多模態干涉波導自我呈像原理誤差的修正

矽光元件波導在現今的科技發展是非常快速的，因為矽光元件的製程符合光積體電路(PICs)，並且由於矽及二氧化矽高折射率的差異比(HIC)可使得元件尺寸微小化。矽光波導在應用上也有重大的表現，像是光學濾波器(filter)、光學轉換器、方向耦合器及功率分配器。另外，在光積體電路中，多模態干涉耦合器是一種不可獲缺的元件，像是光學轉換器、共振型濾波器、陣列波導光柵分波多工器和(極化)功率分配器。多模態干涉耦合器具有堅實與簡單化的優點。多模態干涉耦合器是由-自我呈像原理(self-image principle)所推得，簡而言之即是由輸入的訊號場分解為各個模態的場型大小(可視為傅立葉分析)，再經由每個模態場的干涉現象所推得。不過，在高折射率差異比與微小化的多模態干涉元件仍有它的缺點。原因就在於推得自我呈像原理的公式有兩個假設。有效寬度近似於實際寬度：因為穿透深度在高折射率差異下很小的緣故，使得在每個模態下有有效寬度近似於實際寬度的假定。入射角小：由於入射角很小的假定，使得 k_yv^2≪k_0^2 n_r^2。但是在小尺寸元件之下，穿透深度無法忽略，使得會產生相對大的有效寬度，所以並不能將有效寬度視為實際寬度。另外，元件在高折射率差異之下，在完全反射的定律中可以告訴我們，入射角度的條件將會變大，所以也不能視每個模態下 k_yv^2≪k_0^2 n_r^2。在上述的條件中顯示，在小尺寸及高折射率差異的多模態干涉耦合器，自我呈像原理的公式將會產生誤差，並且這些誤差會使得輸出的訊號強度衰減，因此我們需要對自我呈像原理的公式做一些修正。修正的原理是由波動方程式和細微擾動法(perturbation method)去推得更精確的原理。也就是在波導之中做一些折射率差異的變化。此篇論文所使用的範例為1×1的絕緣層上覆矽通道型波導，並且利用三維光束傳播法(3D-BPM)為主的模擬工具去驗證理論上推導的精確度。在原理和光積體電路製程的原故之下，我們將覆蓋一層光阻在波導之上來用以改變波導原有的傳播常數。之後並討論在實際案例的應用，以1×2的通道型波導為例。在此實驗模擬之下，顯示出修正後與原有的波導在效率上有明顯提升，因此，此方法在提升波導的效率是有效的。因為此概念分析是一個展新的概念，實驗室希望能利用這個技術得到更好的效率提升及利用此方法在其他的光積體電路之上。

關鍵字

光積體電路(PICs) ；高折射率差異(HIC) ；多模態干涉耦合器(MMIs) ；自我呈像原理(self-mage principle) ；細微擾動法(perturbation method) ；三維光束傳播法(3D BPM)

並列摘要

Nowadays, silicon photonic waveguides have been developed quickly because their devices are suitable for the fabrication of photonic integrated circuits (PICs) and they have small sizes from the property of high index contrast (HIC) between silicon (Si~3.46) and silica (SiO2~1.44). Silicon photonic waveguides also have widely used, such as optical filters, optical switches, optical directional couplers and power splitter. Furthermore, a multimode interference (MMI) coupler is an important element in various PICs, like optical switches, resonator filters, arrayed-waveguide grating (de)multiplexers and (polarization) power splitters. MMI couplers have the advantages of their compactness and simplicity and the working function is easier. MMI is from a straight thought, it is called self-image principle. To speak it briefly, self-image principle is to divide an input optical profile into every existing mode, this step is almost like the Fourier transform and then analyzes the interference of each mode. However, there still are drawbacks in MMI devices with HICs materials and small size structure. Because in order to get the self-image length, which is based on two assumptions: (a) The “effective” width W_e, we can approximate as the physical width W_m, i.e., W_e=W_m. (b) The angle of incident is very small, i.e., k_yv^2≪k_0^2 n_r^2. However, in small and HIC MMI devices, the self-image length is not the exact length of N-fold image and it will cause some power losses which reduce the output efficiency. Therefore, we drive the scalar wave equation and use perturbation method to correct the self-image length. In this work, it takes the 1×1 silicon on insulator (SOI) channel waveguide splitter to test and verify our revised method. The three-dimensional beam propagation method (3D-BPM) and TE polarization are utilized to simulate the analysis. From the theory and according to the fabrication of photonic integration circuits (PICs), we chose the photoresist on the top of waveguide to manipulate the propagation constants. And then it will take 1×2 SOI channel waveguide for the case of power splitter. From our simulation results, it shows that the efficiency is larger with the modified structure than that with the original one. As a result, the method in this paper can be helpful for improving the efficiency. Because the method in this paper is a new concept, we hope this method can improve much more efficiency in MMI devices and find other applications in PICs in the future.

並列關鍵字

photonic integrated circuits(PICs) ； high index contrast(HIC) ； multimode interference(MMI) ； self-image principle ； perturbation method ； 3-D beam propagation method (3-D BPM)

參考文獻

[1] H. Nishihara, “Recent advancement on optical integrated circuits,” Conference on Computer and Communication Systems, 1990.

[2] R. Soref, “The Past, Present, and Future of Silicon Photonics,” Selected topics in quantum electronics, Vol. 12, No. 6, pp. 1678－1687, 2006.

[3] M. Naydenkov, and B. Jalali, “Advances in Silicon-on-Insulator Photonic Integrated Circuit (SOIPIC) technology,” International SOI Conference, 1999.

[4] B. Jalali, and S. Fathpour, “Silicon Photonics” Lightwave tech., Vol. 24, 2006

[7] S. Lardenois, D. Pascal, L. Vivien, E. Cassan, and S. Laval, “Low-Loss Submicrometer Silicon-on-Insulator Rib Waveguides and Corner mirrors,” Opt. Lett., Vol. 28, No. 13, pp.1150－1152, 2003.

國際替代計量

多模態干涉波導自我呈像原理誤差的修正

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