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論文名稱(中文) 在光子波動力學的理論框架下用時域有限差分法模擬Hong-Ou-Mandel現象
論文名稱(英文) Modeling of Hong-Ou-Mandel Phenomenon by Finite-Difference Time Domain Method under the Theoretical Framework of Photon Wave Mechanics
校院名稱 成功大學
系所名稱(中) 物理學系
系所名稱(英) Department of Physics
學年度 107
學期 2
出版年 108
研究生(中文) 許書尉
研究生(英文) Shu-Wei Hsu
學號 L26064187
學位類別 碩士
語文別 中文
論文頁數 44頁
口試委員 指導教授-蔡錦俊
口試委員-周忠憲
共同指導教授-張世慧
中文關鍵字 Hong-Ou-Mandel干涉現象  光子波動力學  非定域積分  Riemann-Silberstein向量場  50%/50%分光器 
英文關鍵字 Hong-Ou-Mandel interference phenomenon  photon wave mechanics  non-local integral  Riemann-Silberstein vector field  50%/50% beam splitter 
學科別分類
中文摘要   本研究利用光子波動力學(PWM)的理論框架,模擬Hong-Ou-Mandel (HOM) 干涉現象。在此,不同於量子場論的創生、湮滅算符表述,光子態得以由光子波函數依E+icB的複數形式精確地描述,其所遵循的運動方程式正好是古典電磁學中的Maxwell方程,因而適合以FDTD進行數值計算。
  光子波函數的機率由非定域積分的形式給出。此形式要求孿生模態的引入,才能和波包模態構成雙正交基底系統,從而具有Lorentz不變性。因此,其係數平方被詮釋為定域能量密度。
  二維分光器設計為漸逝波耦合的機制,透過數值計算,√3的介質折射率確保了不同的入射模態能有同樣的分光效果。
  經過模擬後,所得結果與HOM 實驗並不相同。有趣的是,其下部包絡符合HOM dip的形狀。看來PWM的理論旨趣並不僅止於理論的完備,或是模擬的需求,它更有助於我們更深地理解基本粒子的特性。
英文摘要 This work simulates the Hong-Ou-Mandel (HOM) interference phenomenon by using the theoretical framework of the photon wave mechanics (PWM). Here, comparing with the creation operator and annihilation operator formalism of the quantum field theory (QFT), photon wave function (PWF) describes the photon state explicitly in the E+icB form, and the equation of motion obeyed is just the Maxwell’s equations in the classical electromagnetics. Therefore, the finite-difference time domain method is suitable for numerical calculations. The probability of the photon wave function is given in the form of non-local integral. This form requires the introduction of dual modes to form the biorthogonal basis system with the wave-packet mode, thus possessing the Lorentz-invariance. Therefore, their modulus square is interpreted as the local energy density. The two-dimensional beam splitter is designed in the mechanism of evanescent wave coupling. Through the numerical calculation, the medium refractive index of √3 ensures that the splitting effects of different incident modes are the same. After the simulation, the result is different from HOM experiment. But interestingly, its lower envelope matches the shape of the HOM dip. This work shows that the theoretical interest of PWM is not only for the completeness of theories or the demand of simulations, but also helping us to understand more deeply the properties of fundamental particles.
論文目次 中文摘要 I
英文延伸摘要 II
誌謝 IX
目錄 X
圖目錄 XI
第一章. 序論 1
第二章. Hong-Ou-Mandel干涉現象 3
第三章. 光子波動力學(PWM) 8
3.1. 光子波函數及其運動方程式 8
3.2. 量子場論(QFT)的波包模態 11
3.3. 理論的應用:行進波包 13
第四章. 分光器設計 14
第五章. 模擬方法 20
5.1. 時域有限差分法(FDTD)簡介 20
5.2. 全場/散射場(TF/SF)技術 23
5.3. HOM干涉現象的模擬架構 27
第六章. 模擬結果 32
第七章. 結論 40
參考文獻 42

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