A design method of a gibbs-wulff optical vortex array mask

Abstract

A design method of a Gibbs-Wulff optical vortex array mask plate, steps are as follows: obtaining an electric field expression of a Gibbs-Wulff optical vortex array, combining the amplitude, phase of the Gibbs-Wulff optical vortex array with a blazed grating, obtaining a complex transmittance function of the Gibbs-Wulff optical vortex array mask plate, and the mask plate described based on the complex transmittance function is the Gibbs-Wulff optical vortex array mask plate. The present application utilizes the principle of computer holography, and obtains the amplitude modulation phase mask plate of the Gibbs-Wulff optical vortex array through computer coding, so that the Gibbs-Wulff optical vortex array with controllable boundary and controllable structure and arrangement mode in the boundary can be generated. Thus, the present application has important application value in the fields of particle manipulation and optical micro-machining.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of microparticle manipulation and optical microfabrication, in particular to a design method of a mask plate of a Gibbs-Wulff optical vortex array with controllable boundary and controllable structure and arrangement mode within the boundary. BACKGROUND

[0002] Optical vortex (OV) is a new research hotspot in the field of international optics and photonics due to its carrying of orbital angular momentum, and is widely used in high-capacity optical communication, holographic optical tweezers, optical information storage and optical microfabrication and other frontier fields. Compared with traditional microfabrication preparation schemes, the material surface processed by OV has more clear and smooth characteristics, and in addition, the spiral structure also shows excellent optical and mechanical properties.

[0003] Optical vortex array (OVA) composed of multiple OV has attracted extensive attention and research due to its ability to provide more abundant mode distribution and degrees of freedom

Opt. Lett. 41, 1474 (2016); Photonics Res. 6, 641 (2018); Opt. Express 26, 22965 (2018)

Appl. Phys. Lett. 116, 011101 (2020); Science 372, 403 (2021)

[0004] In summary, there is currently a lack of OVA laser mode that can be applied to the fields of multi-microparticle manipulation and boundary-controllable optical microfabrication. SUMMARY

[0005] To solve the above problems, the purpose of the present application is to provide a design method of a Gibbs-Wulff optical vortex array mask plate, which generates a Gibbs-Wulff optical vortex array with controllable boundary and controllable structure and arrangement mode within the boundary.

[0006] The application utilizes the principle of computer holography, and obtains an amplitude modulation phase mask of a Gibbs-Wulff optical vortex array through computer coding, so that a Gibbs-Wulff optical vortex array with a controllable boundary and a controllable structure and arrangement mode in the boundary can be generated, and therefore the application has important application value in the fields of particle manipulation and optical microprocessing.

[0007] The technical scheme adopted by the application is a design method of a Gibbs-Wulff optical vortex array mask, and the steps are as follows:

[0008] S1, obtaining an electric field expression of the Gibbs-Wulff optical vortex array:

[0009]

[0010] wherein (x, y) is a Cartesian coordinate system of a spatial light modulator (SLM) plane, is a polar coordinate system of the SLM plane, N is the number of vortices in the Gibbs-Wulff optical vortex array, k is a wave number, l is a topological charge value of the vortex, n and alpha are respectively a refractive index and a cone angle of a cone lens, and S is a position matrix of each vortex in the Gibbs-Wulff optical vortex array;

[0011] S2, combining the amplitude and phase of the Gibbs-Wulff optical vortex array with a blazed grating to obtain a complex transmittance function of the Gibbs-Wulff optical vortex array mask, and the complex transmittance function is specifically expressed as:

[0012] t=H0(x,y)exp[j(angle(H(x,y))+P0)]

[0013] wherein || represents a modulus operation on a complex amplitude, H0(x, y)=H(x, y)·T, T is a phase modulation function of a macro-pixel, and angle() is an angle function;

[0014] S3, the mask described based on the complex transmittance function is the Gibbs-Wulff optical vortex array mask.

[0015] As a preferred scheme, the phase expression of the blazed grating is P0=2πx / d, wherein d is a period of the blazed grating.

[0016] Technical effects of the application:

[0017] The mask designed in the application can generate a Gibbs-Wulff optical vortex array with controllable boundaries, and the structure and arrangement mode in the boundaries are controllable. The array structure is diversified, the size is adjustable, the arrangement mode (simple stacking and dense stacking) is controllable, the array can realize the characteristics of macrostructure stability in boundary conditions and maximum utilization, compared with the previous array without spatial limit, the controllability of the array structure boundary, the spatial utilization of optical microprocessing and the range of microparticle light manipulation are significantly improved. Therefore, it has very important application prospect in optical microprocessing and microparticle manipulation technology. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 It is a Gibbs-Wulff optical vortex array mask generated by the application with different structures. The arrangement mode is dense stacking, the parameter selection is τ = π / 3, and the structures are regular triangle, regular quadrilateral, regular pentagon and regular hexagon, and the structure parameters are selected as s = 3, 4, 5 and 6 respectively.

[0019] Figure 2 It is Figure 1 The Gibbs-Wulff optical vortex array generated by the mask shown. DETAILED DESCRIPTION

[0020] Figure 1 It is a mask of the Gibbs-Wulff optical vortex array embodiment generated by the application. The specific embodiment is:

[0021] Firstly, based on the phase shift technology, we can know that the electric field expression of the Gibbs-Wulff optical vortex array (GWOVA) is:

[0022]

[0023] Where (x, y) is the Cartesian coordinate system of the spatial light modulator (SLM) plane, is the polar coordinate system of the SLM plane, N is the number of vortices in the GWOVA, k is the wave number, l is the topological charge (TC) of the vortex, n and α are the refractive index and cone angle of the cone lens respectively, and S is the position matrix of each vortex in the GWOVA;

[0024] The phase expression of the blazed grating is P0 = 2πx / d. Where d is the period of the blazed grating, which functions to generate the electric field expression of the above Gibbs-Wulff optical vortex array in the experiment;

[0025] A mask plate of a Gibbs-Wulff optical vortex array with controllable structure and arrangement mode in a boundary, characterized in that an amplitude and a phase of the Gibbs-Wulff optical vortex array are used together with a blazed grating, and a complex transmittance function of the mask plate is specifically expressed as:

[0026] t=|H0(x,y)|exp[j(angle(H(x,y))+P0)]

[0027] wherein || represents a modulus operation on a complex amplitude, H0(x,y)=H(x,y)·T, T is a phase modulation function of a macro-pixel, and angle() is an angle function;

[0028] The mask plate described based on the complex transmittance function is the Gibbs-Wulff optical vortex array mask plate.

[0029] In the experiment, the value of the close arrangement mode parameter τ is set as π / 3, and for the complex transmittance function of the Gibbs-Wulff optical vortex array, different values of the structure parameter s are sequentially selected, and the Gibbs-Wulff optical vortex arrays with different shapes and vortex numbers are obtained. Figure 1 The mask plate of the Gibbs-Wulff optical vortex array obtained by taking the structure parameter s at intervals of 1 from 3 to 6 and the close arrangement mode parameter τ=π / 3.

[0030] Embodiment 1:

[0031] Taking a mask plate with a size of 1024×1024 as an example, a mask plate of a Gibbs-Wulff optical vortex array with controllable structure and arrangement mode in a boundary is given for a laser with a wavelength of 532 nm. The arrangement mode parameter of the mask plate is selected as τ=π / 3, and the structure parameters are selected as s=3, 4, 5, and 6, respectively. According to the mask plate transmittance function in the specific embodiment, the mask plate of the Gibbs-Wulff optical vortex array with controllable structure and arrangement mode in a boundary is finally obtained.

[0032] Figure 1 It is the mask plate of the Gibbs-Wulff optical vortex array with different parameters used in the embodiment. This mask plate of the Gibbs-Wulff optical vortex array can be realized by a spatial light modulator. Taking a PLUTO-VIS-061 phase spatial light modulator of a German Holoeye company as an example, the pixel size is 8 μm, the filling factor is 93%, and the resolution is 1920pixel×1080pixel. In the experiment, a continuous wave solid-state laser with a wavelength of 532 nm is used, and the power is 50 mW.

[0033] Figure 2As shown, it is the Gibbs-Wulff optical vortex array of different shapes generated in the embodiment under the close-packed mode. As can be seen from the figure, we obtain the Gibbs-Wulff optical vortex array with controllable shape under the close-packed mode, and the single vortex in the experiment is clear, and the different array structure shapes are clear.

[0034] In summary, the application proposes a specific design scheme and implementation scheme of the Gibbs-Wulff optical vortex array with controllable structure and arrangement mode within the boundary, and taking the structure parameter s as an example, the arrangement mode parameter τ = π / 3 is taken as an example, and the technical implementation route of the mask plate of the Gibbs-Wulff optical vortex array with controllable structure and arrangement mode within the boundary is proposed for the laser with a working wavelength of 532 nm.

[0035] The mask plate for generating the Gibbs-Wulff optical vortex array described above only expresses a specific embodiment of the application, and cannot be understood as a limitation on the protection scope of the application. It should be pointed out that for ordinary skilled persons in the art, under the premise of not departing from the basic idea of the application, some deformations and improvements can be made to the specific implementation details proposed in the patent, and these all belong to the protection scope of the application.

Claims

1. A method of designing a Gibbs-Wulff optical vortex array mask, characterized by: The steps are as follows: S1, obtain the electric field expression of Gibbs-Wulff optical vortex array: wherein, x , y ) is a Cartesian coordinate system of the SLM plane, ( ρ , φ ) is a polar coordinate system of the SLM plane, N is the number of vortices in the Gibbs-Wulff optical vortex array, k is the wave number, l is the topological charge of the vortex, n and α are the refractive index and the cone angle of the conical lens, respectively, S is the position matrix of each vortex in the Gibbs-Wulff optical vortex array; S2, combining the amplitude, phase of the Gibbs-Wulff optical vortex array and a blazed grating, obtaining a complex transmittance function of the Gibbs-Wulff optical vortex array mask, and the specific expression of the complex transmittance function is: where || denotes the modulus of complex amplitude, H 0 (x, y) = H(x, y) · T , T is the phase modulation function of the macro-pixel, and angle() is the angle function; S3, the mask plate described based on the complex transmittance function is the Gibbs-Wulff optical vortex array mask plate; and the phase expression of the blazed grating is: P0 = 2π x / d , where d is the period of the blazed grating.

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