本研究發展一半解析法以快速計算具有三維金屬與多層介電質組態之表面電漿波導布拉格光柵。相較於全三維數值模擬方法如有限元素法(Finite-Element Method)或時域有限差分法(Finite-Difference-Time-Domain Method)，此半解析法可大幅減少所需之計算時間與計算資源。於此近似過程中，三維電漿子波導布拉格光柵結構之橫向與縱向變化將分別被考慮。首先，將具有對於波導寬度作正弦調變之光柵單位週期切分為數個區段，每一區段皆近似於一直線型之「金屬-多層介電質-金屬」表面電漿波導。利用三維數值方法做模態分析，直線波導之模態分布以及相對應之有效折射率可於考慮電場與磁場之所有分量之計算後獲得。此一包含所有區段之序列可被合成為一個一維多層有損介質光柵。而經轉換後之一維有損多層介質光柵之禁帶與反射率頻譜可利用嚴格之傳輸線法計算而得。將此半解析法應用於設計以第二階模態合成之表面電漿波導光柵，並且以三維全向量(full-vector)之時域有限差分法及有限元素法做數值模擬驗證。經由數值模擬與半解析法近似結果計算所得之布拉格波長，其誤差值介於0.0012~0.0399，顯示此半解析法具有相當程度之可靠性。對於具有較多週期數量或是利用第三階模態合成之光柵，其結果亦經由模擬取得並於本論文中加以討論。對半解析法所合成之結構稍做調整所得之表面電漿波導光柵具有中心波長位於1540 nm及半高全寬頻寬(full-width-at-half-maximum bandwidth) 12.7 nm之禁帶，且其位於禁帶之傳輸率為17.77%。此波導光柵之總長小於9 另一方面，本研究亦利用模擬熱退火最佳化演算法對以半解析法合成之光柵於三維數值模擬計算中進行最佳化設計。以一具有50 nm之半高全寬頻寬且中心波長位於1550 nm之禁帶為目標頻譜，並要求其傳輸率於通帶與禁帶分別為85%及0%。經由此最佳化之方式，最終可得到最佳化之頻譜其禁帶具有半高全寬頻寬42.6 nm，且其中心波長為1544 nm，於通帶及禁帶則分別具有約80%及4.496%之傳輸率。結果與所設定之目標頻譜相符。In this research, a semi-analytical approach is developed to facilitate the design of three-dimensional (3D) plasmonic waveguide Bragg gratings in metal/multi-insulator/metal (MMIM) configuration. When compared to the full-vector 3D numerical simulations, this method consumes less time and computational resources. In this method, the unit cell of the sinusoidally-width-modulated grating is approximated by a series of straight MMIM waveguides. By using the 3D finite-element method (FEM), the guided modes and their mode distributions/effective indices supported by the straight MMIM waveguide can be obtained. The corresponding 1D grating can then be constructed by replacing the straight waveguides with layers of the corresponding effective indices. It can then be conveniently analyzed by the transmission-line method, and the forbidden band(s) and the reflectance can be obtained accordingly.The semi-analytical approach is verified by the 3D full-vector numerical simulations based on the finite-difference-time-domain method and FEM for gratings synthesized using the 2nd-order mode. It is shown that the errors (absolute values) in the Bragg wavelength range from 0.0012 to 0.0399. This shows that the semi-analytical approach is valid and very reliable. For gratings using more unit cells and those synthesized using the 3rd-order mode, their corresponding spectra are also studied numerically and discussed in this thesis. A modified MMIM plasmonic Bragg grating which has a FWHM bandwidth of 12.7 nm centered at 1540 nm with a total length of < 9 is achieved. The transmission at the Bragg wavelength is 17.77%.Finally, the 3D MMIM waveguide grating synthesized using the semi-analytical approach is optimized using 3D full-vector numerical simulations incorporated with the simulated annealing algorithm. The optimized transmission spectrum of a 7710-nm long MMIM grating has a bandwidth of 42.6 nm centered at 1544 nm, and the transmittance in the pass band and stop band is about 80% and 4.496%, respectively. The final transmission spectrum fits well with the predefined spectrum.
