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研究生:蕭甫宸
研究生(外文):Fu-ChenHsiao
論文名稱:以Landau-Zener法分析波導模態轉換器於非絕熱轉換之頻寬特性
論文名稱(外文):Bandwidth Analysis of Waveguide Mode Converters Based on Landau-Zener Analysis of Non-adiabatic Energy Crossing
指導教授:曾碩彥曾碩彥引用關係
指導教授(外文):Shuo-Yen Theng
學位類別:碩士
校院名稱:國立成功大學
系所名稱:光電科學與工程學系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:英文
論文頁數:57
中文關鍵詞:量子力學波導光學
外文關鍵詞:waveguidequantum mechanicswave optics
相關次數:
  • 被引用被引用:0
  • 點閱點閱:98
  • 評分評分:
  • 下載下載:6
  • 收藏至我的研究室書目清單書目收藏:0
這些年來,許多研究團隊逐漸對於量子力學與波導光學的相似性和應用層面逐漸感到興趣,並且也利用了這兩個領域之間的相似性發展出許多有趣的元件和突破了許多傳統上在波導光學部分所遇到的瓶頸。其中一項研究主題,就是所謂的波導模態的轉換器,藉由在波導上蝕刻出周期性的結構,達到在波導裡建構出周期性的折射率變化,更進一步達到模態轉換的目的。以往的研究顯示,依照絕熱理論所推算出來的折射率變化結構,可以讓模態轉換的路徑依循著絕熱轉換路線,並且得到近乎100%的模態轉換效率。然而,在不同的輸入波長之下,會導致波導轉換器系統產生波長的失調誤差。而這種失調情況即會造成波導轉換器在做模態轉換時,偏離絕熱路線,並且嚴重的影響模態的轉換效率。因此,我們期望能夠分析在存在失調誤差的情況之下波導模態轉換器的轉換效率,藉此我們才可以設計出最適用的折射率變化結構。然而,依照傳統的偶合模態理論(Coupled Mode Theory)或是光束傳播分析法(Beam Propagation Method)都無法提供一個解析的分析結果讓我們可以得到轉換效率與波導結構參數之間的關係。因此,在本篇論文中,我們引用的藍道基納分析法(Landau-Zener Method),針對在波導模態轉換器中,因為波長失調所產生的非絕熱的轉換點進行分析,藉此得到了一個在存在波長失調情況之下的模態轉換效率的解析解。此外,我們還利用了這個解析解,來去預測在不同的波導結構參數之下,模態轉換的效率與趨勢。
Mode conversion can be achieved in multimode waveguides using optical analogy of stimulated Raman adiabatic passage. According to this, we can describe the mode conversion in a step-index multimode waveguide with detuning as a three-level atomic system and analyze it by using the analogies between quantum mechanics and wave optics. In this thesis, we derived the couple mode equation for adiabatic mode conversion via an intermediate mode with wavelength detunings for an engineered step-index multimode waveguide. The Landau-Zener model of non-adiabatic crossing is used to analyze the spectral response of the mode converters and shown to be in good agreement with numerical solutions of the coupled mode equations. The analytical expressions from Landau-Zener analysis offer useful insight into the spectral properties of the mode converters and suggest bandwidth tenability of these photonic devices. Furthermore, we demonstrate bandwidth tenability of the mode converter by some numerical examples.
ABSTRACT........................I
摘要 .......................II
ACKNOWLEDGE...................III
TABLE OF CONTENTS..............IV
LIST OF FIGURES................VI
1 Introduction..................1
2 Quantum mechanics of the atom-radiation interaction......................4
2.1 Hermitian operator..........4
2.2 Form of the Hamiltonian in atom-radiation interaction......................5
2.3 Light-matter interaction in a two-level atomic system and the Rotating Wave Approximation(RWA)
.................................8
2.4 The Hamiltonian of three-level atomic system with wavelength detuning.............12
2.5 The evolution in a three level system under two-photon resonance.......................16
3 Wave optics..................22
3.1 Wave equation for electric field in optical waveguide.......................22
3.2 Coupled-wave analysis......24
3.3 Coupled-mode equation under the codirectional coupling condition.......................28
3.4 Analogies between wave optics and quantum mechanic........................30
4 Landau-Zener analysis with non-adiabatic crossing of eigenvalues.....................33
4.1 Non-adiabatic crossing analysis of energy levels Landau-Zener analysis...........34
4.2 Landau-Zener transitions and population transfer in a three-level system driven by two laser pulses
................................38
4.3 Bandwidth tunability of the mode converters......................48
4.3.1 Bandwidth tunability depend on spatial delay of coupling
coefficient.....................48
4.3.2 Bandwidth tunability depend on the length of the waveguide.......................52
5 Conclusion...................55
Reference.......................56
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