Photonic crystals (I) Bloch's theorem, photonic band structure, and energy flow
PHOTONIC CRYSTALS @ GEORGIA TECH
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Transcript of PHOTONIC CRYSTALS @ GEORGIA TECH
PHOTONIC CRYSTALS @ GEORGIA TECH
E. Graugnard, J. S. King, Curtis Neff, Davy Gaillot, Tsuyoshi Yamashita, D. Heineman, and C. J. Summers
School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA, USA
Photonic Crystals
• Photonic Crystal – periodic modulation of dielectric constant• Exhibits a “Photonic Band Gap” (PBG) where propagation of a range of
photon energies is forbidden.• For visible wavelengths, periodicity on order of 150 – 500 nm.• Introduction of “dielectric defects” yield modes within the PBG.• Luminescent 2D & 3D PC structures offer the potential for controlling
wavelength, efficiency, time response and threshold properties (phosphors, displays, solid state lighting, etc.).
x
z
y
Periodic in one direction
Periodic in two directions
Periodic in three directions
1D 2D 3D
(Joannopoulos)
Photonic Crystal Properties
• Density of states of radiation field in free space & photonic crystal
• Photonic band gap and associated defect mode are used to create waveguides, microcavities, resonators, couplers and filters.
• Luminescent 2D & 3D PC microcavity structures offer the potential for controlling the wavelength, efficiency, time response and threshold properties by embedding a defect in a photonic crystal structure. (LEDs, Lasers, Phosphors)
(Sakoda)
Photonic Crystals:Dimensionality Defined
• 1-, 2-, & 3-D photonic crystals are all 3-D structures
• Dimensions refer to number of dimensions in which the photonic bandgap exists
• Dielectric constant modulated in 1, 2, or 3 directions.
• Modulation of dielectric constant on the order of the wavelength of illumination source.
1D
2D
3D
Bragg stack
Square lattice of
rods
Inverse opal
Real Photonic Crystals:Applications for thin films
1-D
2-D
3-D
The Bragg Stack:‘1D Photonic Crystal’ Treatment
• Treat structure with periodicity in order to cast into reciprocal space.
• a = lattice constant• b = reciprocal lattice
constant• Also, plane waves can be
represented by k vector in reciprocal space
a
)()( axx
2
k
b
0 2/a 4/a
Result of the Bragg Stack
• Dispersion lines: plot of the frequency vs. k vector considering the given structure.
• Similar result to 1-D multiple quantum well problem in solid state physics
• The ‘Photonic Band Gap’ is a range of frequencies where a solution does not exist.
k
k
a
a
2
a
a
2 0
c
an
2
Photonic Band Gap
Results Compared:Photonic Crystal vs. Traditional Optics
• Reflected waves interfere constructively
• Band gap corresponds to high reflectivity
• Thickness of each layer:
n0layer or
4
layer = wavelength in medium
0 = free space wavelength
n = refractive index of layer
a
a
0n
2D Photonic Crystals
a
Square Lattice
ar
Triangular Lattice
X M
MX
n
M K
Real Space Reciprocal Space Band Diagram
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
MK
n
2D Photonic Crystals:Methods of Visualizing Properties
• Band Surface– Plot of eigen-solutions
in the irreducible Brillouin zone
– Complete information but difficult to analyze
• Band Diagram– Plot of the boundaries
of the band surface
– Useful for identifying band gaps and general band shifts
• Dispersion Curve– Iso-frequency contours
of the band surface
– Useful for identifying refraction and propagation effects
Dispersion Curve Analysis:Refraction Effects
• The dispersion curve can be used to predict the refraction effects of a photonic crystal.
InterfaceO
n1
n2()
k0n1
k0n2()
O
n1
n2()
k0n1
k0n2()
Conventional Materials Photonic Crystals
Principle of Self-Collimated Beams
• Conservation of the transverse component of the wave vector
• Group velocity is normal to the dispersion curve
• Possible to achieve nearly parallel beam propagation
4/0
/a
Isotropic Media Photonic Crystal
Nearly Parallel Beam
2D Virtual Waveguides
Beam spreading in an isotropic material
Beam spreading in a photonic crystal virtual waveguide
Sharp Turns
No cross talk
Virtual Waveguide System Simulation using FDTD
• Photonic band gap perfect mirrors
• Signals can cross with no interference
• Small deviations in beam width and wavelength can be accommodated
1550nm 8.55m
1555nm 9.97m
1545nm 7.12m
2D Superlattice
2D Superlattice
• Based on triangular lattice but with two different hole sizes.
0
0.1
0.2
0.3
0.4
0.5
n
MX
X’
M X X’ M
2D Superlattice:Dispersion Curve
• Large refraction characteristics with small change in incident beam angle
• Effect does not require a band gap
• Effect can be ‘tunable’ by using electro-optic materals
-60
-50
-40
-30
-20
-10
0
10
20
30
-18 -13 -8 -3
Incident Angle
Ref
ract
ed A
ngle
Isofrequency contour
Application: Beam steering/rastering in optical communications or displays
3D Photonic Crystals:Opals & Inverse Opals
• For 3D PC’s: “top-down” approaches are difficult. – “Bottom-up” approach: self-assembly
• Most common 3D photonic crystal is the opal.– Close-packed silica spheres in air
• Opal is used as a template to create an inverse opal.– Close-packed air spheres in a dielectric material
3D-PC Opal26% air
Inverse Opal74% air for high
dielectric contrast
ALD
SiO2 Opal Films
• Opal films are polycrystalline, 10 m thick, FCC films with the (111) planes oriented parallel to the surface.
• For visible spectrum, lattice constant ~ 140 – 500 nm.
300 nm1 µm
Challenge: growth of uniform films within a dense, highly porous, high surface-area, FCC matrix
Inverse Opal:Fabrication
• Self-assembled silica opal template
– 10 μm thick FCC polycrystalline film, (111) oriented.
• Infiltration of opal with high index materials
– ZnS:Mn n~2.5 @ 425 nm (directional PBG)
– TiO2 (rutile) navg~ 3.08 @ 425 nm (omni-directional PBG)
Sintered Opal Infiltrated Opal Inverted Opal
Self Assembly
ALD Etch
ALD of TiO2 at 100ºC
433 nm opal infiltrated with TiO2
433 nm TiO2 inverse opal
(111)
• TiO2 infiltration at 100ºC produces very smooth and conformal surface coatings with rms roughness ~2Å.
• Heat treatment (400C, 2 hrs.) of infiltrated opal converts it to anatase TiO2, increasing the refractive index from 2.35 to 2.65, with only a 2Å increase in the rms surface roughness.
300 nm
433 nm opal infiltrated with 20 nm of TiO2
Cross-sections
2 µm
Optimized TiO2 Infiltration
433 nm TiO2 inverse opal
• Pulse and purge times were increased to optimize infiltration in opals with small sphere sizes.
Specular Reflectivity
• Measurements: 15° from normal • Probes changes in -L photonic band structure (111)
(a) sintered, (b) as-infiltrated, and (c) inverse opals
400 600 800 10000.0
0.2
0.4
0.6
0.8
1.0
Nor
mal
ized
Ref
lect
ivity
Wavelength (nm)
(a) (c) (b)
330 nm opal
ZnS:Mn
200 nm opal
TiO2
200 300 400 500 600 700 800
(c)Nor
mal
ized
Ref
lect
ivity
Wavelength (nm)
(a)(b)
-L PPBGs -L PPBGsFlat band peaksFlat band peaks
Photonic Crystal Properties• Photonic band diagrams: ω vs. k (reciprocal space representation)
• Calculated from wave form of Maxwell’s equations.
• Plane wave expansion (PWE)
• Finite-difference time domain (FDTD)
• Photonic band gaps (PBG)
• Pseudo-photonic band gaps (PPBG)
• Flat bands, low group velocity
• Superprism and giant refraction
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
k-vector
Norm
alized
Fre
qu
en
cy
X U L W
mse6059Source-->Exec.metalpc.f90 --> metalpcThis file: \My documents\GT project\PcP project\FDTD\defect\band diagram\band diagram air_Si.xls
# ixmax= 20# iymax= 20# izmax= 20# dx=1# ikmax= 16# nmax =32768# n_pts_store=16 # radius=0.5# eps_b=11.9# eps_s=1# sig_b=0# sig_s=0FPBG ratio=3.5%
K
PPBG
FCC Brillouin zone
U
PBG
Inverse Opal Reflectivity:Theoretical Comparison
300
400
500
600
700
800
900
1000
1100
Wa
vele
ng
th (
nm
)
L
Normalized Reflectivity Band Diagram
2-3 PPBG
Fabry-Perot fringes
Flat band peaks
400
500
600
700
800
900
1000
1100
Wa
vele
ng
th (
nm
)
L
Normalized Reflectivity Band Diagram
2-3 PPBG
Flat band peaks
300
400
500
600
700
800
900
1000
10-11
PPBG's
Wa
vele
ng
th (
nm
)
Normalized Intensity
L
Band Diagram
2-3 PPBG
5-68-9
• TiO2 infiltration of 330 nm opal.• ~88% filling fraction• 2.65 Refractive Index
• Agreement: full index attained!
Sintered Opal
Infiltrated Opal Inverse Opal
Opal Defect Engineering
Silica Opal with Defect
Infiltrated OpalInverted Opal Structure
(With Defect – soon!)
Inverse Opal:Defect Mode Calculations for PcP
• What is the main idea behind Photonic Crystal Phosphor ?
– Combining a 3D inverse opal with nanophosphors as a local defect in the Pc lattice
• Specific frequencies in the Photonic Band-Gap of the inverse structure are inhibited except for the defect modes
• A broad luminescent material spectrum within this band-gap would be filtered by the resonant frequency and therefore tuned up
10 20 30 40 50 60 70
10
20
30
40
50
60
70
Si-air Pc slice Luminescent nanocrystal
Photonic Band-Gap Analysis
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0 0.5 1 1.5 2
Defect mode
Fre
quen
cy
Spectrum analysis forPcP
Regular spectrum of a green phosphor
Both spectrum combine and
Emission Energy of phosphor is totally quenched into the defect mode
Regular spectrum of a defect mode
Main Characteristics of PcP:Field of applications
• The cavity mode spectrum lies into the phosphor emission spectrum
– A matching nanophosphor would spontaneously emit in by the confined defect mode in the ultra-high Q-factor cavity
• The nature of the resonant spectrum acts as an optical amplifier and filter and allows Static Tunability of luminescent properties.
– The position and peak cavity spectrum controls the color, luminous intensity and decay time of structure
• Intrinsic properties are therefore controlled by the geometry of the host
• Ultimate tunability would be achieved by optically or electrically biasing materials such as respectively Liquid-crystal or PLZT (instead of air)
– Changing dynamically the refractive index of host materials would affect both position and peak of cavity mode
• The amplified mode leaks upon near-UV pumping and then propagates out
PcPs are perfect candidates for High-Definition Display devices !!!!
Three-Layer Inverse Opal:PcP
• SEM of TiO2/ZnS:Mn/TiO2
inverse opal
330 nm sphere size
Luminescent multi-layered inverse opals fabricated using ALD: PcP
Photoluminescence:ZnS:Mn/TiO2 Composite PcP
400 500 600 700 800
(f)
(c)(e)
(d)(b)
Rel
ativ
e In
tens
ity
Wavelength (nm)
(a)
108%
Mn2+ Cl-
(a) 2-layer TiO2/ZnS:Mn/air (14 nm/20 nm) inverse opal
(b-f) 3-layer TiO2/ZnS:Mn/TiO2 inverse opal after backfilling with TiO2 by(b) 1 nm (c) 2 nm(d) 3 nm (e) 4 nm (f) 5 nm
• 433 nm opal• 337 nm N2 laser excitation• Detection normal to surface
Using ALD of TiO2 to create novel 2D Photonic Crystals.
X. D. Wang, E. Graugnard, J. S. King,
C. J. Summers, and Z. L. Wang
TiO2 Coated ZnO Arrays
Aligned ZnO nano-rods in a hexagonal matrix on a sapphire substrate.
Aligned ZnO nano-rods coated with 100 nm of TiO2 at 100°C.
Summary
• Precise control of thin film growth enables novel photonic crystal structures:– Inverse opals with void space air pockets (enhanced PBG)– Achieved maximum infiltration of 86%– Perfect match between reflectivity and calculated band
structure– Multi-layered luminescent inverse opals: PcP
• Modification of photoluminescence by precise infiltration– Increased Mn2+ peak intensity by 108%
• Pathway for photonic crystal band gap engineering.• Novel 2D PCs created with ALD
– TiO2/ZnO aligned nano-rod arrays
Acknowledgments
• US Army Research Lab: S. Blomquist, E. Forsythe, D. Morton
• Dr. Won Park, U. Colorado
• Dr. Mike Ciftan, US Army Research Office: MURI “Intelligent Luminescence for Communication, Display and Identification”