Photonic Band Gap Materials

Engineeringthe Fundamental

Properties ofLight

PBG Materials: Engineering the Fundamental Properties of Light

Single mode air-waveguides, micro-cavities, bends etc.Diffractionless flow of light without “leaky” modesLight Localization based Integrated Optics in 3+1 Dimensions

Localization of Light:Reduction of Optical PathwaysTrapping of Light in Air2D PBG Hollow core photonic crystal fibers

Engineering the Laws of Refraction: Negative and Out-of-planeRefraction

Micro-fabrication of 3D PBG materials:

Direct laser writing, plasma tuning, and double inversion to Si

Engineering Diffraction:

Si Inverted OpalSi Inverted OpalA. Blanco et. al.Nature 405, 437 (2000)

3D Photonic Band Gap Materials

Near Near PhotonicPhotonic Band GapBand Gapρ(ω)ρ(ω) << << ρρ00(ω) (ω) )=ω)=ω22/(π/(π22cc33) free space) free space

S. John, Phys. Rev. S. John, Phys. Rev. LettLett. 53, 2169 (1984). 53, 2169 (1984)S. John, Phys. Rev. S. John, Phys. Rev. LettLett. 58, 2486 (1987) . 58, 2486 (1987) E. Yablonovitch, Phys. Rev. Lett. 2059 (1987)S.John, R.S.John, R.RangarajanRangarajan, Phys.Rev.B. , Phys.Rev.B. 3838, 10101 (1988), 10101 (1988)

Resonance Regime Generalized Localization

Criterion

Resonance Regime Resonance Regime Generalized Localization Generalized Localization

CriterionCriterion

( ) ( )2* phase space 4π× ≈( ) ( )2* phase space 4π× ≈

2not necessarily 4 kπ 2not necessarily 4 kπ

Modification of AvailableLight Paths due to Resonances

* 2Ioffe-Regel: 1πλ

≈* 2Ioffe-Regel: 1πλ

≈

Localized State of Light in PBG

Electric and Magnetic Fields and Energy Density

Refractive Optics near a Photonic Crystal Surface(i) Conservation of momentum parallel to interface(ii) Refracted ray is normal to iso-frequency surface

Engineered RefractionSuperprism, Negative Refraction

k-space picture for uniform dielectric

Anomalous Refractive Optics at a Silicon Inverse Opal Surface

Iso-frequency surface curvature yieldsnegative refraction, out-of plane refractionmultiple refracted rays, etc… Azimuthal rotation defines

Cylindrical Surface thatintersects Iso-freq Surfaces

Direct Laser Writing of Photonic Crystals

Two-Photon Absorption

M. Deubel, M. Wegener, A. Kaso, and S. JohnApplied Physics Letters 85 (11), 1895 (2004) Voxel lateral size as small as

120nm for 780 nm illumination

Slanted Pore (SP-2) Architecture

Sub-Nanometer Scale Polishing of Photonic Crystal by Plasma Etching

Direct laser WrittenWoodpile

Low Plasma exposure time

High Plasma exposure time

Variables:Plasma flow rateExposure TimeTemperature

Polystyrene Opal with EngineeredSphere DiameterGradient nearSurface

G. von Freymann,T. Chan, S. John,V. Kitaev, G. Ozin,M. Deubel, andM. WegenerPhotonics andNanostructures 2No. 3, 191 (2004)

Synthesis of Silicon PBG materials from Polymer Photoresistby Direct Laser Writing and Double Inversion

(i) Spin coat SU8(ii) Direct Laser Write

and Develop(iii) Room Temp CVD

of SiO2(iv) Remove excess SiO2

by RIE to expose SU8(v) Remove SU8 by oxygenplasma etch and combustion(vi) Disilane CVD(vii) Selective etch of SiO2

to yield silicon PBG

Toronto-Karlsruhe collaboration

Air-Waveguide Omni-Reflector Cladding ?

No Disorder:Rapid leakageinto 3rd

dimensionAttenuation ~ 2dB /micron

Attempt to optimizeConfinementn1=3.5n2=1.56

F1,F2

F1

F2

Dielectric Wave-guide in 2D Photonic Crystal Membrane

Localization in-planeOnly

Disorder:25 nm diameterrandomness

Optical Micro-Chip based on 2D-3D Hetero-structure Design

0

0.1

0.2

0.3

0.4

0.5

Γ X M Γ Y MFr

eque

ncy

[c/a

]0

0.1

0.2

0.3

0.4

0.5

kx

ky

Γ

X

Y

M

3D PC bands

2D PC bands

xyz

Optical Micro-Chips based onDielectric 2D-3D PBG Heterostructures

Composite Band Structure for 2-D array of rods Sandwiched between 3-DInverse Square Spirals

A. Chutinan, S. John, O.ToaderPRL 90, 123901 (2003)

0 0.1 0.2 0.3 0.4 0.50.32

0.34

0.36

0.38

0.4

0.42

0.44

Wave vector[2π/a]

a/λ

0 0.1 0.2 0.3 0.4 0.50.32

0.34

0.36

0.38

0.4

0.42

0.44

3D PC bands

3D PC bands

2D PC bands

0 0.1 0.2 0.3 0.4 0.50.32

0.34

0.36

0.38

0.4

0.42

0.44

Wave vector[2π/a]

a/λ

0 0.1 0.2 0.3 0.4 0.50.32

0.34

0.36

0.38

0.4

0.42

0.44

3D PC bands

3D PC bands

2D PC bands

Radius

[a]Thickness[a]

Bandwidth[nm]

Variation of Gap Modes with Thickness “t” of Micro-chip Layerand Radius “r” of Rods in 2D lattice

Direct Square Spiral 5: Single ModeAir-Waveguide Bandwidth at 1.5 microns

t=0.8ar=0.15a

t=0.3ar=0.15a

0 0.1 0.2 0.3 0.4 0.50

50

100

150

Misalignment ∆[a]

Wav

egui

ding

Ban

dwid

th[n

m]

x-direction y-direction

0.34 0.35 0.360

0.2

0.4

0.6

0.8

1

a/λ

Tran

smis

sion

Effect of Disorder on Single-mode Air-waveguide Bandwidth (1.5 microns)

Single ModeWave-GuidingBandwidth vs.MisalignmentOf Upper 3DPBG CladdingLayer

(Bandstructure)

(FDTD)

At 1.5 microns<100 nm: very robust>200nm: multi-mode

Random rod diameter variationwith 20% FWHM fluctuation (48 nm)causes about 5% backscattering over50 unit cells along waveguide.

3 + 1 Dimensional Integrated Optics

PBG Chip to Chip Interconnects Diffraction-lessLoss-less flowover 200 nmBandwidth

Hundreds of WDM channelsNo cross-talk

Minimal HeatDissipation

Blue boxes areregions wheredielectric isremoved to formvertical link

Slanted Pore SP-2 PBG Material24% 3D PBG

Tetragonal unit cell (a,a,1.4a)Hole radius 0.345aMicro-chip layer t=0.6aSquare lattice of circular rodsof diameter 0.3a

180 nmSingle mode

Air-waveguidebandwidth

0 0.1 0.2 0.3 0.4 0.0.3

0.35

0.4

a/λ

Wave vector[2 π/c]0 0.1 0.2 0.3 0.4 0.

0.3

0.35

0.4

3D PC bands

3D PC bands

Slanted Pore3D PBGCladding

High Bandwidth 3D micro-circuitry in SP2 PBG

Lattice matched planar micro-chip layers provide200 nm of single mode bandwidth

Vertical links act like Fabry-Perot resonators with high transmission bandwidth provided by couplers

(0,0,0)

(a,a,c)

(0,0,0)

yx

z

(a,a,c)

0.335 0.34 0.345 0.35 0.3550

0.2

0.4

0.6

0.8

1transmission

reflection

Inte

nsity

in-plane 90o

U-turn 3.75c U-turn 7.75c

a/λ

Transmission Characteristics for 3D Circuit BendMultiple Fabry-Perot resonances with Q-factor reducedby Coupler (dielectric removed from green box)

FDTD Simulation of Electric, MagneticAnd Poynting Vectors on 3D SP2 Chip

Diffractionless transmission of Light in Air-guideswith sharp3D bends

Bandwidth:200 nm on-chip

100 nm overlapbetween planarand vertical forchip-to-chipinterconnection

A. Chutinan and S. John to be published

SUMMARYLocalization of Light in 3D PBG

Diffractionless Flow of Light and Integrated Optics in 3+1 D:3D air-waveguide circuit paths100-200 nm single mode bandwidth

Microfabrication:Direct Laser WritingPlasma TuningDouble inversion for Silicon

The Designer EM Vacuum:Frequency selective control of spontaneous emission