光柵反射器的品質因子之快速計算

Abstract

本篇論文利用介質平板波導的電磁特性結合電磁理論，去估算出一維和二維光柵反射器的品質因子。不同以往藉由使用數值軟體來模擬光柵反射器的品質因子。在數值模擬的方法中，網格數越多對於結果的精確度就越高但相對的運算時間卻越長。另一方面介質平板波導邊界的電場受到介電質差異的擾動(perturbation)影響的特性，在分析光柵反射器的品質因子時扮演重要的角色。藉此建立理論估算方法，能節省數值模擬在進行全波模擬的耗時。 估算不同厚度的光柵反射器頻率響應的方法則為藉由結合時間的模態耦合理論(Temporal Coupled-Mode Theory, TCMT)和不同介質中穿透反射所產生的相位差來分析。接著利用全波模擬計算出光柵反射器的頻率響應，將理論估算與數值模擬運算出的結果相互驗證。結果說明理論分析方法運算精確且能省去數值模擬所需的大量時間。

In this work, we estimate the quality factor of 1-D and 2-D grating reflectors with properties and theorem of the dielectric slab waveguide. Usually, we calculated the quality factor of grating reflectors with simulation software COMSOL Multiphysics. The more mesh quantities we used with numerical simulation, the higher accurate value of quality factor we gained. Also, it means spending much time. On the other hand, the scattered electric field due to perturbation of dielectric difference plays an important role in analyzing the quality factor of grating reflector. Ergo, we could establish a method of quick quality factor computing based on the theory. We estimate the frequency response of grating reflectors with different waveguide's thickness based on the method which combines Temporal Coupled-Mode Theory and the phase difference causing by transmission and reflection. Then, we use the full-wave simulation to estimate the frequency response, validated the value we computing by the method of theory. As the results, this method could save lots of time causing by simulation and compute accurately.