﻿ 二维光子晶体双重亚波长成像
 光电工程  2019, Vol. 46 Issue (8): 180577      DOI: 10.12086/oee.2019.180577

Dual subwavelength imaging based on two-dimensional photonic crystals
Niu Jinke, Liang Binming, Zhuang Songlin, Chen Jiabi
School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
Abstract: A focusing structure which can achieve negative refraction and dual subwavelength imaging is proposed, which is based on two-dimensional (2D) photonic crystal (PC) which consisting of air holes in silicon. The light radiated from a point source can form two images through a triangular PC. The transmittance of light is increased and the side spot at image2 is eliminated by adding the gratings on the sides of the PC. When the air slit of gratings is w=0.76a and the distance between gratings and PC is dg=0.1a, the minimum half-width of the image1 reaches 0.433λ, the maximum half-width of image2 reaches 0.842λ, which are both lower than incident wavelength. In addition, the PC realizes wide-spectrum dual subwavelength imaging when the incident wavelength varies from 3.19a to 3.26a. The position formulas between images and point source are also demonstrated. Based on the results, we propose a new confocal system based on PC that can achieve subwavelength imaging.
Keywords: photonic crystals    negative refraction    dual imaging    subwavelength imaging    confocal

1 引言

2 理论推导

 图 1 光子晶体第一TE偏振光子带等频面图 Fig. 1 Several EFS contours in the first TE-polarized photonic band of the PC

 $\mathit{\pmb{k}} = \frac{\omega }{c}{n_{{\rm{eff}}}},$ (1)
 $f = \frac{{\omega a}}{{2{\rm{ \mathsf{ π} }}\mathit{c}}} = \frac{a}{\lambda },$ (2)

3 仿真结果

 图 2 等边三角形光子晶体变量示意图 Fig. 2 Variable schematic diagram on an enlarged equilateral triangle PC

 图 3 无光栅和有光栅时光子晶体负折射和亚波长双重成像，其中λ=3.216a光源位于光子晶体下表面0.3 µm处，其横坐标为x=-10 µm。(a)无光栅时光路图；(b)有光栅时光路图；(c)无光栅和有光栅时image1处的能量探测器输出值；(d)无光栅和有光栅时image2处的能量探测器输出值 Fig. 3 Negative refraction and dual subwavelength imaging of the point source through the equilateral triangle PC without grating and gratings λ=3.216a, the point source is located at 0.3 µm below the PC, and its horizontal coordinate is x=-10 µm. (a) No grating; (b) With gratings; (c) Output values of two energy detectors at the image1 when no grating and with gratings; (d) Output values of two energy detectors at the image2 when no grating and with gratings

4 数据分析

 图 4 Image1的半宽度和峰值随(a) w和(b) dg的变化 Fig. 4 The half-width and peak value of image1 various with (a) w and (b) dg

 图 5 当点光源波长从3.11a到3.32a时像点的半宽变化 Fig. 5 The half-width of the images when the wavelength of point source from 3.11a to 3.32a

 图 6 点光源从0移动到-10 μm。(a)两像点半宽变化；(b)两像点的位置变化 Fig. 6 Point source moves from 0 to -10 µm. (a) The half-width of images; (b) Position of images

 ${x_1} = 0.58\left| x \right| - 18.7, {z_1} = - 0.89\left| x \right| + 4.3;$

image2是

 ${x_2} = 0.2\left| x \right| + 18.7, {z_2} = 0.65\left| x \right| + 4.3,$

 图 7 光子晶体共聚焦系统。(a)共聚焦示意图；(b)激光激发路径；(c)荧光反射路径 Fig. 7 Confocal system based on PC. (a) Confocal diagram; (b) Path of laser; (c) Path of fluorescence

5 结论

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