雙倍自由頻譜間距之交錯連結陷波濾波器設計

本研究提出了一個具有雙倍自由頻譜間距特性的交錯連接陷波濾波器設計，此陷波濾波器的結構是將一環形波導放置於波導交錯結構的側向，並且使用一四分之三大環形將交錯結構的傳輸端與交錯端連結起來形成回饋波導。首先，由於我們使用一具有低損耗、低串音及高頻寬之多模干涉型交錯結構，兩互相交錯的波導可先視為互相獨立不干擾的路徑，因此此結構可等效為具有回饋波導的馬氏干涉儀。我們使用傳輸矩陣法來分析此結構的穿透率反應，獲得此結構共振波長最低穿透率的條件，透過游標效應獲得雙倍自由頻譜間距之光程關係式，並且決定共振波長最低穿透率時的耦合強度與結構損耗的關係式。接著，我們先計算不同曲率波導的等效折射率，使用上述所獲得的關係式來設計我們所提出的結構設計參數，並且使用二維有限時域差分法來模擬整個結構的穿透頻譜反應及與傳輸矩陣法分析結果比較。我們所設計的交錯連接陷波濾波器的設計參數如下：環形波導半徑5 μm，回饋波導半徑為7.348 μm，環形結構與交錯結構間距為163 nm，整體面積小於400 μm*μm。此結構之穿透率光譜顯示其自由頻譜間距為55 nm、品質因子為6200和消光比大於40 dB，顯示出此陷波濾波器具有微型化、寬自由頻譜間距和窄半高寬等優點。

關鍵字

積體光學；光波導；環形濾波器；傳輸矩陣法

並列摘要

We propose a cross-connected notch filter with double free spectral range (FSR) by using a ring resonator laterally coupled to a multimode interference based waveguide crossing which has an external feedback waveguide connected from the through port to one of the cross ports. First, the two crossed waveguides can be viewed as two independent and non-interfered paths as a result of the characteristics of low loss, low crosstalk and broad bandwidth of the multimode interference based waveguide crossing, and then this proposed structure can be equivalent to a Mach-Zehnder interferometer (MZI) structure with a feedback waveguide. We use the transfer matrix method to establish an analytical transmission formula of this structure and systematically determine the resonance conditions to accomplish the lowest transmission, the path relation to achieve double FSR by applying Vernier effect and the relation between the coupling strength and the transmission loss to carry out the lowest transmission. Then, we calculate the effective indices of the waveguides with different curvatures, obtain the corresponding design parameters based on the aforementioned relations and use two-dimensional finite difference time domain method to validate our design. The design parameters of our structure are as follows: the radii of the ring resonator and feedback waveguides are 5 μm and 7.348 μm, respectively. The size of the device is less than 400 μm*μm. In addition, this structure has the FSR of 55 nm, quality factor of 6200 and extinction ratio of larger than 40dB, showing this notch filter has the advantages of compactness, wide FSR and high quality factor.

並列關鍵字

integrated optics ； optical waveguide ； ring filter ； transfer matrix method

參考文獻

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國際替代計量

雙倍自由頻譜間距之交錯連結陷波濾波器設計

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