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Research on Band Gap and Negative Refraction of Two-dimensional Photonic Crystal in Triangular Lattice with Ring-shaped Air Holes

Author: KongLingKai
Tutor: ZhengZhiQiang
School: Fujian Normal University
Course: Condensed Matter Physics
Keywords: photonic crystal negative refraction photonic band gap splitter plane wave expansion method finite-difference time-domain method
CLC: O734
Type: Master's thesis
Year: 2009
Downloads: 62
Quote: 2
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Abstract


Photonic crystal is a kind of manufactured material with periodic arrangement of dielectric constant. Photonic band gap structure of photonic crystal indicates its primary property, which is the base of its design and application. The study on photonic band gap structure is an important part of basic research on photonic crystal. At the same time, negative refraction of electromagnetic waves in photonic crystal has attracted much attention because of variety of novel phenomena. In this paper, some research has been done on the photonic band gap and negative refraction of a novel two-dimensional photonic crystal, which is arranged in triangular lattice with ring-shaped air holes.Photonic band gap structures of two-dimensional photonic crystal in triangular lattice with circular/ring-shaped air holes have been calculated by the plane wave expansion method （PWE）. Three kinds of dielectric material （Si, GaAs, Ge） have been chosen as background in order to analysis the effects of the dielectric constant to band structure. The effects of parameters of the structure to band structure have been also analyzed. The results show that the structure composed of higher dielectric constant material has larger photonic band gap, and photonic band gap of the ring-shaped structure composed of Ge is 66% larger than that of the circular one.Negative refraction in two-dimensional photonic crystal with ring-shaped holes is studied in detail. By the calculation of effective index, the relationship between inner radius and the frequencies with neff=-1 is obtained. The results show that the equal-frequency contour is a circle, so a perfect image can be obtained with the increasing of inner radius of ring-shaped holes from 0 to 0.13a and the outside radius 0.40a at normalized frequency 0.30. The simulation by the finite-difference time-domain method （FDTD） verifies the result calculated by PWE method.Based on the principle of negative refraction in photonic crystal, a new type of splitter which can work well with point light source is designed. There are two models put forward in this paper, one is triangular and the other is hexagonal. By the analysis of performance of splitter more ideal structure parameters have been obtained.

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CLC: > Mathematical sciences and chemical > Crystallography > Crystal physics > The optical properties of the crystal
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