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Photonic Crystals: Physics, Devices, and Applications
Wei Jiang*Omega Optics, Austin, Texas
&
Microelectronics Research CenterThe University of Texas at Austin
Nano & Giga ChallengesTempe, AZ; March 15, 2007
* Email: [email protected] or [email protected]
2
Outline
• Introduction• Superprism Effect: Physics, Device &
Applications• Silicon Photonic Crystal Waveguide
Modulator
3
Chase
Telecommunication Network Hierarchy: A Quick Introduction
NYCNYSE
UT IBM
AMD
San Jose
Cisco
SunIntel
WAN: Wide Area Network (WDM)
MAN: Metropolitan Area Network (WDM)
LAN: Local Area Network (Ethernet)
*WDM: Wavelength Division Multiplexing
fiber link Citi
• One promising solution:Optical Interconnects
• Using devices similar to telecomm
Electrical interconnect bottleneck
Austin
4
Metro WDM Links
Wavelength Division Multiplexing (WDM)
Lasers
VOA’s DeMUXVOA’s
* VOA: Variable Optical Attenuator** Photonic crystal picture source: MIT Joannopoulos group website, & Park et al. Science (2004).
Amplifiers
Switches
Receivers
MUX MUXDeMUX
add
dropinput
5
Introduction: From 1D to 2D and 3D structures
Γ X M Γ
freq
uenc
yω
(2π
c/a)
= a
/ λ
00.10.20.30.40.50.60.70.80.91
2D Photonic Band Gap
UÕ L Γ X W K
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0
L'
LK'
ΓW
U'XU'' U
W' K
z
3D Photonic Band Gap
Ref: ab-initio.mit.edu/photons/
Γ XM
5
• “Optical Insulator” vs. “Optical Conductor”• Initially, proposed for threshold-less laser (compact cavities)• Later, waveguides, modulators, sensors, demultiplexers…
6Ref: http://ab-initio.mit.edu/photons/
Point Defect : light cavities
Line Defect:waveguides
2D slab PCW: 2D slab + line defect
6
Defects
oxideSiair
holes Substrate
Conventional dielectric waveguide
7
Photonic crystal: from concept to devices
PBG for localization
John
PBG for laserYablonovitch
Woodpile3D PC
Lin, Ho (1998)
1987
Woodpile3D PC cavityNoda (2004)
2D slab defect laserPainter &
Scherer (1999)
Electrically driven 2D slab PC laser
Park & Lee (2004)
SuperprismKosaka (1997)
Refraction theory
Jiang (2005)
SuperprismMonemi & Adibi (2006)
2D PC slabKrauss (1996)
2D PCW in slabMIT (2000)
Slow light in PCW
Notomi (2001)
WDM,Sensor
lasers
Wave-guides
PCW couplingNTT; IBM
(2004)
Channel drop filter Fan&Joannopoulos
(1998)
Filter & CCW Xu&Yariv (2000)
Multi-λJiang (2003)
PCW Switch Vlasov (IBM)
Omega/UT 2005GHz Modulator
Omega/UT (2007)
Filters,OADM
Switch/Modulator
Multi-λNoda (2003)
1997 2007A very brief summary—my sincere apologies for not being able to cover lots of important work in such a short time
Slow-light device Solajcic&Joannopoulos
(2002)
2D slab laserBell Lab/MIT
(1998)
8
Superprism Effect: Physics, Devices, & Applications
• Introduction: superprism effect• Difficulties in modeling & related physics problem• Our general, rigorous theory• Demultiplexer Design• Polymeric Photonic Crystal Fabrication• Other Applications
9
Superprism Effect -Anomalous Light Refraction on Photonic Crystal Surface
H. Kosaka et al., Phys. Rev. B 58, 10096 (1998).
H. Kosaka et. al. Appl Phys. Lett., 74, 1370 (1999).
• Strong wavelength-dependent refraction
∆λ/λ=1% ∆θ=50°
∆θ ≅5000(∆λ/λ)∆θ ≅10 (∆λ/λ)
Photonic CrystalConventional
Periodic nanostructures cause the optical properties of photonic crystals to be highly anisotropic
10
Difficulties in designing superprism devices
• Wavelength demux•Mostly used Finite Difference Time Domain (FDTD) simulations•Demand prohibitive computational resources• In practice
Use large dλ, orSimulate smaller device
Chung & Hong, Appl. Phys. Lett. 81, 1549 (2002).
Baba & Nakamura, J. Quantum Electron. 38, 909 (2002).
0.61
0.48
0.46
0.27
λ’
A sense of “small”
dλ/λ>3% !!
Grid spacing ~0.05λ
11
Modeling methods Categorized by Efficiency
Transfer MatrixKKR
Single cell methods
Internal Field Expansion, Transfer Matrix
1D supercell
FDTD, spherical wave
Whole space
Need a single-cell modeling method that can handle arbitrary lattice type & arbitrary surface orientation.
12
Outline of Our Theoretical Technique
• Solved the eigenvalue, eigenmodes given kx ,ω, solve for ky, E(G)
• Boundary matching for N up modesSolve a set of linear equations for
N transmission coefficient ts & N reflection coefficient rl
• Two issues (complicated math)Forward/backward modes partition• Only N up modes are physically meaningful in y>0
Identify degeneracy related to the surface orientation
0)'()()(])()[('
222 =−++++− ∑ GG'GGG
EEGkGk yyxx εωx
y
PC
α
θ
ε I
q
vg
Jiang et al. Phys. Rev. B 71, 245115 (2005).
13
Difficulties
• Number of equations and number of unknowns both depend on the surface orientation
• Two types of surface orientation
Crystallographic surface with integer Miller indices: (100), (121), (253) …Quasi-periodic surface: (1,π,0), (√2, 0,1)
• Quasi-Periodic Surface can be obtained by flatly terminating an ordinary periodic medium
Penrose tiles: 5-fold symmetry
A1
a
No periodicity
Jiang et al. Phys. Rev. B 71, 245115 (2005).
14
Mode degeneracy depends on surface orientation
1st BZ
(h1h2)=(01) (h1h2)=(23)
const. kxline
Real Space
ReciprocalSpace
Yu & Fan PRE 2004A slight change of surface orientation may
cause one refracted beam to split into many
dispersion surface (constant-ω contour)(~Fermi surface, constant-E contour)
Jiang et al. Photonics West 2004
15
Results and Efficiency of Our Method
• FDTD: Calculate field in the whole spaceinefficient• Our Theory: One Cell per Surface• Complete, Rigorous theoretical framework of photonic crystal refraction
Any lattice type and arbitrarysurface orientationBoth planar wave, Gaussian Beam, and arbitrary beam profileQuasi-periodic surface
θscreen
Negativerefraction
Jiang et al. Phys. Rev. B 71, 245115 (2005).
16
Demultiplexer Design: What bevel(s) is best
input
λnλn-1λ1 λ2
wide PC region—bulky
λnλn-1
λ1
photonic crystal
input
λ2
compact
Beam splitting for 30o bevel,High loss
17
Applications
• Negative index materials (NIM)• Laser Beam Steering with Electrical
Control• Sensing (sensitive to index change)• Grating Diffraction (“Virtual Photonic
Crystal”)
∆θ ≅10 ∆λ/λ∆θ ≅5000 ∆λ/λ
∆θ ≅10 ∆n∆θ ≅5000 ∆n
Conventional medium
photonic crystal Ultra-high dispersion translates into 500 times higher sensitivity to the change of refractive index
18
Fabrication- Holography & Nanoimprint
Prism Holography- First holographic PC with a stopband covering S+C bands for fiber-optic communication wavelengths- Simpler and cheaper than the grating approach
J. Chen, W. Jiang et al. Appl. Phys. Lett. vol. 90, 093102 (2007).
AFM 3D topology
Nanoimprint• low cost, high thru-put
L. Wang, W. Jiang et al. JAP (accepted)
19
Compact, Low-voltage Si Photonic Crystal Waveguide Modulators
- Outline
• Basic ideas & Physics• Design considerations• High J, V, and P issues for GHz
modulation in Silicon• Measurement & Results
20
Intel’s Silicon Modulator
Liu et al, Nature 2004
• Overcame the GHz barrier for silicon modulator• Large size undesired
21
►Modulation efficiency enhancementthrough highly-dispersive PCWs
Advantage: Significant reduction in interaction length
smaller device & low power consumption
Working Mechanism:
LV
LddL
g00
1~ ωωωββφ ∆∆=∆=∆
0→=pc
g ddVβω
L for same ∆Ф
Photonic Crystal Waveguide Modulator:Basic Principles
►Index tuning through plasma dispersion effect
Soljacic et al JOSA B 2002.
nnnN effe ∆=∆⎯⎯ →⎯∆⎯⎯ →⎯∆ 100 Plasma dispersion
Slow lightPCW
Light travels slower in a PCW and has more time interacting with electrons. This results in enhanced light-matter interaction.Refractive index of silicon
∆β
∆β=∆ω0/vg
22
siliconair holes
Photonic Crystal Waveguides - Basics
• Photonic crystalwaveguide: Physics
mode dispersion relation & field patternSlow Light
oxide
Horizontal: photonic band-gap guiding(all-angle in-plane Bragg Reflection)
Vertical: index guiding
23
A host of structures
(d)
p-doped poly-Sin-Si
electrode
(e)
(a)oxide
air holes
electrode
n++ p++
(c)substrate
n-Si thin oxide
Need thick poly-Si to reduce metal absorption, this causes:• Multi-mode PCW• High current density• Not planarized
electrodes
Electrical driver
From Day ONE:• Need to connect inner electrode to the outside• Integration with on-chipelectrical driver• Not trivial
air holes
electrode
n++ p++(b)substrate
“intrinsic” Si
oxide
Shih et al APL, 2004.
24
-- -
+
Photonic crystal laser
Park et al. Science 2004
Photonic crystal as an Optical Insulator AND an Electrical Conductor
++
+-
--
Resistance R~1.4 R0
+-• Resistance R~4 R0• Insufficient vertical carrier diffusion causing poor overlap of ∆Ne(x) & optical field I(x)
Conventional modulatorPhotonic Crystal modulator
25
P-I-N Diode Modulator:Modulation mechanism
• High Voltage problem: 6.5V (intel), ~20V (Cornell)
• Scaling Law Regardless of detailed transport mechanism(s)
∆t=qwcore(∆Nh)c/J or J=2qwcore(∆Nh)cf• Example: Let J=qnµE gives
Drift time limit: t=wcore/µE• The parameters present are somehow fixed:
wcore~1µm (~λ) (∆Nh)c~3x1017 cm-3 for Silicon (from Soref & Bennett JQE 1987)
• Minimum AC current density J~104A/cm2 for 1GHzhigh injection regime—important implications: need low R,
hehe
hehe
NNNNnnn
∆×+∆×=∆+∆=∆
∆×+∆×−=∆+∆=∆−−
−−
1818
8.01822
100.6105.8])(105.8108.8[
ααα
26
P-I-N Diode Modulator:Modulation mechanism (cont’d)
M. Lipson, Nanotechnology 2004
High injection regime &Non-ideal diode behavior:• Ideal diode
∆Nh=(ni2/Ndi) exp(qVj/kBT)
I~exp(qVj/kBT)
• Non-ideal∆Nh=ni exp(qVj/2kBT)I~exp(qVj/2kBT)
At Vj=V0 (contact potential)• Ideal diode
∆Nh=Na~5×1019 cm-3
• Non-ideal diode∆Nh=(NaNdi)1/2~2.3×1017 cm-3
Magic number for Si modulator
27
Fabrication & Spectrum
•Slow group velocity: c/40• Expected modulator interaction length reduction: 20X ~ 40X• High Group velocity Dispersion (GVD)
28
Device Structure, Simulation, and Testing Result
N- (I)
1x1015/cm3
W I = 4µm2µm
P+
5x1019/cm3
N+
5x1019/cm3
Lateral electrodes
Buried oxide
Si substrate
N- (I)
1x1015/cm3
W I = 4µm2µm
P+
5x1019/cm3
N+
5x1019/cm3
Lateral electrodes
Buried oxide
Si substrate
L. Gu, W. Jiang et al. Appl. Phys. Lett. 90, 071105 (2007).
80 µmπD~36µm2.5mmInteraction Length
42%90%N.A.Modulation depth (1GHz)
2V20V6.5VPeak Voltage
Omega /UT CornellIntel
29
Summary
• Photonic crystals bring compact photonic devicesA compact wavelength demultiplexer
• In some devices (e.g. modulators), reduced device size also helps reduce current, voltage and power consumption
demonstrated a compact, low-voltage, high-speed Si modulator using photonic crystal waveguides
• Solid state physics theory for transmission through naturally cut quasi-period surface, and for more general interface transmission problems of any lattice and any surface orientation
• Scaling law of high speed silicon modulator & minimum current density for gigahertz modulation
30
Acknowledgement
• UT Faculty membersProf. Ray T. ChenProf. Sanjay BanerjeeProf. Michael BeckerProf. Herbert L. BerkProf. Joe C. CampbellProf. Ananth DodabalapurProf. Ben Streetman, Dean
• Chen group membersMaggie ChenXiaonan ChenJiaqi ChenLanlan GuBrie HowleyYongqiang Jiang Boem-suk Lee Xuejun LuLi WangXiaolong Wang
• Outside ResearchersProf. Paul BindingProf. Shanhui FanProf. Nick X. Fang Prof. Joe HausProf. Sajeev JohnProf. Lifeng LiDr. Yao LiDr. Richard Soref
• Other MER StudentsWeiping BaiHao ChenXiangyi GuoNing LiDingyuan Lu
• SponsorsDr. Robert NelsonDr. Gernot Pomrenke
Additional support to Chen Group• DARPA• State of Texas, Sematech• SPRING