CN109581547B - A method for preparing Gyroid topological photonic crystal based on holographic interference technology - Google Patents

A method for preparing Gyroid topological photonic crystal based on holographic interference technology Download PDF

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CN109581547B
CN109581547B CN201811443720.XA CN201811443720A CN109581547B CN 109581547 B CN109581547 B CN 109581547B CN 201811443720 A CN201811443720 A CN 201811443720A CN 109581547 B CN109581547 B CN 109581547B
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王霞
赵秋玲
尤凯
吕浩
刘静
张帅一
滕利华
谭永炎
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Qingdao University of Science and Technology
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Abstract

The invention belongs to the technical field of photonic crystal preparation, and relates to a method for preparing a Gyroid topological photonic crystal based on a holographic interference technology.

Description

一种基于全息干涉技术制备Gyroid拓扑光子晶体的方法A method for preparing Gyroid topological photonic crystal based on holographic interference technology

技术领域：Technical field:

本发明属于光子晶体制备技术领域，涉及一种在光学波段具有丰富光学特性并且可探测Weyl费米子的三重周期性的Gyroid结构的制备方法，特别是一种基于全息干涉技术制备Gyroid拓扑光子晶体的方法。The invention belongs to the technical field of photonic crystal preparation, and relates to a preparation method of a triple periodic Gyroid structure with rich optical properties in an optical waveband and capable of detecting Weyl fermions, in particular to a preparation method of a Gyroid topology photonic crystal based on a holographic interference technology. method.

背景技术：Background technique:

1929年,德国科学家外尔(Hermann Weyl)指出，当费米子的质量为零时,可以区分为具有左旋和右旋两种不同手性的粒子,这就是Weyl费米子，类似于光可分为左旋偏振光和右旋偏振光，这种费米子等效电子质量为零，那么就能极大提高电子的传输效率，另外一个优点就是它具有拓扑保护的特性，所以鲁棒性(Robust)更强，这在量子计算机中可以大展拳脚。Weyl费米子的发现不仅具有非常重要的科学意义，也可能会带来未来革新性技术突破。但是近百年来人们却一直没有能够在实验中观测到Weyl费米子。In 1929, German scientist Hermann Weyl pointed out that when the mass of fermions is zero, they can be divided into particles with two different chirality, left-handed and right-handed. Left-handed polarized light and right-handed polarized light, the equivalent electron mass of this fermion is zero, then the transmission efficiency of electrons can be greatly improved. Another advantage is that it has the characteristics of topological protection, so the robustness (Robust) is better. Strong, which can be very powerful in a quantum computer. The discovery of Weyl fermions is not only of great scientific significance, but may also lead to innovative technological breakthroughs in the future. But for nearly a hundred years, people have not been able to observe Weyl fermions in experiments.

2015年7月31日和8月17日,Physical Review X和Nature Physics分别以"Experimental Discovery of Weyl Semimetal TaAs”和"Observation of Weyl Nodes inTaAs”为题,在线发表了中国科学院物理研究所丁洪研究小组在Weyl半金属的研究成果，该研究组利用角分辨光电子能谱技术测量了TaAs的电子结构，直接观测到Weyl锥形的能带，这是自1929年Weyl费米子被提出以来，首次得到实验证实。On July 31 and August 17, 2015, Physical Review X and Nature Physics published online the research of Ding Hong from Institute of Physics, Chinese Academy of Sciences under the title of "Experimental Discovery of Weyl Semimetal TaAs" and "Observation of Weyl Nodes in TaAs" respectively. The research results of the group in Weyl semimetals, the research group used angle-resolved photoelectron spectroscopy to measure the electronic structure of TaAs, and directly observed the energy band of the Weyl cone. This is the first time since the Weyl fermion was proposed in 1929. experimentally confirmed.

2015年，麻省理工学院研究员Lu Ling等在微波段Gyroid光子晶体中引入宇称破缺，在理论上预言并在实验上观测到了光子晶体能带结构中的Weyl点。Weyl费米子的实现为三维光学拓扑绝缘体的实现提供了基础。In 2015, MIT researcher Lu Ling et al. introduced parity breaking in microwave-band Gyroid photonic crystals, theoretically predicted and experimentally observed Weyl points in the energy band structure of photonic crystals. The realization of Weyl fermions provides the basis for the realization of three-dimensional optical topological insulators.

近年来，科研人员通过胶体自组装和激光直写等技术成功制备Gyroid光子晶体，并对其进行观测研究，但是，还未有在可见光波段制备Gyroid光子晶体的相关报道。激光全息干涉技术基于多光束干涉理论，能够通过调控干涉光束的数目、光波矢、偏振等参数来调控干涉结构，近年来已在光子晶体、准晶、超材料等微纳结构制备中得到广泛应用，因此，寻求一种基于全息干涉技术制备Gyroid拓扑光子晶体的方法。In recent years, researchers have successfully prepared Gyroid photonic crystals by techniques such as colloidal self-assembly and laser direct writing, and conducted observational studies on them. However, there is no report on the preparation of Gyroid photonic crystals in the visible light band. Laser holographic interference technology is based on multi-beam interference theory, which can control the interference structure by adjusting the number of interfering beams, light wave vector, polarization and other parameters. In recent years, it has been widely used in the preparation of micro-nano structures such as photonic crystals, quasicrystals, and metamaterials. , therefore, a method for preparing Gyroid topological photonic crystals based on holographic interference technology is sought.

发明内容：Invention content:

本发明的目的在于针对现有技术存在的不足，提供一种在可见光波段经济快速地大面积制备Gyroid光子晶体的方法。The purpose of the present invention is to provide a method for preparing Gyroid photonic crystal in a large area economically and rapidly in the visible light band, aiming at the deficiencies of the prior art.

为了实现上述目的，本发明利用空间中的四束相干光干涉叠加制备Gyroid光子晶体，具体过程为：In order to achieve the above-mentioned purpose, the present invention utilizes the interference superposition of four beams of coherent light in space to prepare the Gyroid photonic crystal, and the specific process is as follows:

(1)通过分光得到四束任意波长的相干激光光束，各相干激光光束在x-y投影面的夹角相等，相邻光束投影夹角均为90°，四束相干激光光束波矢分别为:(1) Four coherent laser beams of arbitrary wavelengths are obtained by splitting, the angles of each coherent laser beam on the x-y projection plane are equal, and the projection angles of adjacent beams are all 90°, and the wave vectors of the four coherent laser beams are:

Figure GDA0002475934050000021
Figure GDA0002475934050000022
其中λ为相干光的波长；
Figure GDA0002475934050000021
Figure GDA0002475934050000022
where λ is the wavelength of coherent light;

空间电场矢量分别为：The space electric field vectors are:

Figure GDA0002475934050000023
Figure GDA0002475934050000023

(2)由于空间电场矢量均为空间中的椭圆偏振光，需要将其转换至沿z轴正方向传播的椭圆偏振光，通过旋转矩阵法实现空间中椭圆偏振光的旋转，不同的空间电场矢量对应不同的旋转矩阵Ri(i＝1,2,3,4)分别为(2) Since the space electric field vectors are all elliptically polarized light in space, it needs to be converted to elliptically polarized light propagating in the positive direction of the z-axis, and the rotation of elliptically polarized light in space is realized by the rotation matrix method. Different space electric field vectors Corresponding to different rotation matrices R i (i=1, 2, 3, 4) are respectively

Figure GDA0002475934050000024
Figure GDA0002475934050000024

Figure GDA0002475934050000025
Figure GDA0002475934050000025

Figure GDA0002475934050000026
Figure GDA0002475934050000026

Figure GDA0002475934050000027
Figure GDA0002475934050000027

上述四束相干激光光束经过空间中旋转之后得到沿着z轴正方向传播的椭圆偏振光，分别为The above four coherent laser beams are rotated in space to obtain elliptically polarized light propagating in the positive direction of the z-axis, respectively

Figure GDA0002475934050000031
Figure GDA0002475934050000031

Figure GDA0002475934050000032
Figure GDA0002475934050000032

Figure GDA0002475934050000033
Figure GDA0002475934050000033

Figure GDA0002475934050000034
Figure GDA0002475934050000034

四束椭圆偏振光在空间汇聚干涉叠加得到Gyroid光子晶体；Four beams of elliptically polarized light converge in space to obtain Gyroid photonic crystal;

(3)采用斯托克斯参数校准步骤(2)得到的椭圆偏振光，由斯托克斯参数

Figure GDA0002475934050000035
定义的各个椭圆偏振光参数分别为：
Figure GDA0002475934050000036
(3) Using the Stokes parameter to calibrate the elliptically polarized light obtained in step (2), the Stokes parameter
Figure GDA0002475934050000035
The defined parameters of each elliptically polarized light are:
Figure GDA0002475934050000036

本发明所述旋转矩阵是通过两次矩阵旋转得到的，先将空间电场矢量旋转至xoz或者yoz平面，再绕x轴或者y轴旋转至与z轴重合，两次旋转矩阵之积为此光束空间电场矢量的旋转矩阵。The rotation matrix of the present invention is obtained by two matrix rotations. First, the space electric field vector is rotated to the xoz or yoz plane, and then rotated around the x-axis or the y-axis to coincide with the z-axis. The product of the two rotation matrices is the beam. The rotation matrix of the space electric field vector.

本发明所述激光偏振态通过对应的波片进行调整，根据椭圆偏振光参数设计固定相位差Δ的石英波片，Δ与波片的厚度d成正比，根据旋转之后的电场矢量得到各束椭圆偏振光的相位差Δ分别为：247.7°、270°、90°、292.3°。The laser polarization state of the present invention is adjusted by the corresponding wave plate, and a quartz wave plate with a fixed phase difference Δ is designed according to the elliptical polarization parameters, Δ is proportional to the thickness d of the wave plate, and each beam ellipse is obtained according to the electric field vector after rotation. The phase differences Δ of polarized light are: 247.7°, 270°, 90°, and 292.3°, respectively.

本发明与现有光子晶体制备技术相比，具有以下优点：一是拓展了激光全息干涉技术的新应用，在不增加光束数目的基础上，通过引入椭圆偏振光束，实现新颖拓扑Gyroid光子结构的制备；二是通过特定设计的波片来实现椭偏光的偏振调节，根据预先计算的光束偏振态参数，按照一定的角度旋转即可获得不同偏振态的椭偏光；三是该技术制作成本低，光路搭建便捷有效，所得的晶格对称性、晶格周期、介质占空比等均可调控；四是在介观尺度上能够较大面积制备可见光波段的Gyroid光子晶体。Compared with the existing photonic crystal preparation technology, the invention has the following advantages: firstly, it expands the new application of laser holographic interference technology, and on the basis of not increasing the number of beams, by introducing elliptically polarized beams, the novel topology Gyroid photonic structure is realized. The second is to realize the polarization adjustment of the elliptically polarized light through a specially designed wave plate. According to the pre-calculated beam polarization state parameters, the elliptical polarization of different polarization states can be obtained by rotating at a certain angle. The construction of the optical path is convenient and effective, and the obtained lattice symmetry, lattice period, and medium duty cycle can be adjusted. Fourth, Gyroid photonic crystals in the visible light band can be prepared in a large area on the mesoscopic scale.

附图说明：Description of drawings:

图1为本发明制备的Gyroid光子晶体结构图，其中(a)Gyroid的2×2×2个单元的透视图，(b)沿[100]方向结构图，箭头表示螺旋的弯曲旋转方向，(c)沿[111]方向结构图，螺旋轴[100]，[010]和[001]方向显示为较大(较小)的螺旋线。Fig. 1 is the structure diagram of the Gyroid photonic crystal prepared by the present invention, wherein (a) a perspective view of 2 × 2 × 2 units of Gyroid, (b) a structural diagram along the [100] direction, the arrow indicates the bending rotation direction of the helix, ( c) Structure diagram along the [111] direction, the helix axis [100], [010] and [001] directions are shown as larger (smaller) helices.

图2为本发明制备Gyroid光子晶体的椭圆偏振光的光束构型。FIG. 2 is the beam configuration of the elliptically polarized light for preparing the Gyroid photonic crystal according to the present invention.

图3为本发明所述圆偏振光光束构型图的yoz平面视图(a)、xoz平面视图(b)、xoy平面视图(c)。3 is a yoz plan view (a), an xoz plan view (b), and an xoy plan view (c) of the circularly polarized light beam configuration diagram according to the present invention.

图4为本发明所述圆偏振光光束构型图所需四束椭圆偏振光的偏振状态，其中(a)

Figure GDA0002475934050000041
(b)
Figure GDA0002475934050000042
(c)
Figure GDA0002475934050000043
(d)
Figure GDA0002475934050000044
4 is the polarization state of the four elliptically polarized light beams required by the circularly polarized light beam configuration diagram according to the present invention, wherein (a)
Figure GDA0002475934050000041
(b)
Figure GDA0002475934050000042
(c)
Figure GDA0002475934050000043
(d)
Figure GDA0002475934050000044

图5为本发明所述圆偏振光光束构型图配置计算机模拟干涉所得结果，其中(a)对角视图；(b)主视图；(c)俯视图；(d)左视图。5 is the result obtained by computer simulation of the configuration of the circularly polarized light beam configuration according to the present invention, wherein (a) a diagonal view; (b) a front view; (c) a top view; (d) a left view.

具体实施方式：Detailed ways:

下面通过实施例并结合附图对本发明作进一步说明。The present invention will be further described below through embodiments and in conjunction with the accompanying drawings.

本实施例利用空间中的四束相干光干涉叠加制备Gyroid光子晶体，具体过程为：In this embodiment, the Gyroid photonic crystal is prepared by the interference superposition of four beams of coherent light in space, and the specific process is as follows:

(1)通过分光得到四束任意波长的相干激光光束，各相干激光光束在x-y投影面的夹角相等，相邻光束投影夹角均为90°，四束相干激光光束波矢分别为:(1) Four coherent laser beams of arbitrary wavelengths are obtained by splitting, the angles of each coherent laser beam on the x-y projection plane are equal, and the projection angles of adjacent beams are all 90°, and the wave vectors of the four coherent laser beams are:

Figure GDA0002475934050000045
Figure GDA0002475934050000046
其中λ为相干光的波长；
Figure GDA0002475934050000045
Figure GDA0002475934050000046
where λ is the wavelength of coherent light;

空间电场矢量分别为：The space electric field vectors are:

Figure GDA0002475934050000047
Figure GDA0002475934050000047

(2)由于空间电场矢量均为空间中的椭圆偏振光，需要将其转换至沿z轴正方向传播的椭圆偏振光，通过旋转矩阵法实现空间中椭圆偏振光的旋转，不同的空间电场矢量对应不同的旋转矩阵Ri(i＝1,2,3,4)分别为(2) Since the space electric field vectors are all elliptically polarized light in space, it needs to be converted to elliptically polarized light propagating in the positive direction of the z-axis, and the rotation of elliptically polarized light in space is realized by the rotation matrix method. Different space electric field vectors Corresponding to different rotation matrices R i (i=1, 2, 3, 4) are respectively

Figure GDA0002475934050000048
Figure GDA0002475934050000048

Figure GDA0002475934050000051
Figure GDA0002475934050000051

Figure GDA0002475934050000052
Figure GDA0002475934050000052

Figure GDA0002475934050000053
Figure GDA0002475934050000053

上述四束相干激光光束经过空间中旋转之后得到沿着z轴正方向传播的椭圆偏振光，分别为The above four coherent laser beams are rotated in space to obtain elliptically polarized light propagating in the positive direction of the z-axis, respectively

Figure GDA0002475934050000054
Figure GDA0002475934050000054

Figure GDA0002475934050000055
Figure GDA0002475934050000055

Figure GDA0002475934050000056
Figure GDA0002475934050000056

Figure GDA0002475934050000057
Figure GDA0002475934050000057

四束椭圆偏振光在空间汇聚干涉叠加得到Gyroid光子晶体；Four beams of elliptically polarized light converge in space to obtain Gyroid photonic crystal;

(3)采用斯托克斯参数校准步骤(2)得到的椭圆偏振光，由斯托克斯参数

Figure GDA0002475934050000058
定义的各个椭圆偏振光参数分别为：
Figure GDA0002475934050000059
(3) Using the Stokes parameter to calibrate the elliptically polarized light obtained in step (2), the Stokes parameter
Figure GDA0002475934050000058
The defined parameters of each elliptically polarized light are:
Figure GDA0002475934050000059

本实施例所述旋转矩阵是通过两次矩阵旋转得到的，先将空间电场矢量旋转至xoz或者yoz平面，再绕x轴或者y轴旋转至与z轴重合，两次旋转矩阵之积为此光束空间电场矢量的旋转矩阵。The rotation matrix described in this embodiment is obtained through two matrix rotations. First, the space electric field vector is rotated to the xoz or yoz plane, and then rotated around the x-axis or y-axis to coincide with the z-axis. The product of the two rotation matrices is this Rotation matrix of the beam space electric field vector.

本实施例所述激光偏振态通过对应的波片进行调整，根据椭圆偏振光参数设计固定相位差Δ的石英波片，Δ与波片的厚度d成正比，根据旋转之后的电场矢量得到各束椭圆偏振光的相位差Δ分别为：247.7°、270°、90°、292.3°。The laser polarization state in this embodiment is adjusted by the corresponding wave plate, and a quartz wave plate with a fixed phase difference Δ is designed according to the elliptically polarized light parameters. Δ is proportional to the thickness d of the wave plate, and each beam is obtained according to the electric field vector after rotation. The phase differences Δ of elliptically polarized light are: 247.7°, 270°, 90°, and 292.3°, respectively.

实施例：Example:

本实施例制备Gyroid光子晶体的具体步骤如下：The specific steps of preparing the Gyroid photonic crystal in the present embodiment are as follows:

(1)取4束相干激光在空间中分布如图2所示，入射方向与z轴正向夹角为

Figure GDA0002475934050000061
取
Figure GDA0002475934050000062
相干激光光波波长为488nm，各相干激光光束在x-y平面投影相邻之间夹角均为90°，图3为上述光路构型图yoz平面、xoz平面视图、xoy平面视图；(1) Take 4 coherent laser beams distributed in space as shown in Figure 2, the angle between the incident direction and the positive z-axis is
Figure GDA0002475934050000061
Pick
Figure GDA0002475934050000062
The wavelength of the coherent laser light wave is 488 nm, and the included angle between the projections of each coherent laser beam on the xy plane is 90°.

(2)保持上述光束配置其他条件不变，通过旋转矩阵法使各光束的偏振态为图4中所需偏振态，该4束光在空间干涉可以得到如图5(a)所示的三维光子晶体结构，即三重周期性Gyroid光子晶体结构，(b)(c)(d)分别为其主视图、俯视图、左视图；(2) Keeping the above beam configuration and other conditions unchanged, the polarization state of each beam is made to be the required polarization state in Figure 4 by the rotation matrix method. The spatial interference of the four beams can obtain the three-dimensional shape shown in Figure 5(a). Photonic crystal structure, namely triple periodic Gyroid photonic crystal structure, (b)(c)(d) are its front view, top view and left view respectively;

(3)采用斯托克斯参数校准图4中的4个椭圆偏振光的偏振态，即可以通过测量光束的透射光强确定Stokes参量，从而验证光束的偏振态。(3) The Stokes parameter is used to calibrate the polarization states of the four elliptically polarized lights in Fig. 4, that is, the Stokes parameter can be determined by measuring the transmitted light intensity of the light beam, thereby verifying the polarization state of the light beam.

本实施例制备的三重周期性Gyroid光子晶体结构在xoy内的结构形状如图1所示，不同的结构单元沿着不同方向具有螺旋弯曲。The structural shape of the triple periodic Gyroid photonic crystal structure prepared in this example in the xoy is shown in FIG. 1 , and different structural units have helical bends along different directions.

本实施例采用多光束单次曝光干涉实现，通过改变干涉光束的曝光量，可以调节结构的占空比。In this embodiment, the multi-beam single exposure interference is implemented, and the duty ratio of the structure can be adjusted by changing the exposure amount of the interference beam.

本实施例所述激光光束波长理论上无限制，实际操作中以可见光进行干涉制备，有助于获得周期尺寸在光波长量级的Gyroid光子晶体结构，获得光学波段的带隙特征。The wavelength of the laser beam described in this embodiment is theoretically unlimited. In practice, visible light is used for interference preparation, which is helpful to obtain a Gyroid photonic crystal structure with a period size on the order of the wavelength of light, and to obtain band gap characteristics in the optical band.

Claims (1)

1.一种基于全息干涉技术制备Gyroid拓扑光子晶体的方法，其特征在于利用空间中的四束相干光干涉叠加制备Gyroid光子晶体，具体过程为：1. a method for preparing Gyroid topological photonic crystal based on holographic interference technology, it is characterized in that utilizing four coherent light interference stacking in space to prepare Gyroid photonic crystal, and concrete process is: (1)通过分光得到四束任意波长的相干激光光束，各相干激光光束在x-y投影面的夹角相等，相邻光束投影夹角均为90°，四束相干激光光束波矢分别为:(1) Four coherent laser beams of arbitrary wavelengths are obtained by splitting, the angles of each coherent laser beam on the x-y projection plane are equal, and the projection angles of adjacent beams are all 90°, and the wave vectors of the four coherent laser beams are:
Figure FDA0002423141140000011
Figure FDA0002423141140000011
 其中
Figure FDA0002423141140000012
λ为相干光的波长；in
Figure FDA0002423141140000012
λ is the wavelength of coherent light; 空间电场矢量分别为：The space electric field vectors are:
Figure FDA0002423141140000013
Figure FDA0002423141140000013
 (2)由于空间电场矢量均为空间中的椭圆偏振光，需要将其转换至沿z轴正方向传播的椭圆偏振光，通过旋转矩阵法实现空间中椭圆偏振光的旋转，不同的空间电场矢量对应不同的旋转矩阵分别为(2) Since the space electric field vectors are all elliptically polarized light in space, it needs to be converted to elliptically polarized light propagating in the positive direction of the z-axis, and the rotation of elliptically polarized light in space is realized by the rotation matrix method. Different space electric field vectors The corresponding rotation matrices are
Figure FDA0002423141140000014
Figure FDA0002423141140000014
Figure FDA0002423141140000015
Figure FDA0002423141140000015
Figure FDA0002423141140000016
Figure FDA0002423141140000016
Figure FDA0002423141140000017
Figure FDA0002423141140000017
 上述四束相干激光光束经过空间中旋转之后得到沿着z轴正方向传播的椭圆偏振光，分别为The above four coherent laser beams are rotated in space to obtain elliptically polarized light propagating in the positive direction of the z-axis, respectively
Figure FDA0002423141140000021
Figure FDA0002423141140000021
Figure FDA0002423141140000022
Figure FDA0002423141140000022
Figure FDA0002423141140000023
Figure FDA0002423141140000023
Figure FDA0002423141140000024
Figure FDA0002423141140000024
 四束椭圆偏振光在空间汇聚干涉叠加得到Gyroid拓扑光子晶体；Four beams of elliptically polarized light converge in space to obtain Gyroid topological photonic crystal; (3)采用斯托克斯参数校准步骤(2)得到的椭圆偏振光，由斯托克斯参数
Figure FDA0002423141140000025
定义的各个椭圆偏振光参数分别为：
Figure FDA0002423141140000026
(3) Using the Stokes parameter to calibrate the elliptically polarized light obtained in step (2), the Stokes parameter
Figure FDA0002423141140000025
The defined parameters of each elliptically polarized light are:
Figure FDA0002423141140000026
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