調變光子晶體平板方向耦合器的非耦合點研究

Abstract

以三角晶格排列的光子晶體製成耦合器，其兩條色散曲線會相交於非耦合點(decoupling point)，當光以非耦合點的頻率入射其中一條波導時，入射光波只會在入射的波導中傳播，並不會耦合至另一條波導。藉由廣義的緊束縛理論對兩條缺陷波導間的耦合效應加以分析，我們發現當橫向調變耦合器的兩條線缺陷間距時，由於耦合係數產生改變，非耦合點的本徵頻率會有藍移的現象，因此改變了方向耦合器的非耦合點頻率及耦合長度。另一方面，沿著波傳播方向縱向移動兩條波導，能使正方晶格的方向耦合器產生非耦合點。 在此論文中我們也運用數值方法，對兩種不同型態：介電柱與空氣洞所構成的方向耦合器的色散關係加以模擬；並且成功的運用緊束縛理論，解釋上述將缺陷調變所引起的現象。再藉由模擬所得到的結果，提出對光子晶體耦合器的非耦合點頻率進行調變的設計規則。

Two dispersion curves of the photonic crystal (PC) coupler with triangular lattice will cross at the so-called decoupling point. When a light wave launched into one of the waveguide at the frequency of this point, it will propagate only in the incident waveguide without coupling into the other one. Using the extended tight-binding theory (TBT) to analyze the coupling effects between two defect waveguides, we found that the eigenfrequency of the decoupling point blue shifts as adjusting the separation of two line defects transversely of the coupler. The magnitude of coupling coefficients wound also change to affect the decoupling frequency and the coupling length of the directional coupler (DC). Longitudinal shifting two waveguides along the wave propagation direction can also shift the dispersion of the square lattice DC so that the decoupling point would exist in the square lattice DC. In this thesis, we use numerical methods to simulate dispersion relations of two different types of DCs: dielectric rod and the air-hole types. Moreover, we successfully use the TBT to explain these phenomena and give a designing rule based on the TBT for tuning the decoupling frequency of the PC coupler.