Mechanisms of Confinement À · ² Occf.ee.ntu.edu.tw/~ypchiou/Photonic_Crystals/Chapter9... ·...
Transcript of Mechanisms of Confinement À · ² Occf.ee.ntu.edu.tw/~ypchiou/Photonic_Crystals/Chapter9... ·...
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
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Mechanisms of Confinement
Photonic crystal fibersMicrostructured optical fibers
Bragg fiber Holey fiber (bandgap guiding)
Holey fiber (index guiding)
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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
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Italian, from mille fiori a thousand flowers ornamental glass producedby cutting cross sections offused bundles of glass rodsof various colors and sizes
MillefioriMillefiori
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Millefiori
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Millefiori
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Millefiori
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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
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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
PCF FabricationPCF Fabrication
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PCF FabricationPCF Fabrication
Stack-and-drawExtrusion (cf: double crucible)DrillingPolymerization in a moldInjection molding
Polymer PCF preform
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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
PCF FabricationPCF Fabrication
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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
PCF FabricationPCF Fabrication
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<=
Misc. Preform
Square subpreformHoneycomb subpreform
Both structures are stable in drawingProcess due to solid canes.
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IndexIndex--Guiding PCFGuiding PCF
in air
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IndexIndex--Guiding PCFGuiding PCF
Degenerate fundamental modes
nearly x-polarized nearly y-polarized
60 +1200 C6 symmetry
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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
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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
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Veff is finite.
V
In conventional fiber
Endless SingleEndless Single--Mode FibersMode Fibers
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Transverse larger, trapped
Transverse smaller, leak
Endless SingleEndless Single--Mode FibersMode Fibers
Sieve
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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
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Finned waveguideSlab waveguide
n_clad unchanged
V h1/ =hco/ =0.8
Endless Single Mode (Finned WG)Endless Single Mode (Finned WG)
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Despite a factor of 3X increase in frequency,the mode pattern are very similar.
=2
=6
h1/ =0.8 hco/ =0.3
Finned Dielectric WaveguidesFinned Dielectric Waveguides
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Saturated Vh1/ = 0.8hco/ = 0.1- 2.3
Both TE and TMh1/ = 0.8hco/ = 1.8
Finned Dielectric WaveguidesFinned Dielectric Waveguides
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Rastogi and Chiang, OL, V. 26, No. 8, pp. 491, 2001
Segmented Cladding FibersSegmented Cladding FibersCylindrical counterpart of finned planar waveguides
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2 1
Single core modeHigher cladding modes
n_cl increases monotonically with r.
Segmented Cladding FibersSegmented Cladding Fibers
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Cladding index is stronglywavelength-dependent.
V < 2.405
400 to 1500 nm single mode for core diameter = 12 m
Segmented Cladding FibersSegmented Cladding Fibers
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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
Segmented Cladding FibersSegmented Cladding Fibers
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Uniform cladding in radial direction
Radial Effective Index Method:Assume quasi-separable
Matrix method for r-dep. equation
Segmented Cladding FibersSegmented Cladding Fibers
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Segmented Cladding FibersSegmented Cladding Fibers
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LeakageLoss of SCF
V. Rastogi and K. S. Chiang, OFC, 697, (2003)
A = 10 m, b = 62.5 m=0.007= 1550 nm
SCFSCF
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LP01 0.3 dB/km @ 1550nm
Leakage:SCF-2 < SCF-1
Due to field confinement
Single mode @ 1000 ~ 1700 nm
SCFSCF
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The Scalar Limit and LP ModesThe Scalar Limit and LP Modes
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Usu. in
Ez determined from Ex and Ey
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The Scalar Limit and LP ModesThe Scalar Limit and LP Modes
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LP aprox. for high index contrast in PCF?
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The Scalar Limit and LP ModesThe Scalar Limit and LP Modes
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LP modes
=> Doubly degenerate=> Four nearly degenerate
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The Scalar Limit and LP ModesThe Scalar Limit and LP Modes
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Band Gap Guidance in Holey FibersBand Gap Guidance in Holey Fibers
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Band Gap Guidance in Holey FibersBand Gap Guidance in Holey Fibers
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Band Gap Guidance in Holey FibersBand Gap Guidance in Holey Fibers
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Band Gap Guidance in Holey FibersBand Gap Guidance in Holey Fibers
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conventional TIR guidance
Cregan, Science, 285, 153, 1999
BandgapBandgap--Guiding PCFGuiding PCF
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Total Internal Reflection
n_cl < k < n_co
> kn evanescent
triangular air-filling
Band gap=> Hollow core guidance
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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
BandgapBandgap--Guiding PCFGuiding PCF
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Near fieldFar field
I/P: 458 nm laserFiber length: 50 mm
Bandgap guiding is much more sensitive.
Highly birefringence (mm)Large dispersion
BandgapBandgap--Guiding PCFGuiding PCF
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In air or vacuum guidingHigh power + Low dispersion+ Low nonlinearity + low loss (theory)
White light illumination
BandgapBandgap--Guiding PCFGuiding PCF
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Bragg fibersBragg fibers
Reduced to 1-D problem.
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Band gaps of Bragg fibersBand gaps of Bragg fibers
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Guided modes of Bragg fibersGuided modes of Bragg fibers
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CoreCore--guided modes in hollowguided modes in hollow--core Bragg fibercore Bragg fiber
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Losses in hollowLosses in hollow--core fiberscore fibers
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Absorption suppression factor Absorption suppression factor // 00
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InterInter--modal couplingmodal coupling