Photonic band-gap formation and light localization in ... · Photonic band-gap formation and light localization in photonic amorphous diamond 羽田野研セミナー 2011/5/25 K

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




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


air-fraction 78%


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.


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>, …


required.

t

r

t |r1> |r2> |r2> |r2>

t=<ri|H|ri+1>

t

t

r

t t



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




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




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


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>, …


required.

t

r

t |r1> |r2> |r2> |r2>

t=<ri|H|ri+1>

t

t

r

t t



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.

Documents

Photonic band-gap formation and light localization in ... · Photonic band-gap formation and light localization in photonic amorphous diamond 羽田野研セミナー 2011/5/25 K