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
Wavelength (nm)
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!