臺灣博碩士論文加值系統

在微波頻段的實驗量測中，我們觀察發現電磁波透射光子晶體稜鏡會有負責射偏折的現像，其偏折可直接以司乃爾定律定義出折射率。此外在研究當中我們並以時域有限差分演算法來進一步驗證負偏折現象。在理論分析當中，發現群折射率與相折射率的乘積值才具有物理意義。藉由k．p理論分析偏折現象時，可以獲知群折射率與相折射率的乘積與微波段實驗負折射偏折結果相謀合。如此一來我們可以利用量測光透射光子晶體的偏折狀態來建構光子能帶結構。並且根據k．p理論，電磁波在光子晶體中的群速度可以定義為準粒子的有效質量與動量的比值且電磁波在光子晶體當中傳播的行為就像具有質量的準粒子。

We have observed the electromagnetic waves undergo negative refraction in a two-dimensional photonic crystal prism in microwave frequency regime. By measuring the refraction angles of EM waves propagating through a PCP, and applying the Snell’s law to the exit interface of PC and air, we deduced the negative refractive indices which are consistent with the simulated results by using the finite-difference time-domain (FDTD) method. We show that only the product of phase index and group index has the physical meaning. The calculated product of phase index and group index derived from the extended k p theory fit reasonably well with the experimental data. Thus, it is possible to reconstruct the photonic band structure from measurement of refraction angles for light propagation through the PC. And, according to the extended k p theory, the group velocity of EM waves in PC can be defined as the ratio of momentum to relativistic effect mass of a quasi-particle. The EM wave propagating in PC behaves like a massive quasi-particle.

Content
Abstract (in Chinese)………………………………………………………ⅰ
Abstract (in English)………………………………………………………ⅱ
Acknowledgements……………………………………………………..…ⅲ
Contents……………………………………………………………………ⅳ
List of Figures………………………………………………………..….…ⅵ
Chapter I Introduction………………………………...…………..…..………1
1-1 Background……………………………………………………….……1
1-2 Motivation………………………………………………………...……2
1-3 Organization of the thesis………………………………………………3
Chapter II Theory and methodology…………………………………4
2-1Introduction………………………………………………………………4
2-1.1 Refraction phenomenon in homogenous medium………………4
2-2.2 Refraction phenomenon in photonic crystal……………………5
2-2 Refractive index in photonic crystal……………………………………10
2-2.1 Phase velocity, Group velocity, and Energy velocity…………10
2-2.2 Calculation of Group Velocity…………………………………12
2-3 Electromagnetic simulation using the FDTD method…………………14
2-3.1 Introductions to the FDTD algorism……………………………14
2-3.2 One dimension free space formulation …………………………15
2-3.3 Simulation in periodic structure ………………………………15
2-4 k p theory ……………………………………………………………20
Chapter III Experiment………………………………………………24
Chapter IV Results and Discussion…………………………………27
4-1 The photonic crystal sample measurement ……………………………27
4-2 The refraction angle measurement ……………………………………28
4-3 The negative refraction index discussed in k p theory and Hellmann-Feynman theory…………………………………………....……31
4-4 The negative refraction phenomenon simulated with the FDTD method……………………………………………………………………37
4-5 The negative refraction phenomenon…………………………42
Chapter Ⅴ Conclusion……………………………………………………44
References …………………………………………………………………46

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