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Overview of course
Capabilities of photonic crystals
Applications
MW 3:10 - 4:25 PM
Featheringill 300
What is a photonic crystal?
Structure for which refractive index
is a periodic function in space
1-D photonic
crystal
2-D photonic
crystal
3-D photonic
crystal
z
y
x
y
x
y
What is a photonic crystal?
Propagation of light over a particular
wavelength range is forbidden (called
photonic band gap – PBG)
PBG
80
wa/2pc
Reflectance (%)
100
60
40
20
0
1000
1400
1800
Wavelength (nm)
PBG
1-D PBG: Intuition
1-D Photonic Crystal Defect
• “Defect” in photonic crystal terminology
–
–
–
–
Break in periodicity of dielectric function
Localization of electric field
Allowed mode in photonic bandgap
Resonance in optical spectrum
1-D Photonic Crystal Theory
• Derived Fresnel reflection/transmission coefficients at
single interface
• Derived compact mathematical treatment for multilayer
films:
Photonic crystal terminology
• Air band = band “above” PBG (higher
frequency/lower wavelength)
– Power of modes in low e regions
• Dielectric band = band “below” PBG (lower
frequency/higher wavelength)
– Power of modes in high e regions
• PBG arises due to difference in field energy location
Effect of Photonic Crystal Composition
nL = 1.5
nH = 2.6
Stopband width
increases as
index ratio of
nH/nL increases
Reflectance
nH = 2.4
nH = 2.2
nH = 2.0
700
900
1100
1300
1500
Wavelength (nm)
* Band gap ALWAYS appears in 1-D photonic crystal for any dielectric contrast
Multilayer Mirrors: Number of Periods
Reflectance
Reflectance
Height of high reflectance stopband increases
with the number of periods
1
4 periods
0.8
5 periods
6 periods
0.6
10 periods
0.4
0.2
0
0.5
0.7
0.9
1.1
1.3
Wavelength
(microns)
Wavelength
(microns)
1.5
1.7
1.9
Effect of Optical Thickness
Resonance wavelength determined by optical thickness of layers
thi
tlo
Reflectance
173nm 257nm
0.6
148nm 222nm
1
1.4
Wavelength (mm)
1.8
113nm
170nm
88nm
135nm
Changing Incident Angle
30 degrees
Resonance
wavelength and
microcavity quality
decrease as angle of
incidence increases
(keeping refractive
index & thickness of
layers constant)
Reflectance
20 degrees
10 degrees
0 degrees
600
800
1000
1200
Wavelength (nm)
1400
1600
1-D Photonic Crystal Fabrication
• Thin film deposition – high precision
control of material formation in one
dimension (from monolayers to microns)
– Physical vapor deposition
– Chemical vapor deposition
• Start with clean surface
• Minimize impurities during deposition
– Reduce pressure to increase mean free path
1-D Photonic Crystal Fabrication
• Thermal evaporation
–
–
–
–
Heat material to be deposited until it evaporates
Resistive heating
Electron beam heating
Mechanical pump~50 mTorr; diffusion pump with cold trap~10-6
Torr; cryopumps ~10-8 Torr
• Sputtering
– Remove surface atoms or molecules by bombardment with
energetic ions
• Chemical vapor deposition
– Film deposited by chemical reaction or pyrolytic decomposition
in gas phase
• Electrochemical etching
– Porous silicon formation (chemical dissolution driven by
application of current or voltage)
• Molecular beam epitaxy
Molecular Beam Epitaxy
• Deposition of atoms one
layer at a time under
UHV (1 monolayer/s)
– Cryopanels
–  10-10 torr
• Same lattice orientation
– Problems with strain
• Pure elements heated in
individual effusion cells
(Knudsen cells)
• RHEED monitor
http://www.ece.utexas.edu/projects/ece/mrc
/
groups/street_mbe/mbechapter.html
Examples of 1-D Photonic Crystals
•
•
•
•
•
•
Bragg mirrors
1-D PBG microcavities
VCSELs
1-D PBG waveguides
Omniguide
Omnidirectional mirrors
2-D Photonic Crystals
• Dielectric constant
periodic in two
directions and
homogeneous in third
• PBG appears in plane
of periodicity
Notation:
TE: H normal to the plane, E in the plane
TM: E normal to the plane, H in the plane
E-pol (TM-like) and H-pol (TE-like)
TM
E-pol
TE
H-pol
Motivation
To create “complete Photonic Band Gap (PBG)”
complete PBG:
1) Exists independently of
i) polarization;
ii) crystal orientation.
2) Most likely to occur for lattices with nearspherical Brillouin zones
3) In 2-D, the hexagonal real-space lattice has
hexagonal Brillouin zone
closest to circular.
E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,”
Physical Review Letters 58 (20), 2059-2062 (1987).
Rule of Thumb
Lattice of isolated high-e regions
Connected lattice of low-e “pockets”
Transverse Magnetic (TM)
band gap
Transverse Electric (TE)
band gap
Compromise: High-e regions both isolated and linked by narrow air veins
complete PBG
e=12, r=0.2a
Red = TE (E-field parallel to plane of periodicity)
Blue = TM (E-field perpendicular to plane of periodicity)
r=0.3a
http://ab-initio.mit.edu/photons/tutorial/photonic-intro.pdf
Complete Photonic Band Gap
J. D. Joannopoulos, P. R. Villeneuve, and S. H. Fan, “Photonic crystals: Putting a new twist on light,”
Nature 386 (6621), 143-149 (1997) .
The Hexagonal Lattice
high-e cylinders
in
low-e material
low-e cylinders
in
high-e material
i) better mechanical
resistance
ii) ease of fabrication
D. Cassagne, C. Jouanin, and D. Bertho, “Photonic Band-Gaps in a 2-Dimensional Graphite Structure,”
Physical Review B 52 (4), R2217-R2220 (1995).
2-D Photonic Crystals
• Characterized by gap-midgap ratio
• Gap maps are convenient references for
designing PBGs at particular frequencies
Assumes e=11.4
Fabrication of 2-D Photonic Crystals
• Pattern generation
– Contact lithography (~1mm)
– Projection lithography (stepper) (~.5mm)
– Electron beam lithography (~.05mm)
– Holographic (interference) lithography (~.1mm)
• Pattern transfer to substrate
– Dry etching (e.g., RIE)
– Wet etching (e.g., HF, KOH)
Examples of 2-D Photonic Crystals
•
•
•
•
•
Waveguides
Microcavities
Photonic crystal lasers
Photonic crystal fiber
Add/drop filters
2 mm
Results
Structure proposed
• Electrons supplied laterally from
top electrode
• Holes injected directly through
bottom post
• Recombination occurs at proximity
of central post
• Peripheral dielectric as mechanical support
• Sub-micron central post as: (1) electric wire (2)mode selector
(3) heat sinker
• Q degrades rapidly when post size becomes larger; however,
smaller post size leads to resistance and thermal problem
while giving us only a small improvement for Q
Schematic of 2-D Photonic Crystal Slab
Line and point
defects introduced
 Point defects trap
photons like defects
in a semiconductor
trap holes and
electrons
 Trapped photons
resonate and are
emitted upward

….and testing
•
The air-filling fraction in the cladding
(including the interstitial holes) is 39%
and the pitch is 4.9 μm.
•
The fibre in figure has an external dia of
105 μm and core dia of 14.8 μm.
•
3-cm-long samples were held vertically,
illuminated from below with white light
(using a tungsten halogen lamp) and the
light transmitted through them was
observed using an optical microscope.
•
Transmission spectra through the air
core was also measured.
3-D Photonic Crystals
• True optical analog of traditional semiconductor
crystal lattice
– Dielectric function periodic in all three directions
• Very few periodic arrangements of two materials
gives rise to complete 3-D PBG
• Opals/Inverse Opals
• Diamond lattice of spheres
• “Wood-pile” or “layer-by-layer” periodic structure
Examples of 3-D Photonic Crystals
•
•
•
•
•
•
Opals
Inverse opals
Woodpile structure
Superprism
Spot size converter
Square spiral
1.5 mm
Opals
An amorphous non-crystalline variety of silica
which is softer and less dense than quartz.
Opals are known for their distinctive
iridescent luminous qualities which are
actually inclusions that can refract light in a
rainbow of colors, called "fire", that change
with the angle of observation (Dichroism).
Opals contain a large amount of water and
susceptible to cracking. Opal is the birthstone
for October.
Artificial Opals- Self Assembled FCC
H. Mıguez, et al, Langmuir 1997, 13, 6009-6011
Images (2)
Doping and patterning
Defects are randomly distributed !
Fabrication of full 3-D crystal
GaAs on InP
stripes stacked
by wafer fusion
 Observe
minimum in 1st
order of
incident laser
beam when
stripes shifted
by half period

3-D Sharp Bend Waveguide
3-D sharp bend waveguide fabricated by
removing one stripe from one of the layers
 Sandwiched by complete photonic crystals

Single Defect Cavity Structure
Single defect cavity is
formed by adding dielectric
material in one spot in the
crystal
 Goal is to achieve zerothreshold laser arrays
 Numerical analysis of the
single defect cavity
performed by plane-wave
expansion method and
finite-difference timedomain (FDTD) method

Schematic structure of PC’s fabricated on a Si substrate.
Photographs demonstrating the superprism phenomena
wavelength
0.99 µm
1.00 µm
TM
wave
Wavelength sensitive propagation , negative refraction
PC-SSC interface between waveguides
Tunable Photonic Crystals
• Ability to change light propagation in controlled manner
based on application of external stimulus
–
–
–
–
Transmission/reflection intensity
Wavelength of emission (laser)
Direction of light propagation
Speed of light propagation
• Methods
–
–
–
–
–
–
–
Liquid crystals (electrical/thermal)
Thermal
Biological binding
Electrical injection
Electrostatic force
Strain
Swelling
Tunable photonic crystals with liquid crystals
• 1-D
– Electrical & thermal tuning of filters (porous silicon
and Si/SiO2)
– Electrically tunable lasing
• 2-D
– Thermal tuning of PBG of porous silicon and III-V
structures
– Electrically tunable photonic crystal laser
• 3-D
– Electrical & thermal tuning of inverse opals & opals
– Thermal tuning of porous silicon
• Photonic crystal fiber
Liquid crystal tuning
TEMPERATURE
ELECTRIC FIELD
no field
applied E field
E
For positive anisotropy LC
“hot”
(isotropic)
“cold”
(nematic)
5Å
E7 liquid crystal: no ~ 1.5, ne ~ 1.7
Tc ~ 58°C
2 nm
* Response time is slow because based on molecular reorientation (typically ms)
Porous silicon 1-D photonic crystals
Resonance red shift (nm)
Resonance red shift (nm)
THERMAL TUNING
E7 liquid crystals
25
macropore
mesopore
20
15
(isotropic)
10
(nematic)
5
0
25
35
45
55
65
25
20
15
10
5
0
75
24 26 28 30 32 34 36 38 40 42
Temperature, C
Resonance red shift (nm)
Resonance red shift (nm)
Temperature, C
7
6
ZLI-4788 liquid crystals
5
mesopore
4
3
2
1
0
30
40 50 60 70
Temperature, C
5CB liquid crystal
macropore
mesopore
80
7
6
5
4
3
2
1
0
-1
BL087 liquid crystals
mesopore
30 40 50 60 70 80 90 100
Temperature, C
Electrical tuning of photonic crystal laser
using LC
• Tuning range limited by small LC birefringence (Dn=0.052)
– Needed low LC index to maintain sufficient light confinement
– If birefringence too large and LC disordered, scattering is a problem
• Surface anchoring and LC alignment also play role
Q-switched LC photonic crystal laser has now been demonstrated
Photonic crystal fiber with LC
MDA-00-1445 LC with Tc=94°C
77°C
89°C
91°C
94°C
Pure thermal effect can be good or bad…
Thermo-Optic Effect depends on Q-factor
The higher the Q-factor, the more sensitive the
PBG device is to temperature variations
dB attenuation
60
50
40
Dn = 0.1
Dn = 0.01
Dn = 0.001
Silicon
500ºC
50ºC
5ºC
30
20
10
0
100
1000
Q factor
10000
Porous silicon viral mirocavity biosensor
PROBES (IMMOBILIZED cDNA)
TARGETS (PHAGE LAMBDA DNA)
Normalized Photoluminescence Intensity (a.u.)
BACTERIOPHAGE LAMBDA
Immobilized cDNA
Phage Lambda DNA
650
700
750
800
Wavelength (nm)
850
900
Tuning via free-carrier injection
S. W. Leonard et al., Phys. Rev. B 66, 161102 (2002)
• Silicon refractive index change induced by injecting free
carriers with 800nm, 300fs laser pulses
– Tuning on femtosecond time scale (limited by pulse width)
– Faster than LC tuning based on molecular reorientation
• Potential application: ultrafast all-optical switching
(Ti:Sapphire)
(OPA)
Mechanical: electrostatic force and strain
Apply voltage:
air gap thickness changes
Apply differential strain on
microactuators:
strain deformation affect light
propagation in waveguide
Glucose sensing using polymerized crystalline colloidal arrays
(Asher research group)
SWELLING!