多模干涉光子晶體波導元件與B型抗諧振反射光波導光子晶體波導元件之研究

Abstract

本文運用模態匹配法，藉由直波導和彎折波導之場形積分的最大化來改善光子晶體彎折波導的傳輸效率。本文也利用多模干涉效應 (multimode interference effect) 設計一種光子晶體步階式漸變耦合器，此耦合器具有不同的分段長度。多模干涉效應亦用來設計一種極短長度的光子晶體極化分光器 (polarization beam splitter)，此極化分光器的長度只有7個晶格常數。另外，有別於傳統波導利用內部全反射機制導光，本論文提出B型抗諧振反射光波導(ARROW-B)結構之光子晶體波導，在波導的水平方向和垂直方向分別以光子能隙(photonic band gap)和B型抗諧振反射作為導光的機制，以利垂直方向和單模光纖的耦合。除了高傳輸效率的直波導之外，此結構亦要當作高效率的彎折波導、耦合器及其他光子晶體元件的設計平台。模擬結果顯示B型抗諧振反射光波導(ARROW-B)結構之光子晶體波導具有高傳輸效率和低彎折損耗，同時光子晶體在水平方向藉步階式漸變耦合結構可使得此波導元件與單模光纖的直接耦合效率有效提昇。

A mode matching approach to improve the transmission efficiency of photonic crystal (PC) waveguide bends through maximization of the overlap integral of fields between the straight waveguide and the waveguide bend is presented. The multimode interference (MMI) effect is used to design a PC step tapered coupler with different section lengths. The theoretical design method for a compact PC polarization beam splitter (PBS) based on the MMI effect is shown. The length of the MMI section can be only seven lattice constants. In addition, in contrast to conventional waveguides utilizing the total internal reflection to guide the light, the PC slab waveguide based on a type-B antiresonant reflecting optical waveguide (ARROW-B) structure is proposed for improving the butt-coupling efficiency with a single-mode fiber in the vertical direction. Optical confinement in this device is supported by the photonic band gaps and antiresonance reflection in the lateral and vertical direction, respectively. Besides high-transmission PC waveguides, efficient waveguide bends, couplers and other PC devices could be built on this platform. Simulations show that an ARROW-B-based PC waveguide has high transmissions and low bending losses. With the aid of a PC step tapered coupler, the butt-coupling efficiencies between a single-mode optical fiber and a PC waveguide with an ARROW-B structure can be high for TM and TE modes.