave transmission measurements
Parallel-polarized component Tp
Ballistic transport
l
Cross-polarized component Tc
Diffusive transport
Kagawa (RCAST, Univ. Tokyo)
transmitter receiver
Microwave transmission spectra (PCD)
asymmetric gap
isotropic gap
Parallel-polarized
component
Cross-polarized
component
The six spectra are for different
incident beam directions and
different polarization directions.
Microwave transmission spectra (PAD)
Diffusive transport and localization
3/2 l
)/exp( 0tI
ns5.10
)/exp( lLTp
L: sample thickness
mm57.1 dl
dl 5.1
l
I-R condition is
nearly satisfied. sample
Light localization
平均
自由
行程
( l
)
波長 (λ) a
a
周波数 ( f )
Geometric
optics Rayleigh
大
ε-const.
小
4
aa
a
Rayleigh
scattering
Geometric
optics
l
localization
2l
non-interference
2l
2l
Ioffe-Regel
condition
Interference
localization
Outline
1. Background -- Research field of photonic crystals What are photonic crystals? How can they be useful? History of the field …
2. Discovery of photonic amorphous diamond (PAD) What is the PAD? What is new about it? PBG formation Light localization … 3. Microwave transmission experiments Fabrication of PAD Transmission spectra PBG formation Light localization …
4. Summary and future works
Summary
Characteristics of photonic bands and
light propagation in PAD
1. Contrary to the common belief, an amorphous structure
named photonic amorphous diamond (PAD) has been found
to form a 3D-PBG.
2. The 3D-PBG has been demonstrated to be completely
isotropic, which, in principle, cannot be realized in
conventional photonic crystals.
3. In passbands, the PAD has exhibited diffusive light-
propagation, where the scattering mean free path decreases
significantly as the frequency approaches the band edge,
indicating a precursor of light localization.
4. Localized- states have indeed been identified at the band
edges by a numerical calculation.
Future works
1. Theoretical elucidation of gap formation mechanism
・Why is it four-coordinated network?
2. Fabrication in the size of optical wavelength
1. Nearly free electron approximation
E
k 0
k
E
a/2πa/2π 0
r
r
V
2. Tight binding approximation
E
0
E
0 E
0
E
0
band gap
band gap
|k1>, |k1>, |k1>, …
Bragg scattering (i.e. long-range order) is
required.
t
r
t |r1> |r2> |r2> |r2>
t=<ri|H|ri+1>
t
t
r
t t
Band-gap formation mechanism
Bragg scattering (i.e. long-range order) is
not required.
Structure of photonic amorphous diamond
Photonic crystalline diamond
tetrahedral
configuration
(tetrapod)
periodically
connected
randomly
connected
Photonic amorphous diamond
model structure of the atomic arrangement of amorphous Si or Ge
(continuous random network (CRN))
・no trace of diamond-lattice periodicity
・definite short-range tetrahedral order
Bond-angle
distribution
Bond-length
distribution
Dielectric and air bands
tot
air
V
V
d
d
rrE
rrE
2
2
|)(|
|)(|CF
PCD
PAD
PBG formation mechanism
・At the lower-band top, |E|2
concentrate in dielectric regions.
・At the higher-band bottom,
|E|2 concentrate in air regions.
(requirement from
Maxwell’s eqs.)
0))()(( rEr
E should flow within the dielectric (air) network without source nor sink.
To realize this,
・The dielectric (air) regions must
connect to form a network.
・Are four-coordinated networks
advantageous?
E-field flow in PAD and PCD
Future works
1. Theoretical elucidation of gap formation mechanism
・Why is it four-coordinated network?
2. Fabrication in the size of optical wavelength
Random network structures
Tanaka and Araki
polymer solution, protein solution
colloid….
viscoelastic phase separation porous ceramics
SiC/Si
Tani et al. (2001)
アルミナ
Oshima et al.
Optical microfabrication
Nanoscribe GmbH
www.nanoscribe.de
・resolution of 0.1μm
・Whatever shapes can be fabricated.