3D Photonic Crystal structures
☞ Challenge: large index contrast & periodicity
for the visible range 2-3:1 & ~ 200 nm
Nature's Photonic Crystals
1-D:
Courtesy N_yotarou. Image
from Wikimedia Commons,
http://commons.wikimedia.org.
Images removed due to copyright restrictions.
Please see
2-D:
http://www.physorg.com/newman/gfx/news/2005/sem_mop.jpg
http://www.physics.usyd.edu.au/theory/seamouse/TheAnimal/spine.x64.jpg
http://www.physics.usyd.edu.au/theory/seamouse/TheAnimal/figure2.jpg
http://www.icmm.csic.es/cefe/Imagenes/manhattan.gif
3-D:
Photonic Materials
k/⁄
→
E
n1
n2
n1
n2
n1
n2
k
k⊥
→
B
Periodic variations in
dielectric properties
cause particular
propagating modes to
be forbidden
a
E. Yablonovitch
PRL 1987
Periodicity can be 1-D, 2-D and 3-D giving rise to
photonic properties of the same dimensionality.
Understanding Band Gaps:
Periodic Dielectric Modulations
f(x) = 0 defines IMDS
Modulations in Principal Directions
Superposition of Modulations in 2D
Periodic Bicontinuous Structures
Marine Biologists
“Cidaris Cidaris: Rectilinear”
Self Ass’y Community:
“Plumber’s Nightmare”
Mathematicians:
“Schwarz’s P Surface”
Image removed due to copyright restrictions.
Please see any image of the Schwarz P surface, such as
http://www.msri.org/about/sgp/jim/geom/minimal/library/P/imag/s_end.jpg
Sea Urchin: Cidaris Cidaris
Image removed due to copyright restrictions.
Please see any page on sea urchin anatomy.
• Cidaris cidaris: found off Shetland Isles
• Inhabit deep water (30m) and usually in
predominantly sandy areas where they can
sometimes be found in large numbers.
Cidaris Cidaris Stereom
Image removed due to copyright restrictions.
Please see
http://www.ucmp.berkeley.edu/echinodermata/stereom.gif
2mm
100μm
• Composed of high magnesium calcite, a calcite (CaCO3) that
incorporates up to 15% MgCO3.
• The skeleton can be seen to be comprised of a threedimensional meshwork, known in the mathematician’s
language as the P-surface.
Photonic Crystal Engineering
of Cidaris Cidaris
• For the native structure, the bandgap will
appear approximately at λ=50 μm.
• Size reduction scheme
Te/air
– (fill, cure, etch, heat, fill…)
(P)DMS/CaCO3
SiO2/Te
SiO2/air
PDMS/air
Original Structure
CaCO3/air
SiO2/Styrene
(P)DMS/PS
Inverse Structure
(P)S/CaCO3
PS/air
P-surface Family: 50% vol, n2/n1 = 4.6
Image removed due to copyright restrictions.
Please see Fig. 1c in Ma, Yung-Hoon, et al.
“Three-Dimensional Network Photonic
Crystals via Cyclic Size Reduction/Infiltration
of Sea Urchin Exoskeleton.” Advanced
Materials 16 (July 5, 2004): 1091-1094
No complete gap!
P-surface Family: 19 vol%, n2/n1 = 4.6
Skeletal graph of tellurium and air (vol fraction = 18.6357%)
0.5
v v
v
v
v v v v v
v v v v v
v v v
v v v
v v v v v v v v v v v v v v
v v v v v v v v v v v v v v
v v v v v v v
Frequency (c/a)
0.4
0.3
v
band 1
band 2
band 3
band 4
band 5
band 6
band 7
band 8
band 9
band 10
0.2
0.1
0.0 L
2 complete gaps!
R
M
L
X
M
Figure by MIT OCW.
Gap Map for n2/n1 = 4.6
Gap maps are useful for finding optimum structures
and fill fractions
0.55
0.50
best
Frequency (c/a)
0.45
Band 5 and 6
0.40
0.35
0.30
Band 2 and 3
0.25
0.20
0
5
10
15
20
25
30
35
40
45
50
Filled volume fraction (%)
Figure by MIT OCW.
Modulations in Principal Directions
f(x,y,z) =sin[2πx] + sin[2πy] +sin[2πz]
Superposition of sinusoidal modulations in 3D
ωa / 2IIc
0.8
Gap Map
0.4
0.0
0.0
0.5
f
Complete Gap
f.o.m. ~ 13%
@ 0.26 dielectric network
n2/n1 = 3.6
1.0
Figure by MIT OCW.
BCP Photonic Crystals
1D: Lamellae
2D: Cylinders
3D: Double Gyroid
(e)
Images removed due to copyright
restrictions.
Please see Fig. 2a in Urbas,
(c)
Augustine, et al. “Tunable Block
(c)(c)
Copolymer/Homopolymer
1 μm
Photonic Crystals.” Advanced
Materials 12 (2000): 812-814
Please see Fig. 2 and 3 in Urbas,
Augustine, et al. “Bicontinuous
Cubic Block Copolymer
Photonic Crystals.” Advanced
250
ber nm
17,
Materials 14 (Decem
2002): 1850-1853
1 μm
1 μm
11 μm
μm
100
Full Width = 6nm
Reflectivity
80
60
40
20
0
200
300
400
500
600
Wavelength (nm)
700
800
Courtesy Elsevier, Inc.,
http://www.sciencedirect.com.
Used with permission.
1D Dielectric Stack: Multilayer Films from
Lamellar Block Copolymers
Symmetric A/B BCP systems form regular lamellae
Tailor period
via blending of
low MW
homopolymers
Polyisoprene n=1.51
Polystyrene n=1.59
lamellar
repeat
spacing
lower Mw
homopolymers
high Mw BCP
Ternary Blending: A/B, hPA, hPB
Two Swelling Models:
• Volumetric
• Linear
L=L0(1+ϕHP1/3)
Low MW
L0
High MW
A. Semenov, Macromolecules 26, 2273 (1993)
L= L0(1+ϕHP)
650
Measured Wavelengths of Peak
Reflectivity
Mixed swelling with 70%
segregated
600
550
205
190
175
Segregation Swelling
500
160
450
145
400
130
Solubilization Swelling
350
115
100
300
0
10
20
30
40
50
60
Lamellar Spacing (nm)
Wavelength of Peak Reflectivity (nm)
Normal Incidence Band Gap Position
vs Homopolymer Fraction
The reflectivity can
be tuned to a selected
wavelength
The morphology
is maintained over
this range of
homopolymer fractions
and the spacing changes
by a factor of two
Percentage of Homopolymer Added to Blend
With a 3 component system, peak can span over visible spectrum
Reflectivity from Block
Copolymer/Homopolymer Blends
Selected Blends of 194k/197k S/I BCP with 13k hPS and hPI
Samples are free
cast in air from
toluene.
Images removed due to copyright
restrictions.
70
Percent Reflectivity
60
Please see Fig. 1a and 2a in
Urbas, Augustine, et al. “Tunable
Block Copolymer/Homopolymer
Photonic Crystals.” Advanced
Materials 12 (2000): 812-814
5%
40%
50
50%
20%
40
30
20
300
400
500
600
700
Wavelength (nm)
Figure by MIT OCW.
Typical reflectivity
is 60% and samples
have a Δλ/λ of 0.15-0.25
Block Copolymer Gels As Sensors
Paint-on pressure sensors
• Photonic polymer solutions from a BCP
and a non-volatile solvent
• Highly viscoelastic with sufficient
solvent
• The layer period is sensitive to
mechanical deformation
Chemically Tunable Photonic Bandgap Gels
Lamellar PS(190K)-b-P2VP(190K)
P2VP block is crosslinked and quarternized
Concept: Collapse Transition Gel Layers
- Selectively modulate the optical thickness of the P2VP layer by swelling,
consequently
changing the photonic bandgap and the reflected color
Æ
Æ
Gel layer volume can be up to 100 times of the initial polymer layer volume
very large differences in refractive index and domain size;
reflected wavelength can be varied with the degree of swelling
Chemically Tunable Polyelectrolyte BCP Gels
Lamellar PS(190K)-b-P2VP(190K)
P2VP block is crosslinked and quaternized
2.5M NH4Cl
1,4 dibromobutane (DBB)
vs. 1 bromoethane (BE)
Y. Kang et al., unpublished
Concept: Rod - Coil Collapse Transition of Gel Layers
Selectively modulate the optical thickness of the QP2VP layer by
swelling/deswelling,
consequently changing the photonic bandgap and the reflected color
Æ
Æ
Gel layer volume can be up to 100 times of the initial polymer layer volume
Very large differences in refractive index and domain size;
Reflected wavelength can be varied with the degree of swelling
Water Swelling of Polyelectrolyte BCP Gels
TEM
Dry
BE only
Crosslinking Controls
Fully Swollen Color
Swollen
Highly Responsive UV to IR Tunability
and Multiorder Band Gaps
Visible
4
4
5
100
3
Reflectivity (%)
5
c = 0.0 M
2
1
3
1
2
c = 0.075 M
4
80
2
calculated data
( φ H2O = 0.91)
60
40
1
experimental data
( c = 0.0 M)
20
0
3
400
2
3
800
1200
1600
Wavelength (nm)
1
NH 4 Cl (M)
2
2.5
1
c = 0.5 M
2.0
1.5
1.0
0.5
0.0
1600
2
1
:experimental data (upper x axis)
c = 1.0 M
1
c = 1.5 M
1
c = 2.0 M
1
Peak Position (nm)
A bsorb a nce (a.u.)
c = 0.25 M
:theoretical calculation (lower x axis)
1200
800
1
c = 2.5 M
dry
400
800
1200
Wavelength (nm)
1600
2
400
3
0.45
0.60
φH O
2
0.75
5
4
0.90
Photonic Block Polymers & Electro-optical Polymers
Using Block Copolymers As Host For Conjugated
Sensory Polymers- Self-Assembled Lasing Cavities
Ability to microphase-separate
In 2D and 3D structures
Stimulated emission in
conjugated polymers
OR
BCC
hex
gyroid
OR'
lam
RO
n
R'O
S2
Figure by MIT OCW.
Increasing Weight Fraction
Block A
S1
h⋅υ
S0
h⋅υ′
Grafted Poly(phenylene ethynylenes): Enhanced
Emission and Alignment with Host Matrix
(
)m
O
Higher Quantum Yield
Than Ungrafted Polymer
O
C11H22
O
O
C16H33O
C11H22
O
OC16H33
n
O
Using ABA block
copolymer as
template for PS
grafted PPE
R'
X
X
• Highly anisotropic structure
• No aggregation
n