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

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

Method for preparing Gyroid topological photonic crystal based on holographic interference technology

The technical field is as follows:

the invention belongs to the technical field of photonic crystal preparation, and relates to a preparation method of a Gyroid structure which has abundant optical characteristics in an optical waveband and can detect the triple periodicity of Weyl fermi, in particular to a method for preparing a Gyroid topological photonic crystal based on a holographic interference technology.

Background art:

in 1929, german scientist foreign (Hermann Weyl) pointed out that when the fermi mass is zero, it can be distinguished into particles with two different chiralities of left-handed and right-handed, that is, Weyl fermi, and similarly, light can be divided into left-handed polarized light and right-handed polarized light, and the fermi equivalent electron mass is zero, so that the transmission efficiency of electrons can be greatly improved, and another advantage is that it has the characteristic of topology protection, so that the robustness (Robust) is stronger, and thus the punch can be widely used in quantum computers. The discovery of Weyl fermi not only has very important scientific significance, but also can bring about future innovative technical breakthroughs. However, Weyl Fermi has not been observed experimentally for centuries.

The results of the research on Weyl semimetals by the flood research team of the institute of Physical sciences in China, which measures the electronic structure of TaAs using angle-resolved photoelectron spectroscopy and directly observes the energy bands of Weyl cones, which was first experimentally confirmed since Weyl Fermi was proposed in 1929, were published on line for the Physical Review X and Nature Physics in terms of "Experimental Discovery of Weyl semi-metal TaAs" and "Observation of Weyl Nodes InTaAs" on 7/31 and 8/17, respectively.

In 2015, researchers at Massachusetts institute of technology L u L ing and the like introduced space-symmetry breaks in microwave-band Gyroid photonic crystals, and theoretically predicted and experimentally observed Weyl points in photonic crystal band structures.

In recent years, researchers successfully prepare Gyroid photonic crystals through technologies such as colloid self-assembly and laser direct writing, and perform observation and research on the Gyroid photonic crystals, but there are no reports about preparation of Gyroid photonic crystals in a visible light band. The laser holographic interference technology is based on a multi-beam interference theory, can regulate and control an interference structure by regulating and controlling parameters such as the number of interference beams, light wave vectors, polarization and the like, and is widely applied to the preparation of micro-nano structures such as photonic crystals, quasicrystals, metamaterials and the like in recent years, so that a method for preparing Gyroid topological photonic crystals based on the holographic interference technology is sought.

The invention content is as follows:

the invention aims to provide a method for economically and rapidly preparing a Gyroid photonic crystal in a large area in a visible light waveband aiming at the defects in the prior art.

In order to achieve the purpose, the method prepares the Gyroid photonic crystal by interference superposition of four beams of coherent light in space, and the specific process is as follows:

(1) four coherent laser beams with any wavelength are obtained through light splitting, included angles of the coherent laser beams on an x-y projection plane are equal, projection included angles of adjacent beams are all 90 degrees, and wave vectors of the four coherent laser beams are respectively as follows:

wherein λ is the wavelength of the coherent light;

the space electric field vectors are respectively:

(2) because the space electric field vectors are all elliptical polarized light in space, the elliptical polarized light needs to be converted into elliptical polarized light which is transmitted along the positive direction of the z axis, the rotation of the elliptical polarized light in space is realized by a rotation matrix method, and different space electric field vectors correspond to different rotation matrixes R_i(i is 1,2,3,4) is

The four coherent laser beams are rotated in space to obtain elliptically polarized light propagating along the positive direction of the z axis

Four beams of elliptically polarized light are converged, interfered and superposed in space to obtain a Gyroid photonic crystal;

(3) calibrating the elliptically polarized light obtained in the step (2) by adopting Stokes parameters

The defined parameters of the elliptically polarized light are respectively:

the rotation matrix is obtained by two times of matrix rotation, the space electric field vector is rotated to xoz or yoz plane, then is rotated around the x axis or y axis to be superposed with the z axis, and the product of the two times of rotation matrices is the rotation matrix of the light beam space electric field vector.

The laser polarization state is adjusted through a corresponding wave plate, a quartz wave plate with fixed phase difference delta is designed according to elliptical polarization parameters, delta is in direct proportion to the thickness d of the wave plate, and the phase difference delta of each beam of elliptical polarized light obtained according to a rotated electric field vector is respectively as follows: 247.7 °, 270 °, 90 °, 292.3 °.

Compared with the prior art for preparing the photonic crystal, the invention has the following advantages: the method has the advantages that firstly, the new application of the laser holographic interference technology is expanded, and the preparation of a novel topological Gyroid photon structure is realized by introducing elliptical polarized light beams on the basis of not increasing the number of light beams; secondly, the polarization adjustment of the elliptical polarization light is realized through a specially designed wave plate, and the elliptical polarization light with different polarization states can be obtained by rotating according to a certain angle according to the pre-calculated polarization state parameters of the light beam; thirdly, the technology has low manufacturing cost, the light path is conveniently and effectively constructed, and the obtained crystal lattice symmetry, the crystal lattice period, the medium duty ratio and the like can be regulated and controlled; fourthly, the Gyroid photonic crystal with the visible light wave band can be prepared in a large area on a mesoscopic scale.

Description of the drawings:

fig. 1 is a structural view of a Gyroid photonic crystal prepared according to the present invention, in which (a) a perspective view of 2 × 2 × 2 units of Gyroid, (b) a structural view in the [100] direction, arrows indicating the direction of bending rotation of a helix, and (c) a structural view in the [111] direction, and the directions of the helical axes [100], [010], and [001] are shown as larger (smaller) helices.

Fig. 2 shows the beam configuration of elliptically polarized light for producing Gyroid photonic crystals according to the present invention.

Fig. 3 shows the yoz plane view (a), xoz plane view (b) and xoy plane view (c) of the circularly polarized light beam configuration diagram according to the present invention.

FIG. 4 shows the polarization states of four elliptically polarized light beams according to the present invention, wherein (a)

(b)

(c)

(d)

FIG. 5 shows the result of computer simulation interference for the circularly polarized beam configuration of the present invention, wherein (a) is a diagonal view; (b) a front view; (c) a top view; (d) and (4) a left view.

The specific implementation mode is as follows:

the invention is further illustrated by the following examples in conjunction with the accompanying drawings.

In this embodiment, four beams of coherent light in space are superimposed to prepare a Gyroid photonic crystal, and the specific process is as follows:

(1) four coherent laser beams with any wavelength are obtained through light splitting, included angles of the coherent laser beams on an x-y projection plane are equal, projection included angles of adjacent beams are all 90 degrees, and wave vectors of the four coherent laser beams are respectively as follows:

wherein λ is the wavelength of the coherent light;

the space electric field vectors are respectively:

(2) because the space electric field vectors are all elliptical polarized light in space, the elliptical polarized light needs to be converted into elliptical polarized light which is transmitted along the positive direction of the z axis, the rotation of the elliptical polarized light in space is realized by a rotation matrix method, and different space electric field vectors correspond to different rotation matrixes R_i(i is 1,2,3,4) is

The four coherent laser beams are rotated in space to obtain elliptically polarized light propagating along the positive direction of the z axis

Four beams of elliptically polarized light are converged, interfered and superposed in space to obtain a Gyroid photonic crystal;

(3) calibrating the elliptically polarized light obtained in the step (2) by adopting Stokes parameters

The defined parameters of the elliptically polarized light are respectively:

the rotation matrix in this embodiment is obtained by two matrix rotations, in which the space electric field vector is first rotated to xoz or yoz plane, and then rotated around the x axis or y axis to coincide with the z axis, and the product of the two rotation matrices is the rotation matrix of the light beam space electric field vector.

In this embodiment, the laser polarization state is adjusted by a corresponding wave plate, a quartz wave plate with a fixed phase difference Δ is designed according to an elliptical polarization parameter, Δ is proportional to a thickness d of the wave plate, and the phase difference Δ of each elliptical polarized light obtained according to a rotated electric field vector is: 247.7 °, 270 °, 90 °, 292.3 °.

Example (b):

the specific steps for preparing the Gyroid photonic crystal in this example are as follows:

(1) the 4 coherent laser beams are distributed in space as shown in FIG. 2, and the incident direction and the positive direction of the z axis form an included angle

Get

The wavelength of coherent laser light waves is 488nm, the included angles between the adjacent projections of the coherent laser beams on the x-y plane are all 90 degrees, and fig. 3 is a yoz plane, an xoz plane view and an xoy plane view of the optical path configuration diagram;

(2) keeping the other conditions of the beam configuration unchanged, enabling the polarization state of each beam to be the required polarization state in fig. 4 by a rotation matrix method, and enabling the 4 beams to interfere in space to obtain a three-dimensional photonic crystal structure shown in fig. 5(a), namely a three-periodic Gyroid photonic crystal structure, wherein (b) (c) (d) are a front view, a top view and a left view of the three-dimensional photonic crystal structure respectively;

(3) the polarization states of 4 elliptical polarized lights in fig. 4 are calibrated by using Stokes parameters, that is, Stokes parameters can be determined by measuring the transmitted light intensity of the light beam, so that the polarization states of the light beam can be verified.

The structural shape of the triple periodic Gyroid photonic crystal structure prepared in this example in xoy is shown in fig. 1, and different structural units have spiral bends along different directions.

The embodiment is realized by adopting multi-beam single exposure interference, and the duty ratio of the structure can be adjusted by changing the exposure of interference beams.

The wavelength of the laser beam is theoretically unlimited, and in actual operation, visible light is used for interference preparation, so that a Gyroid photonic crystal structure with the period size in the light wavelength order is obtained, and the band gap characteristic of an optical wavelength band is obtained.

Claims (1)

1. A method for preparing Gyroid topological photonic crystals based on holographic interference technology is characterized in that four beams of coherent light in space are used for interference superposition to prepare the Gyroid photonic crystals, and the specific process is as follows:

(1) four coherent laser beams with any wavelength are obtained through light splitting, included angles of the coherent laser beams on an x-y projection plane are equal, projection included angles of adjacent beams are all 90 degrees, and wave vectors of the four coherent laser beams are respectively as follows:

wherein

λ is the wavelength of the coherent light;

the space electric field vectors are respectively:

(2) because the space electric field vectors are all elliptical polarized light in space, the elliptical polarized light needs to be converted into elliptical polarized light which is transmitted along the positive direction of the z axis, the rotation of the elliptical polarized light in space is realized by a rotation matrix method, and different space electric field vectors correspond to different rotation matrixes respectively and are

The four coherent laser beams are rotated in space to obtain elliptically polarized light propagating along the positive direction of the z axis

Four beams of elliptically polarized light are converged, interfered and superposed in space to obtain a Gyroid topological photonic crystal;

(3) calibrating the elliptically polarized light obtained in the step (2) by adopting Stokes parameters

The defined parameters of the elliptically polarized light are respectively:

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