Mechanisms of Confinement À · ² Occf.ee.ntu.edu.tw/~ypchiou/Photonic_Crystals/Chapter9... · 2011-05-30 · Photonic Modeling and Design Lab. Graduate Institute of Photonics and

Photonic Modeling and Design Lab.Graduate Institute of Photonics and Optoelectronics &Department of Electrical EngineeringNational Taiwan University

Photonic Crystals Photonic Crystals –– Chapter 9Chapter 9PhotonicPhotonic--Crystal FibersCrystal Fibers

NTU GIPO & EE Photonic Modeling and Design Lab.YPC2

Mechanisms of Confinement

Photonic crystal fibersMicrostructured optical fibers

Bragg fiber Holey fiber (bandgap guiding)

Holey fiber (index guiding)


Knoue et. al., Jpn J. Appl. Phys. V. 33, L. 1463, 1994

1. Hexagonal arrays of optical fibers2. 1.17 m lattice constant, core diameter 0.90 m after being pulled (64 m)3. ~400 hexagonal array placed together (bundle diameter being ~1.5mm)4. Bundle surround by Pb-O glass5. Core etched by HCl

=1.0 (air rod), =2.5 (Pb-O glass)

No out-of-plane propagationOr waveguiding effects

First 2D Real Photonic CrystalFirst 2D Real Photonic Crystal


Italian, from mille fiori a thousand flowers ornamental glass producedby cutting cross sections offused bundles of glass rodsof various colors and sizes

MillefioriMillefiori


Millefiori


Millefiori


Millefiori


First in 1995, Optoelectronic GroupDept. of Physics, Univ. of Bath

Idea:Trap light in a hollow fiber core by creating a periodic wavelength-scale lattice of microscopicholes in cladding glass.

Hexagonal close packed (hcp) array of small air channels pure dopant Semiconductor

It can be drawn to be meters, even kilometers,using conventional drawing tower.

High index contrastOut-of-plane propagation

PCF FabricationPCF Fabrication


Material: glass (SiO2)n ~ 1.46Highly transparent @ 0.35 – 2 mMinimal loss @ 1.3 and 1.55 mZeros Dispersion @ 1.29 m

Softening point @ 1600 deg.Slow variation of viscosity with temperatureFiber drawing @ 1650 – 2050 deg

PreformStacking of 1 mm diameter capillaries (canes) togetherTypically, ~40 cm in length, 20 mm in diameter

CapillaryDiameter: 0.5 -1mm in diameters Too small: becoming unmanageable quicklyToo large: preform being to large to fit into fiber drawing towerRequired to be uniform for the stable drawing due to high tension




Stack-and-drawExtrusion (cf: double crucible)DrillingPolymerization in a moldInjection molding

Polymer PCF preform


Drawing process of PCFsimilar to that of conventional fibermore critical in drawing parameters

Higher temp.Viscosity decreasesstructure tend to collapse due to

surface tension forces=>Drawn at lower temp. than conventional

Two Stage drawing1st stage: subpreform by cane puller

diameter @ 1-4 mm, Length ~1mmonitor the structure under microscope to ensure no collapse of air holes

2nd stage: use subpreform to draw at similar conditions (temp. etc)

Nucleation:Contamination may result in nucleation sites.=> cleaning the preform at each stage and work in clean environment.

Markel and George, Optics of Nanostructured Materials



HigherTemp.

LowerTemp.

d/ ratio differs for different temp.1.5 mm subpreformd/ ~0.1 with = 1 md/ ~0.5 with = 5 m

Different temperaturediff. collapse rate, diff. air hole size

Small circular hole

Hexagonal large holes and smaller triangular interstitial holes



<=

Misc. Preform

Square subpreformHoneycomb subpreform

Both structures are stable in drawingProcess due to solid canes.


IndexIndex--Guiding PCFGuiding PCF

in air


IndexIndex--Guiding PCFGuiding PCF

Degenerate fundamental modes

nearly x-polarized nearly y-polarized

60 +1200 C6 symmetry


Solid core, small holes

Effectively TIR

d: 300nm hole diameterm spacing

Endlessly single modeCondition: d/

Applications:Large core areaHigh power densityLess nonlinearities

Doping the core to reduce index slightly=> Guidance turn off at threshold

Endless Single Mode by Modified TIREndless Single Mode by Modified TIR


V < 2.405 for single mode

shorter => concentrated in silica=> larger ncl ( )=> V( ) saturated

Step Index Fibers

Photonic Crystal Fiber

FSM Fundamental space-filling mode

Birks et al, OL, V.22, No. 13, pp. 961, 1997

Endless SingleEndless Single--Mode FibersMode Fibers


Veff is finite.

V

In conventional fiber



Transverse larger, trapped

Transverse smaller, leak


Sieve


Endlessly single-mode finned dielectric waveguide

Silvestre et al, JOSAA, V. 15, No. 12, pp. 3067, 1998

shorter => concentrated in silica=> larger ncl ( )=> V( ) saturated

Finned Dielectric WaveguidesFinned Dielectric Waveguides


Finned waveguideSlab waveguide

n_clad unchanged

V h1/ =hco/ =0.8

Endless Single Mode (Finned WG)Endless Single Mode (Finned WG)


Despite a factor of 3X increase in frequency,the mode pattern are very similar.

=2

=6

h1/ =0.8 hco/ =0.3



Saturated Vh1/ = 0.8hco/ = 0.1- 2.3

Both TE and TMh1/ = 0.8hco/ = 1.8



Rastogi and Chiang, OL, V. 26, No. 8, pp. 491, 2001

Segmented Cladding FibersSegmented Cladding FibersCylindrical counterpart of finned planar waveguides


2 1

Single core modeHigher cladding modes

n_cl increases monotonically with r.

Segmented Cladding FibersSegmented Cladding Fibers


Cladding index is stronglywavelength-dependent.

V < 2.405

400 to 1500 nm single mode for core diameter = 12 m



K. S. Chiang and V. Rastogi, OFC, 620 (2002)

Ultra-large core single mode fiber

a = 25 m, b= 62.5 mn1 = 1.4509, n2 = 1.4439 (0.5%)= 0.5

Single mode @ 900 ~ 1700 nm



Uniform cladding in radial direction

Radial Effective Index Method:Assume quasi-separable

Matrix method for r-dep. equation





LeakageLoss of SCF

V. Rastogi and K. S. Chiang, OFC, 697, (2003)

A = 10 m, b = 62.5 m=0.007= 1550 nm

SCFSCF


LP01 0.3 dB/km @ 1550nm

Leakage:SCF-2 < SCF-1

Due to field confinement

Single mode @ 1000 ~ 1700 nm

SCFSCF

NTU GIPO & EE Photonic Modeling and Design Lab.YPC

The Scalar Limit and LP ModesThe Scalar Limit and LP Modes

32

Usu. in

Ez determined from Ex and Ey



33

LP aprox. for high index contrast in PCF?



34

LP modes

=> Doubly degenerate=> Four nearly degenerate



35 NTU GIPO & EE Photonic Modeling and Design Lab.YPC

Band Gap Guidance in Holey FibersBand Gap Guidance in Holey Fibers

36



37 NTU GIPO & EE Photonic Modeling and Design Lab.YPC


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NTU GIPO & EE Photonic Modeling and Design Lab.YPC41 NTU GIPO & EE Photonic Modeling and Design Lab.YPC42

conventional TIR guidance

Cregan, Science, 285, 153, 1999

BandgapBandgap--Guiding PCFGuiding PCF


Total Internal Reflection

n_cl < k < n_co

> kn evanescent

triangular air-filling

Band gap=> Hollow core guidance


Spacing 1.9 mAir hole d=0.55 m

Illuminated with white lightIndex matching fluid used to strip offlight in cladding modes.

Like a Filter



Near fieldFar field

I/P: 458 nm laserFiber length: 50 mm

Bandgap guiding is much more sensitive.

Highly birefringence (mm)Large dispersion



In air or vacuum guidingHigh power + Low dispersion+ Low nonlinearity + low loss (theory)

White light illumination



Bragg fibersBragg fibers

Reduced to 1-D problem.


Band gaps of Bragg fibersBand gaps of Bragg fibers


Guided modes of Bragg fibersGuided modes of Bragg fibers


CoreCore--guided modes in hollowguided modes in hollow--core Bragg fibercore Bragg fiber


Losses in hollowLosses in hollow--core fiberscore fibers


Absorption suppression factor Absorption suppression factor // 00


InterInter--modal couplingmodal coupling

Documents

Mechanisms of Confinement À · ² Occf.ee.ntu.edu.tw/~ypchiou/Photonic_Crystals/Chapter9... · 2011-05-30 · Photonic Modeling and Design Lab. Graduate Institute of Photonics and