次波長光柵波導結構之研究

Abstract

在本篇論文中，我們提出一個適用於直線和彎曲波導中有效率又準確的三維次波長光柵波導模態解析器，其運作原理如下所述。基於次波長光柵波導擁有結構近似線性的色散關係，我們使用轉換矩陣法得到其等效均勻介質折射率，因此三維次波長光柵波導將可視為一均勻三維波導結構，接著再使用有限元素法計算各種此三維次波長光柵波導的模態分布及相關特性。為了驗證我們模態解析器的準確度，我們探討多種不同幾何結構上的直線和彎曲次波長光柵波導，並且透過重疊積分與三維有限時域差分法所解出的模態之間來作比較。其比較結果顯示，我們模態解析器所獲得的模態分佈與三維有限時域差分法所解出的模態具有高達96%之重疊積分值，顯示我們所發展之模態解析器具有高準確度。因此，我們將此模態解析器應用至錐形波導及環形共振腔設計。在錐形波導設計中，我們提出漸變填充因子方式來設計錐形波導來設計於兩種三維次波長光柵波導 ，藉以改變在三維次波長光柵錐形波導中的等效介質折射率和模態。模擬結果顯示此設計可以獲得長度大於2 m以上的錐形波導長度其損耗會低於0.14 dB。另一方面，我們提出半徑3 m的PSWG環形共振腔，透過模態解析器所計算的模態等效折射率值可推算出此設計之共振波長值及自由光譜範圍，且模擬結果顯示此PSWG環形共振腔之消光比為25.72 dB、品質因子為1062.3、半高寬為1.45 nm且其自由光譜範圍為 33nm。

We propose an efficient and accurate mode solver for three dimensional subwavelength grating (3D SWG) waveguides with straight and bend structures. Based on the approximated linear dispersion relation of the SWG structures, we utilize the transfer matrix method (TMM) to obtain the equivalent effective index of a SWG structure, and then a 3D SWG waveguide is equivalent to the conventional 3D waveguide. At last, we use the finite element method (FEM) to realize the modal distributions and related properties of this SWG waveguide. To confirm our mode solver, we investigate several straight and bent SWG waveguides with different geometric parameters and compare to the modes calculated by 3D finite difference time domain (FDTD) method by using the overlap integral. We observe the values of overlap integrals are larger than 96 %, showing that our mode solver is highly accurate. Besides, we apply this mode solver to design tapered waveguides and ring resonators. We propose two SWG tapered waveguides by varying the filling factors along the structures. Then the effective medium indices along the structures are varied and thus the mode is converted along the SWG tapered waveguides. The simulated results show that the taper with its length larger than 2 m has its taper loss of less than 0.14 dB. On the other hand, we use the obtained effective indices of a partial SWG bending structure with a radius of 3 m to calculate the resonant wavelengths and the free spectral range (FSR) of the corresponding PSWG ring resonator. The FDTD simulated results show this PSWG ring resonator has extinction ratio of 25.72 dB, quality factor (Q factor) of 1062.3, FWHM of 1.45 nm and FSR of 33 nm.