﻿ 扇面形散射元构建的二维光子晶体慢光模拟研究 Simulation Study on Slow Light of 2-D Photonic Crystals by Sector Scatterers

Applied Physics
Vol.08 No.08(2018), Article ID:26592,12 pages
10.12677/APP.2018.88049

Simulation Study on Slow Light of 2-D Photonic Crystals by Sector Scatterers

Mingjie Xu1*, Zichuan Xue2*, Qun Xie1, Yuhui Fu1, Le Yu1, Yong Wan1#

1College of Physics Science, Qingdao University, Qingdao Shandong

2Southlands Schools China, Qingdao Shandong

Received: Aug. 6th, 2018; accepted: Aug. 20th, 2018; published: Aug. 27th, 2018

ABSTRACT

In this paper, the air hole photonic crystal model is constructed by sector scatterers, and the linear defect waveguide is constructed. The dispersion curves in TM mode are simulated by using plane wave expansion method, and the group refractive index and group velocity are obtained by changing the parameters of scattering elements. The ideal model with large group refractive index and large bandwidth is obtained by normalized delay bandwidth product and dispersion constant. The waveguide structure is changed as a whole, and the scattering elements are divided into three types: face to face type, back to back type and rotation 30˚. The calculated results are compared and analyzed.

Keywords:Simulation, Sector Scatterers, Photonic Crystal, Slow Light, Linear Defect Waveguide

1青岛大学，物理科学学院，山东 青岛

2青岛索斯兰中学，山东 青岛

1. 引言

2. 模型结构

3. 模拟分析

3.1. 慢光中的基本概念

Figure 1. Sector scatterer

Figure 2. Photonic crystal with hexagonal lattice structure

${n}_{g}=\frac{c}{{v}_{g}}=c\frac{\text{d}k}{\text{d}\omega }$ (1)

${n}_{g}={n}_{eff}+\omega \frac{\text{d}{n}_{eff}}{\text{d}\omega }$ (2)

${n}_{g}\approx \omega \frac{\Delta n}{\Delta \omega }$ (3)

${n}_{g}\frac{\Delta \omega }{\omega }\approx \Delta n$ (4)

$\Delta {n}_{\mathrm{max}}=\frac{{k}_{\mathrm{max}}}{{f}_{1}}-\frac{{k}_{\mathrm{min}}}{{f}_{2}}\approx \frac{{k}_{\mathrm{max}}-{k}_{\mathrm{min}}}{{f}_{1}}$ (5)

$D=\frac{1}{c}\frac{\text{d}{n}_{g}}{\text{d}\lambda }$ (6)

3.2. 色散曲线的规律分析

3.3. 面对面型线缺陷波导的慢光特性分析

Figure 3. Face-to-face line defect waveguide structure

Figure 4. Relationship of dispersion curve with θ

Figure 5. Group refractive index curve of face to face line defect waveguides

Table 1. n g , Δ λ , n g Δ ω / ω , v g in face-to-face line defect waveguide

D的单位是ps/mm∙nm，计算当 $|D|\le 1$ 时，波长的变化范围，即带宽，如表2所示，其最大值可达3.1 nm。若令 $f=1\text{\hspace{0.17em}}\text{Thz}$ ，带宽可达1641.2 nm。

3.4. 背对背型线缺陷波导的慢光特性分析

$r=0.3a,d=0.3a,\theta ={111.7}^{\circ }$ 时， ${n}_{g}=92.6$ ，为最大值。群折射率可以实现39.0~92.6的可调范围。

Table 2. a and Δ λ for | D | ≤ 1 in face to face line defect waveguides

Figure 6. GVD curves of face to face line defect waveguides

Figure 7. Back-to-back line defect waveguide

Figure 8. Group refractive index curve of back-to-back linear defect waveguides

Table 3. n g , Δ λ , n g Δ ω / ω , v g in back-to-back face line defect waveguides

$\lambda =1550\text{\hspace{0.17em}}\text{nm}$$\Delta {n}_{g}=±10%$ ，计算其色散常数D，如图9所示。由表中数据得， $|D|\le 1$ 时，最大带宽可达2.73 nm。取 $f=1\text{\hspace{0.17em}}\text{Thz}$ ，最大带宽可达1649.6 nm。

3.5. 旋转30˚后线缺陷波导的慢光特性分析

Figure 9. GVD curve of a back-to-back line defect waveguide

Table 4. a and Δ λ for | D | ≤ 1 in back-to-back line defect waveguides

Figure 10. Rotating 30˚ post-line defective waveguide

Figure 11. The group refractive index curve of a linear defect waveguide after rotation 30˚

Table 5. n g , Δ λ , n g Δ ω / ω , v g in a linear defect waveguide after rotation 30˚

Figure 12. GVD curve of the waveguide with line defects after rotation 30˚

Table 6. a and Δ λ in a linear defect waveguide after rotation 30˚ when | D | ≤ 1

3.6. 三种模型的比较分析

4. 结论

Simulation Study on Slow Light of 2-D Photonic Crystals by Sector Scatterers[J]. 应用物理, 2018, 08(08): 386-397. https://doi.org/10.12677/APP.2018.88049

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