CN116859586A - Design method for customizable photomask plate with arbitrary shape and structure - Google Patents
Design method for customizable photomask plate with arbitrary shape and structure Download PDFInfo
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- 230000003287 optical effect Effects 0.000 claims abstract description 8
- 238000007493 shaping process Methods 0.000 claims abstract description 8
- 238000005516 engineering process Methods 0.000 claims abstract description 6
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
- G02B27/0012—Optical design, e.g. procedures, algorithms, optimisation routines
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
- G02B27/09—Beam shaping, e.g. changing the cross-sectional area, not otherwise provided for
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Abstract
A design method of a customizable optical mask plate with any shape and structure comprises the following steps: based on the holographic shaping technology and the present round model, an electric field expression of the customizable light beam with any shape is obtained, and the amplitude, the phase and a blazed grating of the light beam are combined to obtain a complex transmittance function of the customizable light beam mask plate with any shape, and the mask plate described based on the complex transmittance function is the customizable light mask plate with any shape. The mask plate designed by the invention can generate structured light with any customizable shape. The topological charge value of the structured light is controllable, and the structured light with amplitude and phase distributed along any preset track can be generated according to actual requirements.
Description
Technical Field
The invention relates to the field of particle manipulation, in particular to a design method of a customizable optical mask plate with any shape and structure.
Background
Since the invention of optical tweezers, optical tweezers technology has developed in a variety of forms, and is an important tool for studying interactions between light and substances on microscopic and nanometer scales. Many applications, ranging from Shan Guangshu optical tweezers to functionally diverse structured optical tweezers, include optical tweezers, benefit from advances in structured light shaping technology. Thus, in recent years researchers have proposed various structural light shaping methods such as two cascaded diffractive optical elements [ Optics Express 16,4479 (2008) ], special spatial light modulators [ Optics letters 31,1675 (2006) ], phase-pitch correction [ Optics letters 28,872 (2003) ], phase cut assembly [ Photonics res.7,1101 (2019) ], and the like. However, these methods produce structured light that is relatively simple and not arbitrary. Recently, rodigo et al have proposed an integration algorithm for structured light shaping that utilizes an analytical expression of the design light field correspondence curve to generate a series of complex light fields distributed along a two-dimensional curve, which can effectively achieve simultaneous control of intensity and phase distribution, expanding the custom range of structured light [ Scientific Reports, 35341 (2016), optics Express 26,18608 (2018) ]. However, due to the limitations of the analytical expressions of the curves, the premise of using this technique is that analytical expressions of the known curves are required to generate structured light corresponding to the curve trajectories. However, in practical applications, the required curve-resolved expression is generally unknown, so that the technique can only produce structured light of a specific shape and cannot be freely customized, so that creating structured light of an arbitrary shape for a specific application (such as particle manipulation) is still lacking when the curve-resolved expression is unknown.
In view of the foregoing, there is currently no laser mode with an arbitrarily customizable amplitude and phase profile for use in the field of complex particle operation.
Disclosure of Invention
The invention aims to solve the defects of the technical problems, and provides a design method for customizing a photomask plate with any shape and structure by utilizing a calculation holographic principle. The mask plate finished by the method can generate structured light with arbitrary amplitude and phase distribution, greatly improves the controllability of the structured light, and has very important application prospect in the field of particle manipulation.
The technical scheme adopted by the invention is as follows:
a design method of a customizable optical mask plate with any shape and structure comprises the following steps:
s1, acquiring an electric field expression capable of customizing a light beam with any shape and structure based on a holographic shaping technology and a present round model:
G(η,ξ)＝F[H(x,y)]
where F () is a fourier transform function, (x, y) is coordinates before fourier transform, (η, ζ) is coordinates after fourier transform, H (x, y) is complex amplitude on an incidence plane, and its expression is:
s2, combining the amplitude, the phase and a blazed grating of the light beam to obtain a complex transmittance function of the customizable light beam mask plate with any shape, wherein the complex transmittance function has the expression:
t＝circle(ρ)exp{j[angle(G(η,ξ))+P 0 ]}
wherein circle (ρ) is a circular diaphragm, ρ is a polar radial variable, exp () is an exponential function based on a natural constant e, and j is an imaginary unit;
s3, the mask plate described based on the complex transmittance function is the customizable optical mask plate with any shape structure.
Preferably, in step S1, whereinIs the length of the curve, phi (x, y, t) determines the phase of the light, expressed as:
wherein ,(t)＝dy 0 (t)/dt,ω 0 is the beam waist width of the beam and m is the topological charge.
Preferably, u '(t) |= [ x' (t) 2 +y'(t) 2 ] 1/2 ,t∈[0,T]X (t) and y (t) are analytical expressions of the curves, expressed as:
where Re () represents the real part of the complex number and Im () represents the imaginary part of the complex number.
As a preferred embodiment, c k The radius and initial rotation angle of each present wheel are determined, and the expression is:
wherein f (n) =x n +iy n N represents the nth key point, (x) n ,y n ) Is the coordinates of each key point on the curve, ω=2pi k/N is the rotation rate of the present wheel.
Preferably, in step S2, 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 plate designed by the invention can generate structured light with any customizable shape. The topological charge value of the structured light is controllable, and the structured light with amplitude and phase distributed along any preset track can be generated according to actual requirements.
Drawings
Fig. 1 is a mask plate that produces structured light with amplitude and phase distribution along triangles, regular hexagons, heptagons, square spirals, doll trajectories, topological lotus m=30.
Fig. 2 is structured light of arbitrary shape generated by the mask plate illustrated in fig. 1.
Detailed Description
FIG. 1 is a mask blank of customizable arbitrary shape structured light produced by the present invention. The specific implementation mode is as follows:
first, based on the holographic shaping technique, we can know that the electric field expression of the structured light with any shape can be customized as follows:
G(η,ξ)＝F[H(x,y)]
where Φ () is a fourier transform function, (x, y) is coordinates before fourier transform, (η, ζ) is coordinates after fourier transform, H (x, y) is complex amplitude on an incidence plane, which can be expressed as:
wherein L＝∫0 T I u' (t) dt is the length of the curve, phi (x, y, t) determines the phase of the light, written specifically as
wherein ,x 0 '(t)＝dx 0 (t)/dt,y 0 '(t)＝dy 0 (t)/dt,ω 0 is the beam waist width of the beam, m is the topological charge;
further, u '(t) |= [ x' (t) 2 +y'(t) 2 ] 1/2 ,t∈[0,T]X (t) and y (t) are analytical expressions of the curve, which can be expressed as:
where N is the number of present rounds, re () represents the real part of the complex number, im () represents the imaginary part of the complex number, c k Determines the radius and initial rotation angle of each wheel, and can be written as
Wherein f (n) =x n +iy n N represents the nth key point, (x) n ,y n ) Is the coordinates of each key point on the curve, ω=2pi k/N is the rotation rate of the present wheel.
The phase expression of blazed gratings is: p (P) 0 =2πx/d. Where d is the period of the blazed grating, which is used to experimentally generate the electric field expression for the customizable arbitrary structured light described above.
The mask plate capable of customizing structured light with any shape is characterized in that the amplitude and the phase of the light beam and a blazed grating are generated by using a wheel model and a holographic shaping technology, and the specific expression of a complex transmittance function is as follows:
t＝circle(ρ)exp{j]angle(G(η,ξ))+P 0 [}
wherein circle (ρ) is a circular diaphragm, ρ is a polar radial variable; . The mask plate described based on the complex transmittance function is the mask plate capable of customizing any structured light.
Fig. 1 is a mask plate that produces structured light with amplitude and phase distribution along a triangle, regular hexagon, heptagon, square spiral, doll shape trajectory, topological lotus m=30.
Examples
Taking 1024×1024 mask plates as an example, a mask plate capable of customizing structured light of any shape is given for laser light with an operating wavelength of 532 nm. The parameters of the customizable optical mask plate with any shape and structure are five different curves, namely triangle, regular hexagon, heptagon, square spiral line and doll shape curve. And finally obtaining the mask plate capable of customizing any structured light according to the mask plate complex transmittance function in the specific embodiment. Fig. 1 shows a customizable arbitrary shape structure photomask under different curves used in the embodiment. Such a mask that can customize light of any shape can be realized by a spatial light modulator. Taking the PLUTO-VIS-016 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 that the structured light with any shape generated in the embodiment, the illustration in the subgraph is a preset geometric shape, and as can be seen from the illustration, we obtain the structured light with any customizable shape, and the shape of the structured light in the experiment is consistent with the height of the preset track.
In summary, the present invention provides a specific design scheme and implementation scheme of a mask plate with any shape of structured light, and takes five curves as an example, and provides a technical implementation route capable of customizing the mask plate with any shape of structured light for laser with a working wavelength of 532 nm.
The above-described mask blank for generating light of a customizable arbitrary shape only represents one embodiment of the present invention and is not 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 (5)
1. A design method of a customizable optical mask plate with any shape and structure is characterized by comprising the following steps: the method comprises the following steps:
s1, acquiring an electric field expression capable of customizing a light beam with any shape and structure based on a holographic shaping technology and a present round model:
G(η,ξ)＝F[H(x,y)]
where F () is a fourier transform function, (x, y) is coordinates before fourier transform, (η, ζ) is coordinates after fourier transform, H (x, y) is complex amplitude on an incidence plane, and its expression is:
s2, combining the amplitude, the phase and a blazed grating of the light beam to obtain a complex transmittance function of the customizable light beam mask plate with any shape, wherein the complex transmittance function has the expression:
t＝circle(ρ)exp{j[angle(G(η,ξ))+P 0 ]}
wherein circle (ρ) is a circular diaphragm, ρ is a polar radial variable, exp () is an exponential function based on a natural constant e, and j is an imaginary unit;
s3, the mask plate described based on the complex transmittance function is the customizable optical mask plate with any shape structure.
2. The method for designing the photomask plate with the customizable arbitrary shape structure according to claim 1, wherein the method comprises the following steps:
in step S1, whereinIs the length of the curve, phi (x, y, t) determines the phase of the light, expressed as:
wherein ,x 0 '(t)＝dx 0 (t)/dt,y 0 '(t)＝dy 0 (t)/dt,ω 0 is the beam waist width of the beam and m is the topological charge.
3. The method for designing the photomask plate with the customizable arbitrary shape structure according to claim 2, wherein the method comprises the following steps:
u'(t)|＝[x'(t) 2 +y'(t) 2 ] 1/2 ,t∈[0,T]x (t) and y (t) are analytical expressions of the curves, expressed as:
where Re () represents the real part of the complex number and Im () represents the imaginary part of the complex number.
4. A method for designing a customizable structured photomask according to claim 3, wherein:
c k the radius and initial rotation angle of each present wheel are determined, and the expression is:
wherein f (n) =x n +iy n N represents the nth key point, (x) n ,y n ) Is the coordinates of each key point on the curve, ω=2pi k/N is the rotation rate of the present wheel.
5. The method for designing the photomask plate with the customizable arbitrary shape structure according to claim 1, wherein the method comprises the following steps:
in step S2, the phase expression of the blazed grating is: p (P) 0 =2πx/d, where d is the period of the blazed grating.
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