Transcript Document
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]
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
| 2 (
E
) 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
APPLICATIONS OF PBG MATERIALS:
Frequency-selective, loss-less reflection Areas impacted: Filters, switches, optical amplifiers 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 7 10 6 10 5 10 4 10 3 10 2 10 1 10 0 1990
Bellcore
1992
Liga Ames Ames
1994
Ames Inverse structures Kyoto Kyoto
1996
Germany
1998
Sandia Sandia
2000 2002 ultarviolet visible light fiber optics C O 2 laser infrared mm waves atmosphere windows 60 and 95 GHz Wireless Communications
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 e o r e i
Bragg scattering:
2d = m w
/c = m
/ d
, m=1,2,…
Mie resonance:
2r/ i = (m+1)/2, m=0,1,2,… Maximum reflection (m=0):
i
2
c
/ w e
i
Gap appears when:
w /
c
/ 2
r
/
d
/ 2
r
e
i
2
r
/
d
1/ e
i
e
i
(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
Average rms error in the dielectric constant D
d
: D( D/R) at half peak
d 0
: D/R at peak value
0.85 0.040
1.60 0.085
2.40 0.135
Lidorikis, Soukoulis
0 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
Average rms error in dielectric const.
D
v
: D( V/V 0 )
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)
A. Blanco et. al. Nature 405, 437 (2002) Silicon inverted opals
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
0.32 cm 0.20 cm 0.08 cm 340 micron 100 micron 1.33 micron 0.20 micron 667 Å
Spacing of Rods
1.120 cm 0.711 cm 0.284 cm 1275 micron 350 micron 4.74
0.711
2370 Å
Midgap Frequency
13 GHz 20 GHz 50 GHz 100 GHz 450 GHz 30 THz 2 x 10 14 Hz 6 x 10 14 Hz
Corresponding Wavelenth at Midgap
23 mm
√
15 mm
√
6 mm
√
3 mm
√
0.66 mm
√
10 micron 1.5 micron 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 -5 -10 -15 -20 -25 -30 -35 -40 -45 10 11 12 13 Frequency (GHz) 14 15
Theory and experiment is in excellent agreement
20 15 10 5 0
K L K X'
An average attenuation of 16 dB per unit cell is obtained
0 -20 -40
Experim ent
-60 -80 -100 0
Noise level Theory
1 2 3 4
Number of unit cells
0 -20 -40 -60 -80 5 -100
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 60 o 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)
3D
Comparison of 2D and 3D results
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.