2021-2022学年高二物理竞赛课件：光子晶体(photonic crystal).pptx

光子晶体光子晶体(photonic crystal)光子晶体光子晶体(photonic crystal)周期性结构调制，波的运动产生色散，形成带结构，带周期性结构调制，波的运动产生色散，形成带结构，带隙之间的波禁止通过，称为禁带。隙之间的波禁止通过，称为禁带。电子的运动电子的运动 光子的运动？光子的运动？光子晶体光子晶体:在高折射率材料的某些位置周期性出现低折射率的在高折射率材料的某些位置周期性出现低折射率的材料材料.这种光的折射率指数的周期性变化产生了光带隙结构，这种光的折射率指数的周期性变化产生了光带隙结构，控制着光在晶体中的运动。控制着光在晶体中的运动。19871987年提出概念年提出概念:E.Yablonovitch(PRL 58,2059)S.John(PRL 58,2486)19901990年理论预言第一个有完整光子带隙的三维光子晶体年理论预言第一个有完整光子带隙的三维光子晶体 (PRL 65,3152)(PRL 65,3152)19911991年实验制备第一个有完整光子带隙的三维光子晶体年实验制备第一个有完整光子带隙的三维光子晶体 (PRL 67,2295)(PRL 67,2295)光子晶体多为人工设计光子晶体多为人工设计,自然界也有自然界也有:蛋白石、蝴蝶翅膀蛋白石、蝴蝶翅膀OpalButterflyTraditional multi-layer film三维光子晶体三维光子晶体二维光子晶体二维光子晶体18871987Photonic Crystalsperiodic electromagnetic mediawith photonic band gaps:“optical insulators”(need a more complex topology)Photonic Crystalsperiodic electromagnetic mediawith photonic band gaps:“optical insulators”magical oven mitts forholding and controlling lightcan trap light in cavitiesand waveguides(“wires”)Photonic Crystalsperiodic electromagnetic mediawith photonic band gaps:“optical insulators”magical oven mitts forholding and controlling lightcan trap light in cavitiesand waveguides(“wires”)Photonic Crystalsperiodic electromagnetic mediaBut how can we understand such complex systems?Add up the infinite sum of scattering?Ugh!Image:http:/cst-www.nrl.navy.mil/lattice/struk/a4.htmlThe Mother of(almost)All BandgapsThe diamond lattice:fcc(face-centered-cubic)with two“atoms”per unit cell(primitive)afcc=most-spherical Brillouin zone+diamond“bonds”=lowest(two)bands can concentrate in linesRecipe for a complete gap:frequency(c/a)The First 3d Bandgap StructureK.M.Ho,C.T.Chan,and C.M.Soukoulis,Phys.Rev.Lett.65,3152(1990).11%gapoverlapping Si spheresMPB tutorial,http:/ab-initio.mit.edu/mpbfor gap at l=1.55m,sphere diameter 330nm光子晶体制备光子晶体制备5mdissolvelatex spheres6-layer 001 silica diamond lattice4-layer 111 silica diamond lattice5m F.Garcia-Santamaria et al.,Adv.Mater.14(16),1144(2002).Layer-by-Layer Lithography Fabrication of 2d patterns in Si or GaAs is very advanced(think:Pentium IV,50 million transistors)So,make 3d structure one layer at a timeinter-layer alignment techniques are only slightly more exoticNeed a 3d crystal with constant cross-section layersA Layered Structure(diamond-like:rods “bonds”)ABC S.G.Johnson et al.,Appl.Phys.Lett.77,3490(2000)Up to 27%gapfor Si/airhole layerA More Realistic Schematic M.Qi,H.Smith,MIT e-beam Fabrication:Top View M.Qi,H.Smith,MIT e-beam Fabrication:Side Views(cleaving worst sample)M.Qi,H.Smith,MIT X-ray Interference LithographyThe GoodLarge area:up to 10 x10cm!Cheap($50k vs.$500k for e-beam)M.Qi,H.Smith,MIT The UglyLayer alignmentstill trickyFrom Rectangular to Hexagonal M.Qi,H.Smith,MIT The Woodpile Crystalan earlier design:(&currently more popular)K.Ho et al.,Solid State Comm.89,413(1994)H.S.Szer et al.,J.Mod.Opt.41,231(1994)Up to 17%gap for Si/air(diamond-like,“bonds”)Figures from S.Y.Lin et al.,Nature 394,251(1998)光子晶体中电磁波的传播方程光子晶体中电磁波的传播方程Maxwell equationFinal equationBloch Equation光子带隙光子带隙DielectricConstantGaAs:13GaAlAs:12Air:1光子晶体和半导体特性的比较光子晶体和半导体特性的比较光被禁止出现在光子晶体的带隙光被禁止出现在光子晶体的带隙-控制光的行为控制光的行为:(1)(1)抑制自发辐射抑制自发辐射(2)(2)缺陷产生单模发光缺陷产生单模发光,光子导线光子导线 (光子计算机光子计算机)