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光子晶体 ( 光纤 ) 技术进展

光子晶体 ( 光纤 ) 技术进展.  前言－历史的突破与新的挑战  一维、二维、三维光子晶体技术  希望在创新. 彭 江 得 清华大学电子工程系 2000 年 11 月 6 日. Introduction. 1970s ：  Heterostructure Junction Technique.  Quartz Fiber Technique. 1990s ：  Rare-earth Doped Fiber Techniqu.  WDM Transmission Technique.

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光子晶体 ( 光纤 ) 技术进展

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  1. 光子晶体(光纤)技术进展  前言－历史的突破与新的挑战  一维、二维、三维光子晶体技术  希望在创新 彭 江 得 清华大学电子工程系 2000年11月6日

  2. Introduction 1970s： Heterostructure Junction Technique Quartz Fiber Technique 1990s： Rare-earth Doped Fiber Techniqu  WDM Transmission Technique  -Multimedia Networks (1015 bit/s ) 100 fibers, 1000 chs, 10Gb/s 2000s Technical break-through in the history of OFC 1980s： Quantum Well Laser Technique ?!

  3. Introduction Loss spectrum 1.0 0.8 Loss ( dB / km) 25 THz 0.4 WDM 0.2 EDFA WDM Channels  Materials Bent Structure ... 20 km Transmissuon fiber 0.1 1450 nm Raman Pump 1.2 1.3 1.4 1.5 1.6 1.7 ( m) Raman amplifier Challenge 1 - Loss Fiber amplifier  Er-doped fiber amplifier (EDFA ) Er-  Fiber Raman amplifier (FRA)

  4. Introduction Solusion  Dispersion compensation fiber (DCF) 20  Dispersion-shifted fiber (DSF) 15  Dispersion-flattened fiber (DFF) 10 5 Dispersion, ps/ nm·nm 0 +＝ 2.5％ +＝ 2.5％ - 5  =0.35%  =0.35%  =0.35% -10 DCF-a DCF-b SMF -15 Problems: Large  ( Ge  )－Loss  , PMD  Small MFD －Nonlinearity  1.7 1.2 1.4 1.6 1.1 1.3 1.5 Wavelength, m  Chirped fiber grating 2 3 1 Radius Challenge 2 - Dispersion Refractive index

  5. Two Dimensional Photonics Crystal Challenge 3 - Optical Nonlinear Effects  Stimulated Scattering －Stimulated Raman scatting (SRS) • Power Depletion, Intersymbol Interference  S/N Degradation －Stimulated Brilloun scatting (SBS) • Power Depletion  S/N Degradation  Modulation of Refractive Index －Self- Phase modulation (SPM) • Spectral Broadening  Dispersion Penalty －Cross- Phase modulation (SPM) • Spectral Broadening  Dispersion Penalty````````````` － Four- Wave Mixing (FWM) • Coherent Interference  Crosstalk, Power Depletion

  6. Introduction Noise Figure B 20 18 16 20 14 18 Y Axis Title 10.00 dBm 12 16 10 8 14 6 12 4 10 2 8 0 1400 1420 1440 1460 1480 1500 1520 1540 1560 1580 1600 1620 1640 6 X axis title 4 2 9 1600 1420 1440 1460 1480 1500 1520 1540 1560 1580 1400 1620 Er-doped fiber amplifier Challenge - ASE in the Fiber Amplifiers Fiber Raman amplifier

  7. Photonics Crystal A photonics crystal is a dielectric structure with a refractive index that varies periodically in space, with a period of the order of  1D 2D 3D  Waves of certain frequencies () can be reflected from the materials.  Waves of certain frequencies () can not enter into or propagate through the materials.  There can be ranges of the propagation constants normal to the periodical plane ( ) where propaga- tion is forbidden. Introduction

  8. One Dimension Photonics Crystals Examples (b ) Periodic layered medium (a ) Diffraction grating (c ) Fiber Bragg grating

  9. One Dimension Photonics Crystals Electric field Wave equation Theory Periodic media Field solution Bloch waves

  10. One Dimension Photonics Crystals Assumption: Kx = Ky = 0, Kz = K ; k · E = 0; isotropic (l’ are scalar) Wave equations: k = K： k = K－ g： k = K + g ： If |K－g | = K (Bragg condition : K =  / )， and K 2 = 20 A(K) and A(K－g) are resonantly coupled. Coupled equations: Dispersion relation: Dispersion relation for the Bloch waves near the Bragg condition

  11. One Dimension Photonics Crystals Spectral band edgs: K－complex (real part－ /), Evanescent waves － “ Forbidden band”  = | +－- |. K－ real, Propagating waves . At the center of the  : Dispersion relation: Forbidden bandgap: gap is proportional to the magnitude of the Fourier expansion coefficient of the  . Im (K)atthe center of the gap is proportional to the fractional bandgapgap/. Photonics “forbidden band”

  12. One Dimension Photonics Crystals In general: |K－ l g | K, l = 1, 2, ···, K 2 =  2 0 Coupled equations: Forbidden band: atK = l  /, (gap ) l=  |l / 0 （l1－ high -order )  1.10 1.05 3 l= 3 10  Im (K) + n/c 2 1.00 0 l = 2 - 1 0.95 l = 1 Re (K) K 0.90  3.0 3.2 3.4 2.8 3.6 3.8 0 K High -order“ forbidden bands”

  13. One Dimension Photonics Crystals Refractive index profile: n1 n2 n1 n2 n1 n2 a b b b a a z Z = (n－2) Z = (n－1) Z = n (n-1) th unit cell n th unit cell Periodic Layered Media General solution: In layer  ( =1, 2) of the nth unit cell : The continuity of Ex and Hy at the interfaces (TE) At z = (n-1)  and z = (n-1)  + b AD - BC=1

  14. One Dimension Photonics Crystals Normal mode: Periodic condition: Eigenvalue equation: Solution: Eigenvectors : Dispersion relation : Bloch Waves Evanescent Bloch waves “Forbidden” band Propagating Bloch waves

  15. One Dimension Photonics Crystals 2 2 (in units of c/)   (in units of c/) ky= ( /c ) n2 sin B TE waves TM waves  4 5 2 3 6  4 5 2 3 6 Ky (in units of 1/) Ky (in units of 1/) Band Structure  The dispersion relation can be represented by a surface in a three-dimensional space ( K, ky,  ).  The intersections of this surface with the planes K=m / are curves which represent band edges.

  16. One Dimension Photonics Crystals n1 n2 b0 aN b a · · · a0  Bragg Reflection  |rN |2 spectrum－fast-varying function of K( ky ,  ) N - 1 nodes ( |rN |2 = 0 )  (N-1 , N-1 )  |rN |2 peaks－at the centers of the forbidden bands N - 2side lobes－Envelope |C|2 /[|C|2 +(sin K)2]  Atband edges (K = m ) : | rN |2 = |C|2 / [ |C|2 + (1/ N )2 ]  In “ Forbidden” gap ( K=m +i K i) :

  17. One Dimension Photonics Crystals ( 11,000  ) 100 ( 55,000  ) 0=1.15m N00=30 STOP BAND 30 AYERS GsAs 0.185m PERIOD PAIRE Al0.3Ga0.7As 50 Percent reflectivity 0 0.9 1.0 1.1 1.2 1.3 1.4 1.5 Wavelength (m) Scanning electron micrograph GaAs / Al 0.3Ga 0.7 As (dark color) (light color) 30 layer pairs  =0.185m

  18. Two Dimensional Photonics Crystal Two Dimensional Photonics Crystal 2D -PCF Model  There can be ranges of the propagation constants normal to the periodical plane ( ) where propaga- tion is forbidden.

  19. Two Dimensional Photonics Crystal (a) HF with hexagonal hole arrangement (b) HF with randomly arranged /sized holes Holey Fibers (HFs)  HFs are made from undoped silica, the cladding is formed by air holes running along the fiber length and the core is formed by a absent hole.  Cladding has a lower effective refraction index than the core.  neffis strongly dependent on both the  and the hole arrangement.

  20. Two Dimensional Photonics Crystal Conventional fiber Photonics crystal fiber a nco n0 nco n0 2 a 2 Structure ncl neff ncl neff Guidancek0nco>  > k0ncl  k0n0>  > k0neff (neff= FSM/k0) kT = (k02n02 - 2) 1/2 kTmax= k0 (n02 -neff2)1/2 kT = (k02nco2-2)1/2 kTmax = k0 (nco2- ncl2)1/2 V value V= k0a (nco2- ncl2)1/2 = a kTmax Wave equation a2 t2 +V2  = 0  Veff = k0 (n02 - neff2)1/2 =  kTmax  2 t2 +Veff2  = 0 Effective-index model for the guidance of FCF VVeff Veff = ? Single mode V< 2.405

  21. Two Dimensional Photonics Crystal r s d d b /2 Endlessly single-mode properties of PCF Short-wavelength limit : 00 2 t2 +Veff2  = 0  invariant function (x/, y/)  Veff (/0)  finite  Veff be depended on the d/ dneffVeff multi-modes dneffVeff single-mode Critical bend radius R： Long 0: Veff= k F1/2(n02-na2)1/2 0 2 , W(0-2 )  Short 0: Veff ,W constant Rc  3/ 0 2 An effective cladding index that rises as wavelength gets shorter  A single transverse mode profile freezing into a constant shape

  22. Two Dimensional Photonics Crystal Operation wavelengths:457.9 nm, 632.8 nm, 850 nm, 1550 nm Near-field pattern Far-field pattern (b) (a) (c) (d) (a) Hexagonal spots with a factor- of -25 difference between innermost and outermost intensity. (b) Fourier transform of the near-filed pattern. (c) Similarity to the Fourier transform of the near- filed pattern in the Fig.(b). (d) Higher-order terms on the pattern showing the integrity of the periodic structure. Filed pattern of the guided mode of PCF Optics Letters, 21 (19):1547-1549, 1996

  23. Two Dimensional Photonics Crystal Example  =180m 2 =22.5 m d = 1.2 m = 9.7 m d/=0.12 0 >458 nm Near-field pattern h= 0.0065 Large mode area (Aeff ) of the PCF  The number of guided modes in a PCF is independent of  /0.  The number of guided modes in a PCF is only depended on d/. Aeff : 1 800m2 by changing Applications: High power waveguide lasers and amplifiers Electron.lett.34 (13): 1347-1348, 1998

  24. Two Dimensional Photonics Crystal a   n  nef (d/) Comparison: SIF  PCF PCF SIF d / ＝ 0.45 d / ＝ 0.45 0.35 0.35 0.25 0.25 0.15 0.15 Dispersing properties (GVD) of PCF Distinctions:  PCF’s－ simultaneously single mode with anomalous GVD(small air holes) SIF’s － always multi-mode when the waveguide GVD is anomalous －Using PDF’s to shift the  of zero GVD to < 1.27m ( material GVD>0.  PCF: largeair holes give a large n and a large normal waveguide GVD －Using PDF’s to cancel the anomalous material GVD at 1.55 m (1000 ps nm-1km -1, over 50 times that of SIF), yielding normal net GVD there- Optics Letters, 23 (21): 1662-1664, 1998

  25. Two Dimensional Photonics Crystal Dispersing properties of PBG Guiding Fiber  Large positive dispersion  1.4 m  1.2－1.7m 0.9－1.2 D =250 ps/km/nm (1550nm)  Flat near-zero dispersion  2.9 m  1.2－1.7m 04－0.9 D = 0 ps/km/nm (1550nm) Dispersion

  26. Two Dimensional Photonics Crystal P P P P The field distribution of the two orthogonal polarization modes Polarization properties of the PBF High speed communication requires: Birefringence:  n <10-7 Non-uniformity : dcore= dcladding= 0.4 , d1=0.44 , the position of the holes P shifted a distance d1/2 towards the center-defect  Birefringence is as large as 5x10-4 at a normalized frequency /=0.9 1.4

  27. Photonics Band gap (PBG) Guiding Fiber Hollow silica tube Solid silica rod The fabrication of the honeycomb fiber a few hundred Solid silica rods + silica capillary tubes

  28. Photonics Band gap (PBG) Guiding Fiber Cladding: array of holes Core: an extra air hole (defect)   2 m, dHole = 0.55=1.1 m dDefect= 0.33=0.66 m Honeycomb fiber 1.45 Total internal reflection 1.40 Radiation line Defect mode 1.35 Model index /k 1.30 PBG banderies 1.25 1.20 Single mode 1.15  Band gap Guidance 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Normalized wavelength, / Below the radiation line: BG1:  0.3~1.6 BG2 :   0.4~0.1 Single mode: 0.4~.6   0.8~3.2 m Photonics Band gap Guidance in PCF  Do not support the fundamental index- guided mode because of low -index core Above the radiation line － For standard fiber or PCFs

  29. Photonics Band gap (PBG) Guiding Fiber Interstitial holes Near-field pattern Guided mode patterns in PBG fiber Near-field pattern 528 nm 458 nm Far-field pattern 633 nm 528 nm 458 nm  The relative intensities of the six lobes was varied and nearly equal.  No other mode field patterns are observed confined to defect region.  No confined mode could be observed at 633nn.

  30. W Si d Example Model Fabrication (a) d (b) d d (c) d (d) Si / SiO2 (e) b Waves of certain can not enter into or propagate through the materials.  = 1.5 m  gap= 14 %  0,center a y z Three Dimensional Photonics Crystal Example

  31. Three Dimensional Photonics Crystal Photonic Crystal Micro-Cavity Characteristics:  Spontaneous emission in the materials is enhanced and can be controlled.  Frequency, polarization, symmetry and field distribution of the modes in defect states can be controlled by changing the geometric symmetry and refractive index of defects.  Energy of modes concentrate on the defects and attenuated exponentially with distance from the center of defects. Evanescent field can be coupled with the external field of modes. Applications： － Photonic Crystal Resonator and Coupled Resonator Optical Waveguide. － Photonic Crystal Mirror, Switcher and Narrow Band Loss-free Filters. － Photonic Crystal LD, Lasers without the threshold and VCSEL.

  32. Three Dimensional Photonics Crystal Examples  Photonic Crystal Coupled Resonator Waveguide (MIT) Si / SiO2  = 1.5 m GaAs/AlGaAs  = 1.5 m

  33. Three Dimensional Photonics Crystal Examples  Photonic Crystal Mcrocavity Laser (CALTECH) QW InGaAsP L = 1.5 m P = 980  = 50 ns

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