Numerical Analysis of Coupling between Two-Dimensional Conventional Dielectric Waveguides and Photonic Crystal Waveguide
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Numerical Analysis of Coupling between Two-Dimensional Conventional Dielectric Waveguides and Photonic Crystal Waveguide Dan Zhang & Hongting Jia & Kiyotoshi Yasumoto
Received: 11 June 2007 / Accepted: 4 June 2008 / Published online: 26 June 2008 # Springer Science + Business Media, LLC 2008
Abstract A problem of coupling between conventional dielectric waveguides and a twodimensional photonic crystal waveguide is analyzed, using the Fourier series expansion method combined with the absorbing boundary condition of a perfectly matched layer (PML). A novel structure for the input and output ends of the photonic crystal waveguide is proposed to increase the coupling efficiency. Numerical examples are demonstrated and discussed to validate the effectiveness of the proposed structure. Keywords Fourier series expansion . Perfectly matched layer . Conventional dielectric waveguides . Photonic crystal waveguide
1 Introduction Photonic crystals are periodic dielectric structures that have a band gap that forbids propagation of a certain frequency range of light. This property enables one to control light with amazing facility and produce effects that are impossible with conventional optics. In particular, the proper introduction of single defect into perfect PCs can create resonant states (guiding modes) within the bandgap, which makes PCs promising for application in various optoelectronic devices, such as low-threshold micro- cavity lasers, high-efficiency light-emitting diodes, and low-loss waveguides. Photonic crystal waveguides (PCWs) have become much more important in highly integrated photonic circuits, since they can be responsible for sharp bends, junctions, couplers, cavities, add-drop filters, and multiplexers. When a PCW is used in integrated photonic circuits, we must connect it to conventional dielectric waveguide. However, the coupling efficiency of a direct conection is not good due to a inherent difference of mode D. Zhang (*) School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China e-mail: [email protected] H. Jia : K. Yasumoto Department of Computer Science, Electrical Engineering Kyushu University, Fukuoka 812-8581, Japan
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Int J Infrared Milli Waves (2008) 29:823–831
field profiles in two waveguide systems. Recently several ideas [1–6] have been reported to improve the coupling efficiency. In this paper we shall propose a novel structure for connectting PCWs to conventional dielectric waveguides and analyze its coupling efficiency. The analysis is based on the Fourier-series expansion technique combined with a PML absorbing boundary condition. It is shown that the coupling efficiency of about 96% is attained by adjusting the refractive indices of a few dielectric rods of the PCW nearest the coupling section.
2 Formulation We considered a two-dimensional photonic crystal waveguide which is connected to conventional dielectric waveguides at the input and output ends along the x axis as shown is Fig. 1. The whole waveguide system is bo
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