三維層疊式光子晶體之穿透與放射頻譜計算分析

本論文主要探討三維層疊式(layer-by-layer)光子晶體，在加入各種面缺陷(planar defects)結構後的穿透(transmission)及放射(emission)特性。文中利用三維平面波展開法及超晶格(supercell)來求得缺陷結構的特徵模態(eigen-mode)；並利用三維時域有限差分法配合平行計算程式來求取各種結構的穿透頻譜和放射頻譜。由頻譜分析和垂直向共振模場我們可以清楚地得知，面缺陷的特徵模態可分為缺陷共振模(defect mode)和帶緣共振模(band-edge resonant mode)兩種。前者只在缺陷層內以共振腔的形式存在；後者除了在缺陷層內形成共振腔外，還會在缺陷層附近的光子晶體結構產生駐波。利用三維層疊式光子晶體可以改變自發性放射(spontaneous emission)，不同偏極化以及位於不同位置的耦極輻射源，都具有不一樣的放射頻譜。研究顯示，在全方位光子能隙的頻率範圍內，任何偏極化方向、任何位置上的耦極，其自發性放射率都會被強烈地抑制；在帶緣頻率(band-edge frequency)上則依耦極偏極化方向和位置而有不同的放射加強。雖然帶緣模態可以加強自發性放射率，但是卻降低了光取出效率。改用具有面缺陷結構的層疊式光子晶體，不但可以在一定頻段範圍內提供很大的放射改變因子，並且可以藉由面缺陷的垂直向共振效應來提高光取出效率。

關鍵字

三維層疊式光子晶體；全方位光子能隙；面缺陷；時域有限差分法；平行計算；穿透頻譜；缺陷共振模；帶緣共振模；自發性放射；耦極輻射；放射頻譜；光取出效率

並列摘要

This thesis studies about the transmission and emission properties of various planar defects in the three-dimensional (3D) layer-by-layer photonic crystal. Two numerical methods have been employed with parallel programming for electromagnetic simulation. One is the 3D plane-wave expansion (PWE) method with supercell technique, which is used for finding eigen-modes of defects. The other is the 3D finite-difference time-domain (FDTD) method, which can simulate the time response and transmission or emission spectrum. Two different kinds of resonant modes, the defect mode and the band-edge resonant mode, have been clarified by spectrum analysis and calculated mode profiles. While the former appears only inside the cavity located at the defect layer, the latter appears not only in the defect layer but also with the standing wave concentrated in the dielectric or the air part of a photonic crystal. The finite three-dimensional layer-by-layer photonic crystal is shown to drastically modify the spontaneous emission rate of an embedded dipole. Simulation shows that the emission spectra are quite different when the position or polarization of the dipole is changed. However, there is always strong suppression of spontaneous emission in the frequency range of complete photonic bandgap (PBG). On the other hand, the emission rate can be enhanced by the large photonic density of state (DOS) at the band edges. Although we can observe high modification factor of spontaneous emission with dielectric or air band-edge modes, the light extraction is lower than that of the free-space radiation. Instead, by appropriately employing a planar defect structure we obtain not only strong enhancement of emission at a frequency range but also large extraction efficiency due to the vertical resonance effect in the defect layer.

並列關鍵字

3D layer-by-layer photonic crystal ； complete PBG ； planar defect ； FDTD ； parallel computation ； transmission spectrum ； defect mode ； band-edge resonant mode ； spontaneous emission ； dipole radiation ； emission spectrum ； extraction efficiency

參考文獻

[1] E. M. Purcell, “Spontaneous emission probability at radio frequencies,” Physical Review, vol. 69, pp. 681 (1946).

[2] K. Ohtaka, “Energy band of photons and low-energy photon diffraction,” Physical Review B, vol. 19, pp. 5057-5067 (1979).

[3] E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Physical Review Letters, vol. 58, pp. 2059-2062 (1987).

[4] S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Physical Review Letters, vol. 58, pp. 2486-2489 (1987).

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

國際替代計量

三維層疊式光子晶體之穿透與放射頻譜計算分析

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