受子與施子型面缺陷結構三維層疊式光子晶體之穿透及放射特性分析

本論文主要探討圓形斷面介電質長條構成之三維層疊式(woodpile)光子晶體與其加入受子與施子型面缺陷(planar defects)結構後的穿透(transmission)及放射(emission)特性。受子型缺陷為移除光子晶體內一部分介電質所構成的缺陷結構；施子型缺陷為增加光子晶體內介電質之體積構成。本文中討論了介電質變化、半徑變化、差排以及混合型四種不同型態的缺陷結構來分析各種面缺陷模態。論文使用超晶格(supercell)平面波展開法來計算缺陷結構的頻率與波向量的關係並以有限時域差分法來模擬在真實空間中各種結構的頻譜以及缺陷模態電場分佈。模擬的結果顯示受子型面缺陷結構的特性為缺陷模態頻率產生在靠近光子晶體能隙低頻帶緣的部分，並且隨著移除的體積增加升高。施子型面缺陷結構的特性為缺陷模態頻率產生在靠近光子晶體能隙高頻帶緣的部分，並且隨著加入的體積增加降低。受子型缺陷模態電場的分佈傾向於集中在缺陷的中心，而施子型缺陷模則集中在缺陷結構與光子晶體交界的部分，缺陷結構的中心反而通常是能量較低的部分。理論與模擬顯示自發性放射(spontaneous emission)會受到放射光場的影響而改變。三維層疊式光子晶體的全方位光子能隙的頻率範圍可以抑制自發性放射，而三維層疊式光子晶體面缺陷結構缺陷模態在適當的條件下則可以增加放射的功率。放射功率增益(抑制)以及不同方向的取出效率會隨著結構的變化而改變，不同偏極化以及位置的偶極輻射源的放射場會因為對稱性而產生不同的物理機制，此特性可以做為操縱自發性放射的方式。

關鍵字

三維層疊式光子晶體；全方位光子能隙；面缺陷；平面波展開法；有限時域差分法；穿透頻譜；缺陷共振模；自發性放射；放射頻譜；光取出效率

並列摘要

This thesis focuses on the transmission and emission properties of various acceptor and donor type planar defects in the three-dimensional layer-by-layer photonic crystal (woodpile) composed of cylinder rods. The acceptor-type defect can be formed by removing some dielectric material in the photonic crystal; the donor type defects can be formed by adding some extra dielectric material. Four types of planar defects which are made by changing dielectric constants, radius of the cylinder, dislocation of the rods and mixed-type are studied in this thesis. The plane-wave expansion method with super-cell technique is used to calculate the dispersion relations of the photonic crystal with or without defects. In addition, the finite-difference time-domain method is then used to calculate the responses in real space and time domain, such as transmission or emission spectrums. The numerical results of the simulations indicate that the frequency of an acceptor-type defect mode is generated near the lower edge of the band gap and rises with the removing volume of the dielectric material. The frequency of a donor defect mode is generated near the higher edge of the band gap (pseudo gap) and decreases with the adding volume of the dielectric material. The field pattern of acceptor type defect modes tends to concentrate in the center of the defect, but the donor type defect modes prefers to concentrate between the defect and original photonic crystal. It is shown by theories and simulations that spontaneous emissions can be manipulated by the field pattern of the source surrondings. Spontaneous emission is inhabited by the complete photonic band gap of the finite three-dimensional woodpile photonic crystals. Meanwhile, the spontaneous emission can be enhanced by the defect modes with proper conditions. The radiation powers and the efficiency of the light extractions in different directions strongly depend on the symmetry of the structure and the field patterns which are determined by the position and the polarization of the dipole source. These properties provide a way to control the spontaneous emission.

並列關鍵字

3D layer-by-layer photonic crystal ； complete photonic band gap ； planar defect ； plane-wave expansion ； finite-difference time-domain ； transmission spectrum ； defect mode ； spontaneous emission ； dipole radiation ； emission spectrum ； extraction efficiency

參考文獻

[ 37] J. M. Shieh, Y. F. Lai, Y. C. Lin, and J.Y. Fang, “Photoluminescence: principles, structure and applications,” Instruments Today (2005).

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[ 3] J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals, Princeton University Press (2008).

[ 4] S. G. Johnson, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Guided modes in photonic crystal slabs,” Physical Review B, vol. 60, 5751-5758 (1999).

國際替代計量

受子與施子型面缺陷結構三維層疊式光子晶體之穿透及放射特性分析

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