CN116027626A - Design method of Gibbs-Wulff optical vortex array mask - Google Patents

Abstract

A design method of a Gibbs-Wulff optical vortex array mask plate comprises the following steps: and obtaining an electric field expression of the Gibbs-Wulff optical vortex array, and combining the amplitude, the phase and a blazed grating of the Gibbs-Wulff optical vortex array to obtain a complex transmittance function of the Gibbs-Wulff optical vortex array mask, wherein the mask described based on the complex transmittance function is the Gibbs-Wulff optical vortex array mask. The invention utilizes the calculation holographic principle, and obtains the amplitude modulation phase mask of the Gibbs-Wulff optical vortex array through computer coding, thereby generating the Gibbs-Wulff optical vortex array with controllable boundary and controllable structure and arrangement mode in the boundary. Therefore, the method has important application value in the fields of particle manipulation and optical micromachining.

Description

Design method of Gibbs-Wulff optical vortex array mask

Technical Field

The invention relates to the field of particle manipulation and optical micromachining, in particular to a design method of a mask plate with a controllable boundary and a Gibbs-Wulff optical vortex array with controllable structure and arrangement modes in the boundary.

Background

Vortex beam (OV) is a great research hot spot in the international optics and photonics fields due to the brand new degree of freedom of carrying orbital angular momentum, and is widely applied to the front-edge fields of high-capacity optical communication, holographic optical tweezers, optical information storage, optical micromachining and the like. In the field of optical micromachining, compared with the traditional micromachining preparation scheme, the surface of the OV-processed material has the characteristics of more clarity, smoothness and the like, and in addition, the spiral structure also shows excellent optical and mechanical properties.

Optical Vortex Arrays (OVA) consisting of multiple OVs have attracted extensive attention and research because of their ability to provide richer mode distributions and degrees of freedom [ opt. Lett.41,1474 (2016); photonics Res.6,641 (2018); opt.Express26,22965 (2018). However, existing OVA modes are not built on application requirements, especially for the optical micromachining field, the need to achieve multifocal parallel machining by OVA [ appl. Phys. Lett.116, 01101 (2020); science372,403 (2021). When carrying out multi-focus parallel micro-processing on materials, if the materials to be processed have limited sizes, the generated OVA should consider the problems of the boundary of the processed materials, the utilization rate in the boundary of the materials, the stability of a macroscopic structure and the like so as to effectively realize the preparation of the microstructure. Therefore, there is an urgent need to develop an OVA with controllable boundaries, and controllable structure and arrangement patterns within the boundaries.

In view of the foregoing, there is currently no OVA laser mode that can be used in the field of multiparticulate manipulation and boundary-controlled optical micromachining.

Disclosure of Invention

In order to solve the defects, the invention aims to provide a design method of a Gibbs-Wulff optical vortex array mask, and the Gibbs-Wulff optical vortex array with controllable boundaries and controllable structure and arrangement modes in the boundaries is produced through the mask.

The invention utilizes the calculation holographic principle, obtains the amplitude modulation phase mask of the Gibbs-Wulff optical vortex array through computer coding, can generate the Gibbs-Wulff optical vortex array with controllable boundary and controllable structure and arrangement mode in the boundary, thereby having important application value in the fields of particle manipulation and optical micromachining.

The technical scheme adopted by the invention is as follows: a design method of a Gibbs-Wulff optical vortex array mask plate comprises the following steps:

s1, acquiring an electric field expression of a Gibbs-Wulff optical vortex array:

where (x, y) is the Cartesian coordinate system of the spatial light modulator SLM plane,

is a polar coordinate system of an SLM plane, N is the number of vortices in a Gibbs-Wulff optical vortex array, k is a wave number, l is a topological load value of the vortices, N and alpha are the refractive index and cone angle of a cone lens respectively, and S is a position matrix of each vortex in the Gibbs-Wulff optical vortex array;

s2, combining the amplitude, the phase and one blazed grating of the Gibbs-Wulff optical vortex array to obtain a complex transmittance function of the Gibbs-Wulff optical vortex array mask, wherein the complex transmittance function specifically comprises the following expression:

t＝H ₀ (x,y)exp[j(angle(H(x,y))+P ₀ )]

where I represents modulo the complex amplitude, H ₀ (x, y) =h (x, y) ·t, T being the phase modulation function of the macro-pixel, angle () being the angular function;

s3, the mask plate described based on the complex transmittance function is the Gibbs-Wulff optical vortex array mask plate.

As a preferred scheme, the phase expression of the blazed grating is: p (P) ₀ =2πx/d, where d is the period of the blazed grating.

The invention has the technical effects that:

the mask designed by the invention can generate the Gibbs-Wulff optical vortex array with controllable boundaries and controllable structure and arrangement modes in the boundaries. The array has the characteristics of diversified structure, adjustable size, controllable arrangement mode (simple stacking and close stacking), stable macroscopic structure, maximized utilization rate and the like, and can realize the array in boundary conditions. Therefore, the method has very important application prospect in optical micromachining and particle manipulation technologies.

Drawings

FIG. 1 is a Gibbs-Wulff optical vortex array mask of different structures produced by the present invention. The arrangement mode is close packing, the parameter is selected to be tau=pi/3, the structure is respectively regular triangle, regular quadrangle, regular pentagon and regular hexagon, and the structure parameter is respectively selected to be s=3, 4,5 and 6.

FIG. 2 is a Gibbs-Wulff optical vortex array generated by the reticle illustrated in FIG. 1.

Detailed Description

FIG. 1 is a reticle of an embodiment of a Gibbs-Wulff optical vortex array produced by the present invention. The specific implementation mode is as follows:

first, based on the phase shift technique we can know that the electric field expression of the Gibbs-Wulff optical vortex array (GWOVA) is:

where (x, y) is the Cartesian coordinate system of the Spatial Light Modulator (SLM) plane,

is a polar coordinate system of an SLM plane, N is the number of vortexes in the GWOVA, k is a wave number, l is a topological load value (TC) of the vortexes, N and alpha are the refractive index and the cone angle of the cone lens respectively, and S is a position matrix of each vortex in the GWOVA;

the phase expression of blazed gratings is: p (P) ₀ =2πx/d. Wherein d is the period of the blazed grating, and the effect of d is to generate the electric field expression of the Gibbs-Wulff optical vortex array in experiments;

a mask with a structure and a controllable arrangement mode in a boundary is characterized in that the amplitude, the phase and a blazed grating of the Gibbs-Wulff optical vortex array are used, and the complex transmittance function of the mask has the following specific expression:

t＝|H ₀ (x,y)|exp[j(angle(H(x,y))+P ₀ )]

where I represents modulo the complex amplitude, H ₀ (x, y) =h (x, y) ·t, T being the phase modulation function of the macro-pixel, angle () being the angular function;

the mask plate described based on the complex transmittance function is the Gibbs-Wulff optical vortex array mask plate.

In the experiment, the parameter tau of the densely distributed mode is pi/3, and for the complex transmittance function of the Gibbs-Wulff optical vortex array, the values of different structural parameters s are sequentially selected, so that the Gibbs-Wulff optical vortex array with different shapes and vortex numbers is obtained. Fig. 1 shows a mask of a Gibbs-Wulff optical vortex array obtained by sequentially taking structural parameters s from 3 to 6 at intervals of 1 and densely distributing mode parameters τ=pi/3.

Example 1:

taking 1024×1024 mask plates as an example, a mask plate with a Gibbs-Wulff optical vortex array with controllable structure and arrangement mode in the boundary is provided for laser with the wavelength of 532 nm. The mask layout mode parameters are selected to be tau=pi/3, the structural parameters are respectively selected to be s=3, 4,5 and 6, and the mask with the structure in the boundary and the layout mode controllable Gibbs-Wulff optical vortex array is finally obtained according to the mask transmittance function in the specific embodiment.

FIG. 1 is a reticle of a Gibbs-Wulff optical vortex array under different parameters used in the examples. The reticle of the Gibbs-Wulff optical vortex array can be realized by a spatial light modulator. Taking the PLUTO-VIS-061 type phase spatial light modulator of Holoeye, germany as an example, the pixel size is 8 μm, the fill factor is 93%, and the resolution is 1920 pixels by 1080 pixels. In the experiment, a continuous wave solid state laser with a wavelength of 532nm was used, with a power of 50mW.

FIG. 2 shows a Gibbs-Wulff optical vortex array of different shapes in a densely packed pattern as produced in the examples. From the figure, the Gibbs-Wulff optical vortex array with controllable shape is obtained in a densely distributed mode, and single vortex in the experiment is clearly visible, and the structures of different arrays are clearly visible in shape.

In summary, the present invention provides a specific design scheme and implementation scheme of a Gibbs-Wulff optical vortex array with controllable structure and arrangement mode in a boundary, and takes a structural parameter s as an example of sequentially taking 3 to 6 from 1 at intervals, and a dense arrangement mode parameter τ=pi/3 as an example, and provides a technical implementation route of a mask of the Gibbs-Wulff optical vortex array with controllable structure and arrangement mode in the boundary for laser with a working wavelength of 532 nm.

The above-described reticle for producing a Gibbs-Wulff optical vortex array represents only one embodiment of the present invention and is not therefore to be construed as limiting the scope of the present invention. It should be noted that it will be apparent to those skilled in the art that numerous modifications and improvements can be made to the specific implementation details set forth in the present patent without departing from the basic concepts of the invention.

Claims (2)

1. A design method of a Gibbs-Wulff optical vortex array mask is characterized by comprising the following steps: the method comprises the following steps:

s1, acquiring an electric field expression of a Gibbs-Wulff optical vortex array:

where (x, y) is the Cartesian coordinate system of the spatial light modulator SLM plane,

is a polar coordinate system of an SLM plane, N is the number of vortices in a Gibbs-Wulff optical vortex array, k is a wave number, l is a topological load value of the vortices, N and alpha are the refractive index and cone angle of a cone lens respectively, and S is a position matrix of each vortex in the Gibbs-Wulff optical vortex array;

s2, combining the amplitude, the phase and one blazed grating of the Gibbs-Wulff optical vortex array to obtain a complex transmittance function of the Gibbs-Wulff optical vortex array mask, wherein the complex transmittance function specifically comprises the following expression:

t＝|H ₀ (x,y)|exp[j(angle(H(x,y))+P ₀ )]

where I represents modulo the complex amplitude, H ₀ (x, y) =h (x, y) ·t, T being the phase modulation function of the macro-pixel, angle () being the angular function;

s3, the mask plate described based on the complex transmittance function is the Gibbs-Wulff optical vortex array mask plate.

2. The method for designing the Gibbs-Wulff optical vortex array mask plate, according to claim 1, is characterized in that: the phase expression of the blazed grating is as follows: p (P) ₀ =2πx/d, where d is the period of the blazed grating.

Images