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摘要
本文基于硅基底空气孔型二维光子晶体(photonic crystals)，提出了一种可以实现等效负折射和亚波长成像的结构。点光源通过三角形光子晶体出射后在两侧形成两个像点。通过在光子晶体两侧添加光栅，增加了光源的透过率，消除了旁斑对双重像点的影响。当光栅的空气带隙宽度w=0.76a和到光子晶体的距离dg=0.1a时，左侧像点image1的最小半宽度达到0.433λ，此时右侧像点image2达到0.842λ，均小于入射波长。另外，当光源波长在3.19a到3.26a范围内时，光子晶体可以实现宽光谱的双重亚波长成像。最后，根据点光源和双重像点的位置变化，求出了关于其坐标x, z的相对关系。
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.
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Key words:
- photonic crystals /
- negative refraction /
- dual imaging /
- subwavelength imaging /
- confocal
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Overview
Overview:In recent years, negative refractive index materials (NIMs) have attracted more attention. There are lots of studies on the special characteristics of NIMs such as negative refraction and subwavelength imaging. As a NIM, photonic crystal (PC) can greatly amplify the evanescent waves and break the diffraction limit, the subwavelength resolution can be achieved.
In this paper, The edge length of PC is L=50a. The point source is placed at 0.3 μm below the edge of PC, and its horizontal coordinate is -10 μm. The light path simulated by Rsoft software. The gratings on both sides of the PC increases the transmission of light, eliminating the influence of the reflected light on dual imaging. As the clear two images are achieved, the positional relationship between two images and the point source is obtained. Based on the results, a confocal system with a triangular PC is proposed. Unlike the conventional confocal system, the PC confocal system has a simple structure, and it achieves imaging by negative refraction.
Dual sub-wavelength imaging is achieved clearly by adjusting the grating gap on PC, it eliminates the effects of reflected light. Through varying the wavelength of the point source, a broad spectrum which can achieve sub-wavelength imaging is found. Then adjust the lateral coordinates of the light source points to obtain the positional relationship between the two image points and the light source points. Based on the above results, the photonic crystal confocal system was designed and verified by simulation. The normalized peak value of image1 is increased from 1.104 to 1.326 and the half-width is decreased from 0.461λ to 0.433λ by adjusting the size of the grating air slit; meanwhile, the side spot at image2 is eliminated when the grating air slit is w=0.76a and distance between gratings and air hole is dg=0.1a. The minimum half-width of images is obtained when the incident wavelength is 3.216a, and the wide-spectrum dual subwavelength imaging is achieved when the incident wavelength varies from 3.19a to 3.26 a, which the minimum half-width is less than 0.44λ. In addition, the position formulas of the images and point source are demonstrated, that provides a reference for the precise location of two images. Based on the results, we propose a confocal system that can achieve subwavelength imaging. Compared with the traditional confocal microscope, this structure does not need objective lens. As its focusing and imaging through the negative refraction of PC, the structure is more simple. Furthermore, dual subwavelength imaging can also be used in other aspects.
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图 1 光子晶体第一TE偏振光子带等频面图
Figure 1. Several EFS contours in the first TE-polarized photonic band of the PC
图 2 等边三角形光子晶体变量示意图
Figure 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
Figure 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
图 4 Image1的半宽度和峰值随(a) w和(b) dg的变化
Figure 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
Figure 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
Figure 6. Point source moves from 0 to -10 µm. (a) The half-width of images; (b) Position of images
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