光子晶体计算

nullnull光子晶體原理與計算 (II) 光的負折射及異常傳播 (Negative refraction and anomalous propagation of light) 光子晶體透鏡 (Photonic crystal lenses) 次波長聚焦 (Subwavelength focusing) Pi-Gang Luan (欒丕綱) Wave Engineering Lab (波動工程實驗室) Institute of Optical Sciences National Central University (中央大學光電科學研究所)負折射 (Negative Refraction)負折射 (Negative Refraction)西元 1968 年由蘇聯科學家 V. G. Veselago 提出 “左手介質” (Left-handed materials) 理論 西元 2000 年, 美國物理學家 D. R. Smith 做出 “人工的” (artificial) 左手介質 同年, 英國物理學家 John. B. Pendry 在 Phys. Rev. Lett. 提出 “完美透鏡” 構想, 而日本 科學家 M. Notomi 仔細 分析 定性数据统计分析pdf销售业绩分析模板建筑结构震害分析销售进度分析表京东商城竞争战略分析 了光子晶體在 “非長波極限” 下的光傳播行為 近年, “光子晶體負折射” 與 “次波長成像” 成為熱門的研究領域 Left-Handed Materials Left-Handed MaterialsD. R. Smith et. al., Physics Today, 17, May (2000). Phys. Rev. Lett. 84, 4184 (2000) ; Science, 292, 77 (2001) The Building Blocks of LHM The Building Blocks of LHMElectric Dipoles Magnetic Dipoles+左手介質的負折射機制: TM 波 左手介質的負折射機制: TM 波 兩種負折射的比較兩種負折射的比較左手介質光子晶體 (利用特殊的色散特性)Negative Refraction by LHM: Beam PropagationNegative Refraction by LHM: Beam PropagationnullNegative Refraction of PC: Beam propagation完美透鏡 ( Perfect Lens)完美透鏡 ( Perfect Lens)J. B. Pendry, Phys. Rev. Lett. 80, 3966 (2000)“All this was pointed out by Veselago some time ago. The new message in this Letter is that, remarkably, the medium can also cancel the decay of evanescent waves. The challenge here is that such waves decay in amplitude, not in phase, as they propagate away from the object plane. Therefore to focus them we need to amplify them rather than to correct their phase. We shall show that evanescent waves emerge from the far side of the medium enhanced in amplitude by the transmission process.”null 表 关于同志近三年现实表现材料材料类招标技术评分表图表与交易pdf视力表打印pdf用图表说话 pdf 面電漿子 (Surface-Plasmon-Polaritons (SPP))SPP exists whenε<0 or μ<0 in the blue region Subwavelength Focusing Effect Surface-Plasmon-Polariton (SPP) Subwavelength Focusing Effect Surface-Plasmon-Polariton (SPP)對 “負折射” 與 “完美透鏡” 的質疑對 “負折射” 與 “完美透鏡” 的質疑 Negative Refraction Makes a Perfect Lens J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000). Left-Handed Materials Do Not Make a Perfect Lens N. Garcia et al., Phys. Rev. Lett. 88, 207403 (2002) Perfect lenses made with left-handed materials: Alice’s mirror? Daniel Maystre and Stefan Enoch, J. Opt. Soc. Am. A, 21, 122 (2004) Is it Possible? Is it Possible? “Left-Handed Materials Do Not Make a Perfect Lens”, N. Garcia and M. Nieto-Vesperinas, PRL 88, 207403 (2002) “Wave Refraction in Negative-Index Media: Always Positive and Very Inhomogeneous”, P.M. Valanju, R. M. Walser, and A. P. Valanju, PRL 88, 187401 (2002)Negative Refraction of Modulated EM Waves APL 81, 2713 (2002)Negative Refraction of Modulated EM Waves APL 81, 2713 (2002) Simple Explanation Simple Explanation斯乃爾定律 (Snell’s Law)斯乃爾定律 (Snell’s Law)一般晶體 (方解石 Calcite) 所導致的負折射一般晶體 (方解石 Calcite) 所導致的負折射http://arxiv.org/abs/cond-mat/0312125 ( 游漢輝教授等 ) 能量速度 (Energy velocity) 與 群速度(Group velocity)能量速度 (Energy velocity) 與 群速度(Group velocity)Wave energy flows along the normal direction of the constant frequency curve (surface)null 等頻率曲線 (Constant Frequency Curve) Square Lattice v.s. Triangular Lattice Subwavelength Focusing by PC Subwavelength Focusing by PC All-angle negative refraction without negative effective index Chiyan Luo, Steven G. Johnson, and J. D. Joannopoulos, J. B. Pendry, Phys. Rev. B 65, 201104 (2002)See also: Phys. Rev. Lett. 90, 107402 (2003) Phys. Rev. B. 67 235107 (2003) Phys. Rev. B. 68 045115 (2003)“Negative refraction and left-handed behavior in two-dimensional photonic crystals” S. Foteinopoulou and C. M. Soukoulis“Negative refraction and left-handed behavior in two-dimensional photonic crystals” S. Foteinopoulou and C. M. Soukoulisnull次波長成像真的需要負折射嗎 ?L. S Chen, C. H. Kuo, and Z. Ye, Phys. Rev. E 69, 066612 (2004) Z. Y. Li and L. L. Lin, Phys. Rev. B 68, 245110 (2003) S. He, Z. Ruan, L. Chen, and J. Shen, Phys. Rev. B 70, 115113 (2004) Structure and Parameters Structure and Parameters nullIncreasing the interlayer distanced=0.707anullDecreasing the interlayer distanced = 0.707a r = 0.3a D = (d-r)/10Negative Refraction? See also Phys. Rev. E 70, 056608 (2004)   Phys. Rev. B 70, 113101 (2004) Negative Refraction? See also Phys. Rev. E 70, 056608 (2004)   Phys. Rev. B 70, 113101 (2004) 大角度入射時, 正方晶格光子晶體中的負折射現象Square lattice, rotated by 45˚ 大角度入射時, 正方晶格光子晶體中的負折射現象Square lattice, rotated by 45˚ 負折射現象—三角晶格負折射現象—三角晶格光子晶體透鏡 –三角晶格光子晶體透鏡 –三角晶格相位波的超光速傳播現像 (Superluminal propagation of phase wave)相位波的超光速傳播現像 (Superluminal propagation of phase wave) 異常反射 (Anomalous Reflection) 異常反射 (Anomalous Reflection) Beyond the Long-wavelength Limit Beyond the Long-wavelength Limita/λ= 0.49a/λ= 0.58 Convex Photonic Crystal Lens (Triangular Lattice) Convex Photonic Crystal Lens (Triangular Lattice)Concave Photonic Crystal Lens (Triangular Lattice)Concave Photonic Crystal Lens (Triangular Lattice)Negative Refraction by PCNegative Refraction by PCSubwavelength imaging does not imply negative refraction Anomalous refraction, anomalous reflection and strong anisotropy are common features for wave propagation in artificial media beyond the long-wavelength limit Mesoscopic phenomena can happen in both nanoscale world and macroscopic world, only the relative size between the wavelength and the wave-environment interaction range is importantWave-Environment Interaction in Mesoscopic World General FeaturesWave-Environment Interaction in Mesoscopic World General FeaturesWave coherence is important Complex boundaries or many scatterers Wavelength ~ Mean scattering distance (Mean free path) Scattering strength (coupling constant) cannot be too small Multiple scattering (the bare waves are repeatedly scattered) The renormalized wave can be very different from the bare waves The actual size is irrelevant, the relative size is the key parameter. So “Mesoscopic” does not imply “Nanoscale” Similar phenomena can happen in quantum and classical (electromagnetic and acoustic) systems Wave equations + Boundary conditions = Physicsnull Wave Propagation in Periodic Structures — Electric Filters and Crystal Lattices “Waves always behave in a similar way, whether they are longitudinal or transverse, elastic or electric. Scientists of the last (19th) century always kept this idea in mind.” --- L. Brillouin