適於不同材料特性之光電問題的有限差分時域法之發展

Development of the Finite-Difference Time-Domain Method for Photonics Problems of Different Material Characteristics

張瀚之(Han-chih Chang)

指導教授 ： 張宏鈞

國立臺灣大學/電機資訊學院/光電工程學研究所/碩士(2007年)

https://doi.org/10.6342/NTU.2007.01914

摘要

本論文之目的在於發展並應用有限差分時域法於不同材料特性之光電問題。我們使用軸向完美匹配層，搭配輔助微分方程，發展並分析有限差分時域法對於各向異性材料、金屬色散材料、以及非線性材料之模擬技巧。在傳統介質材料方面，我們利用有限差分時域法探討二維光子晶體波導與傳統二維介質波導的接面損耗問題；此外，我們針對二維光子準晶體計算其穿透響應，並與二維光子晶體之穿透響應進行比較。在各向異材料方面，首先我們計算由軸向材料植入空氣柱所組成之二維光子晶體於不同光軸指向時之穿透響應；並利用所獲得的物理圖像，探討傳討介質材料中植入液晶柱之二維光子晶體在液晶光軸指向改變時其穿透響應相對應的變化。在金屬色散材料方面，我們討論於可見光波段進行金屬模擬所需要注意的技巧，引入額外的勞倫茲模型(Lorentz model)對傳統廣為使用的祝德模型(Drude model)進行修正，並運用此較準確的金屬材料模型分別模擬由金、銀、銅、以及理想金屬所組成的二維次波長金屬光柵於可見光波段上之遠場穿透響應；此外，我們亦使用三維有限差分時域法分析三維次波長金屬柱在次波長光學顯像上的應用可能與限制。在非線性材料方面，我們探討瞬時克爾效應(instantaneous Kerr effect)於有限差分時域法之模擬技巧，運用於四波混頻過程(Four-wave mixing, FWM)之計算，最後將結果與傳統緩變波包近似(slowly-varying envelop approximation)所得到的理論預測值進行比較。

關鍵字

有限差分時域法 ； 光子晶體 ； 光子準晶體 ； 非線性材料

並列摘要

With the uniaxial perfectly matched layer employed in the model, we develop a full-vectorial finite-difference time-domain (FDTD) method for numerical model of various photonics structures of different materials, including anisotropic, nonlinear, and metallic materials, simultaneously in one single computational domain. Detailed modeling issues of various materials are explicitly elaborated in order to extend the full power of the FDTD algorithm. The junction loss for a two-dimensional (2D) photonic crystal waveguide made of traditional dielectric materials is investigated and explained. We also study the photonic quasicrystals fabricated from multiple exposure techniques. The transmission properties of the 2D photonic quasicrystal slabs are calculated and compared with those of the 2D photonic crystal slabs. Also explored are anisotropic materials, focused on the transmission properties of a 2D air-hole anisotropic photonic crystal slab and a 2D liquid-crystal-hole dielectric photonic crystal slab, which combine the concepts of photonic crystals and anisotropic materials. Important modeling techniques about noble materials in the visible spectral range are discussed to include the absorption band at lower wavelengths (which is missing from the widely used Drude model), and a more realistic model, featuring the combinations of the Drude model and the multiple-pole Lorentz model, is demonstrated. We further apply this more realistic model to investigate the actual absorption effect for the transmission property of 2D metallic nanostrip arrays, with the material ranging from gold, silver, copper, and the perfect conductor. A 3D FDTD simulation is performed on a 3D metallic nanorod array, and the possibility and limitation of this structure as a new tool for subwavelength optical imaging are discussed. Finally the instantaneous third-order nonlinear materials are addressed. Comparisons are made between our nonlinear FDTD simulation and the analytical prediction under the slowly-varying envelope approximation, for the parametric four-wave mixing process.

並列關鍵字

FDTD ； finite-difference time-domain method ； photonic crystal ； photonic quasicrystal ； metallic material ； the Drude model ； the Lorentz model ； subwavelength optical imaging ； instantaneous third-order nonlinearity ； kerr medium ； FWM ； parametric four-wave mixing process

參考文獻

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