Download PHOTONIC BAND GAP STRUCTURES

Photonic Band Gap Materials:
The “Semiconductors” of the future?
C. M. Soukoulis
Ames Lab. and Physics Dept. Iowa State University.
and
Research Center of Crete, FORTH - Heraklion, Crete
Collaborators
 Ames Laboratory, Iowa State University
– Mike Sigalas (Agilent)
– Gary Tuttle, W. Leung
– Ekmel Ozbay (Turkey)
– Rana Biswas
– Mario Agio (Pavia), P. Markos (Slovakia)
– E. Lidorikis (MIT), S. Foteinopoulou
– C.T. Chan (Hong-Kong)
– K.M. Ho
 Research Center of Crete
– E. N. Economou
– G. Kiriakidis, N. Katsarakis, M. Kafesaki
– PCIC
Computational Methods
Plane wave expansion method (PWE)
C.T. Chan, K.M. Ho, E. Lidorikis, S. Foteinopoulou
Transfer matrix method (TMM)
M. Sigalas, I. El-Kady, P. Markos, S. Foteinopoulou
Finite-difference-time-domain-method (FDTD)
M. Agio, M. Kafesaki, E. Lidorikis, S. Foteinopoulou
[email protected]
[email protected]
http://cmpweb.ameslab.gov/personnel/soukoulis
PHOTONIC BAND GAP STRUCTURES:
THE “SEMICONDUCTORS”
OF THE FUTURE?
Semiconductors
PBG Crystals
Periodic crystal potential
Periodic variation of dielectric
constant
Atomic length scales
Length scale ~ 
Crystal structure given by nature
Man-made structures
Control electron flow
Control e.m. wave propagation
1950’s electronic revolution
1990’s optical fibers, lasers,
PBGs --> photonics era
Fermi’s Golden Rule:
hv
1 / 
2
| V | (E )
2
Density of final states
Applications: Microwaves
Dielectric
Photonic Crystal
Efficient planar antennas
Applications: Optical range
Suppression of spontaneous emission
Low-threshold lasers, single-mode LEDs, mirrors, optical filters
visible
Infra-red
mm wave
APPLICATIONS OF PBG MATERIALS:
 Frequency-selective, loss-less reflection
 Filters, switches, optical amplifiers
Areas impacted:
 Automotive electronics - e.g., collision-avoidance
radar (60-77 GHz)
 Electron cyclotron resonance heating for fusion plasma,
diagnostic tool (60-200 GHz)
 Medical and biological application - e.g., microwave
resonance therapy (40-80 GHz), imaging
 Wide bandwidth communication (60, 94 GHz)
 mm waveguides
 Fast electronics - interchip communication
 Remote sensing - e.g., monitoring atmospheric radiation;
observational astronomy
 Lasers and optical devices - improved performance in
efficiency and reduction of background noise
 Photocatalysis
Outline
 Progress in fabricating 3D photonic crystals
 Layer-by-Layer structure (ISU)
 3-cylinder structure (LIGA)
 Inverse opals and ordered silica matrices (many groups)
 Metallic photonic crystals
 Metallic and dielectric bends
 Photonic Crystal Waveguides and Bends (2D slabs or 3D PCs)
 Studies of the losses and effects of disorder
Progress in 3d Photonic crystal frequency
10
Frequency (GHz)
10
10
7
Inverse structures
6
Kyoto
5
Kyoto
10
10
10
10
10
ultarviolet
visible light
fiber optics
Sandia
C O laser
Sandia
2
4
infrared
Liga
3
Germany
mm waves
Ames
atmosphere
windows
60 and 95 GHz
Ames
2
1
Bellcore
Ames
Wireless
Communications
0
1990
1992
1994
1996
1998
2000
2002
Three - cylinder Structure or Yablonovite
E. Yablonovitch
Diamond like symmetry.
PRL 65, 3152 (1990) and Euro. Phys. Lett. 16, 563 (1991)
3-cylinder structure
E. Yablonovitch et. al. PRL 67,
3380 (1991)
Fabrication of 3-cylinder structure by LIGA technique
ISU, FORTH and Mainz
Appl. Phys. Lett. 71, 1441 (1997)
experiment
v=2.4 THz
Appl. Phys. Lett. 71, 1441 (1997)
Diamond lattice gives the largest photonic band gap
Ho, Chan and Soukoulis, PRL 65, 3152 (1990)
Diamond lattice
Ho, Chan and Soukoulis, PRL 65, 3152 (1990)
Photonic band gap formation
A synergetic interplay between microscopic (Mie) and
macroscopic (Bragg) resonances.
d
eo
r
ei
Bragg scattering: 2d = m
 w /c = m  / d, m=1,2,…
Mie resonance: 2r/i = (m+1)/2, m=0,1,2,…
i  2c / w ei  w / c   / 2r e i
Maximum reflection (m=0):
Gap appears when:
 / d   / 2r ei

2r / d  1/ ei
(filling ratio)
Experimental band structure of a fcc lattice of air spheres
Gap
Fcc
Airball(86%)
n=3.5
Yablonovitch & Gmitter, PRL 63, 1950 (1989)
FCC lattice has only a pseudogap
Ho, Chan and Soukoulis, PRL 65, 3152 (1990)
Density of States for a fcc structure of air spheres
figure
Ho, Chan and Soukoulis, PRL 65, 3152 (1990)
Sozuer, Haus and Inguva, PRB 45, 13962 (1992) √
Busch and John, PRE 58, 3896 (1998)
Band structure for a close-packed fcc lattice of air spheres in silicon
Busch and John, PRE 58, 3896 (1998)
DOS for a close-packed fcc lattice of air spheres in silicon
Busch and John, PRE 58, 3896 (1998)
Air Spheres (e=1) in Dielectric (e=10)
fcc arrangement with Air filling ratio ~ 74%
supercell: 333, k-point sampling: 888, total grids: 727272
Disorder In Position
<rms>: Average rms error
in the dielectric constant
Dd: D(D/R) at half peak
d0: D/R at peak value
DOS
<rms> Dd/d0
0.30 0.015
0.85 0.040
1.60 0.085
2.40 0.135
0
Lidorikis, Soukoulis
0.1
0.2
0.3
wa/2c
0.4
0.5
Air Spheres (e=1) in Dielectric (e=10)
fcc arrangement with Air filling ratio ~ 74%
supercell: 333, k-point sampling: 888, total grids: 727272
Disorder In Radius
<rms>: Average rms
error in dielectric const.
Dv: D(V/V0)
DOS
<rms> Dv
0.34 0.1
0.67 0.2
1.00 0.3
1.30 0.4
Lidorikis, Soukoulis
0
0.1
0.2
0.3
wa/2c
0.4
0.5
Carbon structures with 3d periodicity at optical wavelengths
A. Zakhidov et. al. Science, 282, 897(1998)
On-chip natural asembly of silicon photonic bandgap structures
Y. A. Vlasov et. al. Nature, 414, 289 (2001)
Inversed opals infiltrated by liquid crystals
K. Busch and S. John, PRL 83, 967 (1999)
Silicon inverted
opals
A. Blanco et. al. Nature 405, 437 (2002)
Fabrication of photonic crystals by holographic lithography
M.Campell et. al. Nature, 404, 53 (2000)
An easy-to-build structure with a
full photonic band gap
Iowa State layer-by-layer structure:
Science News 144, 199 (1993); Solid State Comm. 89, 413 (1994)
Phys. Rev. B 50, 1945 (1994)
Iowa State University’s layer-by-layer structure
Diameter of
Rods
?
Spacing of Rods
Midgap
Frequency
Corresponding
Wavelenth at
Midgap
0.32 cm
1.120 cm
13 GHz
23 mm
0.20 cm
0.711 cm
20 GHz
15 mm
√
0.08 cm
0.284 cm
50 GHz
6 mm
√
340 micron
1275 micron
100 GHz
3 mm
√
100 micron
350 micron
450 GHz
0.66 mm √
1.33 micron
4.74
30 THz
10 micron
0.20 micron
0.711
2 x 1014 Hz
1.5 micron !!!
667 Å
2370 Å
6 x 1014 Hz
5000 Å
√
!!
??
Science News 144, 199 (1993);
Solid State Comm. 89, 413 (1994)
Phys. Rev. B 50, 1945 (1994)
Iowa State University’s layer-by-layer structure
Iowa State University
Ames Laboratory
Sandia National Laboratory.
Electro magnetic waves are incident
on the side surface
5
0
Transmission (dB)
-5
-10
-15
-20
-25
-30
-35
-40
-45
10
11
12
13
Frequency (GHz)
14
15
Theory and experiment is in
excellent agreement
Frequency (GHz)
20
15
10
5
0

K
L
K
X'

An average attenuation of 16 dB
per unit cell is obtained
0
0
-20
-20
-40
-40
Experim ent
-60
-60
Noise level
-80
-80
Theory
-100
0
1
2
3
4
Number of unit cells
5
-100
Transmission (dB)
Theoretical (dashed line) and
experimental (solid line) transmission
characteristics of the defect structure
0
-10
-20
-30
-40
-50
-60
10
12
14
16
Frequency (GHz)
18
The ISU layer by layer structure fabricated at Kyoto Univ.
S. Noda et. al. Science, 289, 604 (2000)
S. Noda et. al. Science, 289, 604 (2000)
S. Y. Lin et. al. Nature, 394, 251 (1998)
R. Biswas, ISU
Propagation along 90 bends in 3d dielectric structures
S. Noda, Kyoto Univ.
M. Sigalas et. al.
Microwave Opt. Techn. Lett. 23, 56 (1999)
Metallic Structure
Metallic Structure
y
x
Propagation along 90 bends in 3d metallic structures
Transmission along the bend is more than 95% !!
M. Sigalas et. al. Phys. Rev. B 60, 4426 (1999)
Agio and Soukoulis, PRE, 64, 055603R (2001)
Waveguide modes for widths of W1 and W3
Regural waveguides
cannot bend light for
sharp angles
Sharp bends in photonic
Crystals !!!
Guided bends in Photonic Crystals:
- Study of 60o bends in W3 and W5
--Best the smoothest one
in collaboration with PCIC groups
W3 taper+slit double bends
Field profile for a/0.24
Modal analysis
for slit2
Studies of the out of plane losses
Photonic Crystal Slabs
Kafesaki, Agio, Soukoulis, JOSA B (2002)
Comparison of 2D and 3D results
3D
2D
3D results can be derived by an effective 2D system
with a slightly different f and an imaginary e
2D and 3D gaps almost coincide in position and width.
Y-Splitters
Summary and Conclusions
 The layer-by-layer structure has been fabricated at telecom frequencies
 Inverse closed packed structures with high index materials (TiO2, Si, Ge)
 Doping of PBGs with active atoms and molecules will lead to new
frontiers in microlasers, low threshold switches, random lasers
 Metallic PBGs. Connectivity is very important
 Photonic Crystal Waveguides and Bends (3d structures or dielectric slabs)
 Tunable PBGs
 Detailed studies of disorder are very important
Summary:
 The “photon band structure” problem is solved
 Photonic gaps EXIST in diamond like structures
 Structure is optimized to give largest gap
 Localization of light in imminent
Experimental Challenge
Fabricate these new dielectric structures
at optical wavelengths,
then
Applications of photonic gaps in physics
and engineering may become possible.