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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. z. y. x. Photonic Crystals.

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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

z

y

x

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.).

1D

2D

3D

Periodic in one direction

Periodic in two directions

Periodic in three directions

(Joannopoulos)


Photonic crystal properties
Photonic Crystal Properties

  • Density of states of radiation field in free space & photonic crystal

(Sakoda)

  • 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)


Photonic crystals dimensionality defined
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.

Bragg stack

1D

2D

3D

Square lattice of rods

Inverse opal


Real photonic crystals applications for thin films
Real Photonic Crystals:Applications for thin films

1-D

2-D

3-D


The bragg stack 1d photonic crystal treatment
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

b

0 2p/a 4p/a

l


Result of the bragg stack
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.

w =nk

Photonic Band Gap

k

0


Results compared photonic crystal vs traditional optics
Results Compared:Photonic Crystal vs. Traditional Optics

  • Reflected waves interfere constructively

  • Band gap corresponds to high reflectivity

  • Thickness of each layer:

wn

0

llayer = wavelength in medium

l0 = free space wavelength

n = refractive index of layer


2d photonic crystals
2D Photonic Crystals

Real Space

Reciprocal Space

Band Diagram

X

M

wn

G

a

Square Lattice

G

X

M

G

M

K

wn

r

G

a

Triangular Lattice

G

K

M

G


2d photonic crystals methods of visualizing properties
2D Photonic Crystals:Methods of Visualizing Properties

M

G

C

  • 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

k0n1

k0n1

n1

n1

Interface

O

O

n2(q)

n2(q)

k0n2(q)

k0n2(q)

Dispersion Curve Analysis:Refraction Effects

  • The dispersion curve can be used to predict the refraction effects of a photonic crystal.

Conventional Materials

Photonic Crystals


Principle of self collimated beams
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

Isotropic Media

Photonic Crystal

Nearly Parallel

Beam

4/w0

2p/a


2d virtual waveguides
2D Virtual Waveguides

Beam spreading in an isotropic material

Sharp Turns

Beam spreading in a photonic crystal virtual waveguide

No cross talk


Virtual waveguide system simulation using fdtd

1555nm 9.97mm

1550nm 8.55mm

1545nm 7.12mm

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



2d superlattice1
2D Superlattice

  • Based on triangular lattice but with two different hole sizes.

wn

M

G

M

X

G

X’

M

X

X’

G


2d superlattice dispersion curve
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

Refracted Angle

Isofrequency contour

Incident Angle

Application: Beam steering/rastering in optical communications or displays


3d photonic crystals opals inverse opals
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

ALD

Inverse Opal

74% air for high dielectric contrast

3D-PC

Opal

26% air


Sio 2 opal films

1 µm

300 nm

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.

Challenge: growth of uniform films within a dense, highly porous, high surface-area, FCC matrix


Inverse opal fabrication
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)

Self Assembly

ALD

Etch

Sintered Opal

Infiltrated Opal

Inverted Opal


Ald of tio 2 at 100 c

300 nm

ALD of TiO2 at 100ºC

(111)

Cross-sections

433 nm opal infiltrated with 20 nm of TiO2

433 nm opal infiltrated with TiO2

433 nm TiO2 inverse opal

  • 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.


Optimized tio 2 infiltration

2 µm

Optimized TiO2 Infiltration

  • Pulse and purge times were increased to optimize infiltration in opals with small sphere sizes.

433 nm TiO2 inverse opal


Specular reflectivity
Specular Reflectivity

  • Measurements: 15° from normal

  • Probes changes in -L photonic band structure (111)

TiO2

ZnS:Mn

Flat band peaks

-L PPBGs

Flat band peaks

-L PPBGs

200 nm opal

330 nm opal

(a) sintered, (b) as-infiltrated, and (c) inverse opals


Photonic crystal properties1

PPBG

U

FCC Brillouin zone

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)

PBG

  • Photonic band gaps (PBG)

  • Pseudo-photonic band gaps (PPBG)

  • Flat bands, low group velocity

  • Superprism and giant refraction


Inverse opal reflectivity theoretical comparison
Inverse Opal Reflectivity:Theoretical Comparison

  • 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

Infiltrated Opal

Inverted Opal Structure

(With Defect – soon!)

Opal Defect Engineering

Silica Opal with Defect


Inverse opal defect mode calculations for pcp

Si-air Pc slice

Luminescent nanocrystal

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


Photonic band gap analysis
Photonic Band-Gap Analysis

Defect mode

Frequency


Spectrum analysis for pcp
Spectrum analysis forPcP

Regular spectrum of a green phosphor

Regular spectrum of a defect mode

Both spectrum combine and

Emission Energy of phosphor is totally quenched into the defect mode


Main characteristics of pcp field of applications
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
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 tio 2 composite pcp
Photoluminescence:ZnS:Mn/TiO2 Composite PcP

  • 433 nm opal

  • 337 nm N2 laser excitation

  • Detection normal to surface

  • 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


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


Tio 2 coated zno arrays
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
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
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”


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