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”