CN116931146B - Method for constructing spiral cone-shaped zone plate and spiral cone-shaped zone plate manufactured by using same - Google Patents
Method for constructing spiral cone-shaped zone plate and spiral cone-shaped zone plate manufactured by using same Download PDFInfo
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- CN116931146B CN116931146B CN202310948667.3A CN202310948667A CN116931146B CN 116931146 B CN116931146 B CN 116931146B CN 202310948667 A CN202310948667 A CN 202310948667A CN 116931146 B CN116931146 B CN 116931146B
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Abstract
The invention provides a method for constructing a spiral cone-shaped zone plate and the zone plate manufactured by the method, which comprises the following steps: designing a spiral cone phase function according to the characteristic that the spiral cone is limited by azimuth angle and radial coordinates; performing binarization processing on the spiral cone phase function based on a preset binarization function to obtain a plurality of light transmission bands; and combining and constructing the plurality of light transmission bands based on a preset transmittance function to obtain the complete spiral cone-shaped zone plate. The invention breaks through the traditional annular and polygonal zone plate structures to construct a zone plate for generating spiral focused light beams in a focal area, can generate a plurality of spiral light beams and petal-like light beams at the focal plane, can be applied to optical micro-control, and the proposed method for constructing the zone plate for generating the spiral focused light beams is carried out by utilizing a function binarization method and is simple in manufacturing method.
Description
Technical Field
The invention relates to the field of zone plate preparation, in particular to a method for constructing a spiral cone-shaped zone plate and the spiral cone-shaped zone plate manufactured by the method.
Background
A zone plate is an optical diffraction element that can be used for optical imaging and optical tweezers due to its unique focusing properties. Conventional zone plates, such as fresnel zone plates, fractal zone plates, fibonacci zone plates, and the value-Morse zone plates (TMZPs), are composed of alternating transparent and opaque annular zones. In addition, square-shaped section plates have also been widely studied.
An Alda et al proposed a polygonal fresnel zone plate with an arbitrary concentric polygonal ring structure. The Cantor durt was first used to design a new type of zone plate, namely a Cantor durt zone plate. The spiral fractal zone plate may be used to create a series of focused optical vortices with embedded secondary and primary foci. Mohaghaeghian et al propose a binary Multifocal Fresnel Zone Plate (MFZP) with arbitrary focal length and number of foci by superimposing a single Fresnel Zone Plate (FZP) with ideal focal length. In 2017 sabatian et al proposed azimuth phase shifting region plates with petaloid intensity distribution [ consisting of two spiral region plates (SZPs) with opposite sign charge intensities or different topology charge numbers combined ] and spiral phase shifting region plates with multiple spiral intensity patterns [ created by one inward and outward radial phase shifting region plate superposition ]. They then studied the bessel spiral zone plate, which can produce interesting beams of various shapes, such as spiral, annular lattice, optical arm, and multi-spot beam. In addition, compound zone plates have been developed and will likely find application in optical imaging and optical manipulation.
That is, the conventional zone plate is designed in a ring shape and a polygon shape, and there is a great room for innovation in the design of the zone plate.
Disclosure of Invention
In view of this, it is necessary to provide a method for constructing a spiral cone-type zone plate and a spiral cone-type zone plate manufactured by the method, wherein the spiral cone-type zone plate is different from the traditional annular and polygonal structural appearance, a pair of spiral curve-shaped light beams and arrays thereof can be generated at a focal plane, and the spiral cone-type zone plate has potential application in the fields of optical micro-manipulation/image transmission and the like.
In order to achieve the above object, in one aspect, the present invention provides a method for constructing a spiral cone-shaped zone plate, including:
designing a spiral cone phase function according to the characteristic that the spiral cone is limited by azimuth angle and radial coordinates;
performing binarization processing on the spiral cone phase function based on a preset binarization function to obtain a plurality of light transmission bands;
and combining and constructing the plurality of light transmission bands based on a preset transmittance function to obtain the complete spiral cone-shaped zone plate.
In some possible embodiments, the spiral cone phase function is:
ψ(r,θ)＝2πl(θ/2π) n (-r/r 0 )-2πr 2 /(λf)；
wherein r represents a radial coordinate, θ represents an azimuth angle, l represents a topological charge number, n represents a preset power function, r 0 The normalized coefficient representing the radial coordinate r, λ representing the wavelength of incident light, and f representing the focal length.
In some possible embodiments, the preset binarization function is:
wherein k represents a preset intermediate parameter.
In some possible embodiments, the preset transmittance function is:
in some possible embodiments, after obtaining the plurality of light-transmitting bands, the method further comprises:
the preset transmittance function is improved to obtain a composite structure function;
and combining and constructing part of structures which can be rotationally overlapped in the plurality of light transmission bands based on the composite structure function to obtain the composite spiral cone-shaped zone plate.
In some possible embodiments, the composite structure function is:
where rem () represents the remainder and m is a positive integer.
In some possible embodiments, the azimuth angle has a value ranging from 0 to 2pi and the exponent has a fractional value ranging from 0 to 1.
In some possible embodiments, the method further comprises:
changing the value of the preset power function, and/or the value of the topological charge number, and/or the value of the preset intermediate parameter, so as to adjust the structure of the spiral cone-shaped zone plate, and/or adjust the structure of the composite spiral cone-shaped zone plate.
In order to achieve the above purpose, the invention also provides a spiral cone-shaped zone plate, which is manufactured by adopting the construction method of the spiral cone-shaped zone plate.
In some possible embodiments, it consists of a transparent portion of the spiral type and an opaque portion of the spiral type.
The beneficial effects of adopting the embodiment are as follows:
the invention breaks through the traditional annular and polygonal zone plate structures to construct a zone plate for generating spiral focused light beams in a focal area, can generate two symmetrical spiral light beams and petal-like light beams at the focal plane, can be applied to optical micro-control, and the proposed method for constructing the zone plate for generating the spiral focused light beams is carried out by utilizing a function binarization method and is simple in manufacturing method.
Furthermore, the invention also realizes the zone plate with the composite spiral conical structure through cutting and superposition, and the zone plate of the type can generate focused multi-spiral chiral light beams. The zone plate with the spiral conical structure and the focusing spiral light beam or the light beam array generated by the composite structure have potential application in the fields of optical micro-control, optical information storage encryption and the like.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the description of the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a schematic flow chart of an embodiment of a method for constructing a spiral cone zone plate according to the present invention;
fig. 2 is a schematic structural diagram of a first embodiment of a spiral cone zone plate according to the present invention;
fig. 3 is a schematic structural diagram of a second embodiment of a spiral cone zone plate according to the present invention;
fig. 4 is a schematic structural diagram of an intensity distribution of the spiral cone-shaped zone plate shown in (2 c) of fig. 2 in an axial direction;
fig. 5 is a schematic structural diagram of a third embodiment of a spiral cone zone plate according to the present invention;
fig. 6 is a schematic structural view of the intensity distribution of the spiral cone-shaped zone plate shown in fig. 5 (5 b) in the axial direction.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. It will be apparent that the described embodiments are only some, but not all, embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be understood that the schematic drawings are not drawn to scale. A flowchart, as used in this disclosure, illustrates operations implemented according to some embodiments of the present invention. It should be appreciated that the operations of the flow diagrams may be implemented out of order and that steps without logical context may be performed in reverse order or concurrently. Moreover, one or more other operations may be added to or removed from the flow diagrams by those skilled in the art under the direction of the present disclosure. Some of the block diagrams shown in the figures are functional entities and do not necessarily correspond to physically or logically separate entities. These functional entities may be implemented in software or in one or more hardware modules or integrated circuits or in different networks and/or processor systems and/or microcontroller systems.
References to "first," "second," etc. in the embodiments of the present invention are for descriptive purposes only and are not to be construed as indicating or implying a relative importance or the number of technical features indicated. Thus, a technical feature defining "first", "second" may include at least one such feature, either explicitly or implicitly.
Reference herein to "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment may be included in at least one embodiment of the invention. The appearances of such phrases in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. Those of skill in the art will explicitly and implicitly appreciate that the embodiments described herein may be combined with other embodiments.
The invention provides a construction method of a spiral cone-type zone plate and the spiral cone-type zone plate manufactured by the construction method, and the construction method is described below.
Fig. 1 is a schematic flow chart of an embodiment of a method for constructing a spiral cone-shaped zone plate according to the present invention, where the method for constructing a spiral cone-shaped zone plate shown in fig. 1 includes:
s101, designing a spiral cone phase function according to the characteristic that the spiral cone is limited by azimuth angles and radial coordinates;
s102, performing binarization processing on the spiral cone phase function based on a preset binarization function to obtain a plurality of light bands;
s103, combining and constructing the plurality of light transmission bands based on a preset transmittance function to obtain the complete spiral cone-shaped zone plate.
It should be noted that, in the embodiment of the present invention, the influence of the wavelength of the incident light, the focal length of the zone plate, the topological charge number and other related design parameters need to be considered when designing the spiral cone phase function. Of course, in specific design, the main effect on the spiral cone phase function is azimuth and radial coordinates, and the characteristics of the spiral cone are limited by the azimuth and radial coordinates, so that the spiral cone zone plate under different parameters can be formed through the parameter setting of related design parameters such as the wavelength of incident light, the focal length of the zone plate, the topological charge number and the like.
Compared with the prior art, in order to break through the limitation of the traditional annular and polygonal zone plate structure, firstly, a spiral cone phase function is designed according to the characteristic that the spiral cone is limited by azimuth angle and radial coordinates, then a zone plate for generating spiral focused light beams in a focus area is constructed through binarization processing and transmittance function, two symmetrical spiral light beams and petal-like light beams can be generated at the focus plane, the zone plate can be applied to optical micro-control, and the construction method of the zone plate for generating the spiral focused light beams is carried out by utilizing a function binarization method and is simple in manufacturing method.
In a specific embodiment, the spiral cone phase function is:
ψ(r,θ)＝2πl(θ/2π) n (-r/r 0 )-2πr 2 /(λf) (1)；
wherein r represents a radial coordinate, θ represents an azimuth angle, l represents a topological charge number, n represents a preset power function, r 0 The normalized coefficient representing the radial coordinate r, λ representing the wavelength of incident light, and f representing the focal length.
The azimuth angle ranges from 0 to 2pi, and the exponent takes a decimal value from 0 to 1. In general, the exponent n is a factor affecting the shape presentation state of the spiral cone zone plate, and the spiral offset degree of the spiral cone zone plate can be changed by adjusting the exponent n. Similarly, the topological charge number l is also a factor influencing the shape presentation state of the spiral cone zone plate, and the spiral opening degree of the spiral cone zone plate can be changed by adjusting the topological charge number l.
It should be noted that by setting the normalized coefficient r of the radial coordinate r 0 The value range of the phase function can be restrained to a certain extent, and the calculation and the setting of parameters are convenient.
In some embodiments of the present invention, the preset binarization function is:
wherein k represents a preset intermediate parameter.
It should be noted that k is essentially an intermediate variable, which is mainly used to constrain the range of the bit phase function during specific binarization, and is a preset parameter related to the topology charge number l, and in a specific implementation, the determination of each light-transmitting band can be performed as soon as possible by adjusting empirically.
In some possible embodiments, the preset transmittance function is:
it should be noted that the transmittance function and the binarization function complement each other, and the value range of the k parameter needs to be considered, that is, the k parameter affects the number of light transmission bands, so that the integrity of the spiral cone zone plate is affected.
In order to design a more complex compound spiral cone zone plate, in some embodiments of the present invention, after obtaining a number of light transmitting zones, the method further comprises:
the preset transmittance function is improved to obtain a composite structure function;
and combining and constructing part of structures which can be rotationally overlapped in the plurality of light transmission bands based on the composite structure function to obtain the composite spiral cone-shaped zone plate.
In some possible embodiments, the composite structure function is:
where rem () represents the remainder and m is a positive integer.
The composite spiral cone zone plate is obtained by taking the remainder of the variable azimuth angle theta of the function and selecting part of the structures for rotation superposition.
Compared with the prior art, the invention realizes the zone plate with the composite spiral conical structure by cutting and superposition, and the zone plate of the type can generate focused multi-spiral chiral light beams.
Furthermore, the zone plate with the spiral cone structure and the focusing spiral light beam or the light beam array generated by the composite structure have potential application in the fields of optical micro-control, optical information storage encryption and the like.
In some embodiments of the present invention, the method of constructing a spiral cone zone plate further comprises:
changing the value of the preset power function, and/or the value of the topological charge number, and/or the value of the preset intermediate parameter, so as to adjust the structure of the spiral cone-shaped zone plate, and/or adjust the structure of the composite spiral cone-shaped zone plate.
It should be noted that, by changing the preset power function n, and/or the value of the topological charge number l, and/or the value of the preset intermediate parameter k, different spiral cone-shaped zone plates can be visually checked, so as to find the rule, and further design the spiral cone phase function, the binarization function, the transmittance function and the composite structure function as proposed in the above embodiment.
In some embodiments of the present invention, the present invention further provides a spiral cone-shaped zone plate, which is manufactured by using the method for constructing the spiral cone-shaped zone plate provided in the above embodiments.
In some possible embodiments, it consists of a transparent portion of the spiral type and an opaque portion of the spiral type.
In order to further explain the variation of the spiral cone-shaped zone plate manufactured by the method for constructing the spiral cone-shaped zone plate provided by the above embodiment under different situations of changing the power function n, or the topological charge number l, or the value of the preset intermediate parameter k, refer to fig. 2-6 specifically.
Specifically, in some embodiments of the present invention, referring to fig. 2, fig. 2 (2 a), (2 b), and (2 c) respectively show the structural schematic diagrams of corresponding spiral cone zone plates when the topological charge number l=17 and the power exponent n=0 or n=0.5 or n=1.
In this embodiment, the spiral cone phase function adopted is formula (1), in which f=0.5m, λ=532 nm is specifically set, the constants l, n, f, λ are brought into formula (1), corresponding spiral cone phase distribution can be obtained, and phase binarization (0/pi) is implemented by combining formula (2), each obtained light-transmitting wave band is superimposed to generate a corresponding spiral cone wave band plate, the binarization phase wave band plate can achieve higher diffraction efficiency, the generated spiral cone wave band plate is as shown in fig. 2, when the topological charge number takes a certain value (l=17), the power exponent n is changed, when the power exponent is 0, the power exponent n is a conventional annular wave band plate, when n increases (n is 0.5 and 1 respectively), the annular wave bands are split and staggered with each other, and the spiral pattern distribution is presented, as shown in fig. 2 (2 b) and (2 c).
For studying the optical performance and optical strength of the spiral cone-shaped zone plate in fig. 2, please refer to fig. 4, fig. 4 is a schematic structural diagram of the intensity distribution of the spiral cone-shaped zone plate in fig. 2 (2 c) when z=0.01 m,0.2m,0.5m, and 0.6m is the focal position of the zone plate, where z=0.5 m.
In the present embodiment, the axial diffraction characteristics of the spiral cone zone plate shown in (2 c) of fig. 2 were simulated using scalar diffraction theory, wherein the diffraction intensity distribution at the initial plane can be expressed as:
wherein A is 0 The amplitude of incident light is w is Gaussian beam waist width, x, y and z respectively represent the three-dimensional horizontal axis, the vertical axis and the vertical axis of the space where the spiral cone zone plate is located, and i represents complex numbers.
After the incident beam passes through the zone plate, the intensity distribution at axial position z can be expressed as:
wherein FFT and iFFT represent fourier transform and inverse fourier transform, respectively, k=2pi/λ;
further, omega x And omega y The method can be calculated by the following formula:
in this embodiment, taking the zone plate shown in (2 c) in fig. 2 as an example, the diffraction intensity distribution of the zone plate at the positions of z=0.01 m,0.2m,0.5m and 0.6m in the axial direction is calculated according to the formulas (5) - (7), as shown in (4 a) - (4 d) in fig. 4, it can be seen from fig. 4 that a certain distance of light beam propagation after passing through the spiral cone type zone plate will be focused into a spiral light beam in the focal area (as shown in (4 c)).
In some embodiments of the present invention, referring to fig. 3, in fig. 3, (3 a), (3 b) and (3 c) respectively represent the corresponding spiral cone zone plates when the power n=1 and the topological charge numbers l are 5, 10 and 25 respectively, it can be seen that the specific shape of the spiral cone differs when the topological charge numbers l are changed, and is different from the defining topological charge numbers in fig. 2. It should be noted that, for the spiral cone zone plate shown in fig. 3, the calculation of the intensity distribution can be performed by the formulas (5) - (7) as well, which is not described here.
In order to design a more complex composite spiral cone-type zone plate, in some embodiments of the present invention, based on equations (1) and (2), the variable azimuth angle θ of the designed phase function of the spiral cone-type zone plate is left, so that the composite spiral cone-type zone plate can be obtained, and the structure of the composite spiral cone-type zone plate can be determined by equation (4). In general, the structure of the composite helical cone zone plate array can be regulated by changing the parameters k, n, l and m in equation (4).
Specifically, referring to fig. 5, fig. 5 is a schematic structural diagram of a spiral cone zone plate corresponding to a topological charge number l=17, a power exponent n=1, and m is 2, 3, and 4, respectively. In this embodiment, f=0.5m and λ=532 nm are also set, the constants l, n, f, λ and k are brought into the formulas (1) - (2), so that corresponding spiral cone phase distributions can be obtained, and k and m are brought into the formula (4) for remainder, so that corresponding composite spiral cone phase distributions can be obtained, as shown in fig. 5 (5 a) - (5 c), and as can be seen from fig. 5, the combination portions of m different composite spiral cone zone plates are also different.
In this embodiment, the scalar diffraction theory is also used to simulate the axial diffraction characteristic of the compound spiral cone zone plate, please refer to fig. 6 specifically, fig. 6 is a schematic structural diagram of the intensity distribution of the spiral cone zone plate shown in (5 b) of fig. 5 in the axial direction z=0.01 m,0.2m,0.5m, and 0.6m, where z=0.5 m is the focal point position of the zone plate.
In this embodiment, taking the compound spiral cone zone plate shown in fig. 5 (b) as an example, the axial diffraction characteristics of the compound spiral cone zone plate are shown in (6 a) - (6 d) in fig. 6, it can be seen from (6 a) - (6 d) that a light beam propagates a certain distance after passing through the compound spiral cone zone plate, and is focused into a multi-spiral combined light beam in a focal area (shown in (6 c)).
In summary, the method for constructing the spiral cone-shaped zone plate and the spiral cone-shaped zone plate manufactured by the method provided by the embodiment of the invention break through the traditional annular and polygonal zone plate structure to construct the zone plate for generating the spiral focusing light beam in the focal area, can generate two symmetrical spiral light beams and petal-shaped light beams at the focal plane, can be applied to optical micro-control, and the proposed method for constructing the zone plate for generating the spiral focusing light beam is performed by using a function binarization method and is simple in manufacturing method.
Furthermore, the invention also realizes the zone plate with the composite spiral conical structure through cutting and superposition, and the zone plate of the type can generate focused multi-spiral chiral light beams. The zone plate with the spiral conical structure and the focusing spiral light beam or the light beam array generated by the composite structure have potential application in the fields of optical micro-control, optical information storage encryption and the like.
The above describes the construction method of the spiral cone-shaped zone plate and the spiral cone-shaped zone plate manufactured by the construction method, and specific examples are applied to the description of the principle and the implementation mode of the invention, and the description of the above examples is only used for helping to understand the method and the core idea of the invention; meanwhile, as those skilled in the art will have variations in the specific embodiments and application scope in light of the ideas of the present invention, the present description should not be construed as limiting the present invention.
Claims (9)
1. A method of constructing a spiral cone zone plate comprising:
designing a spiral cone phase function according to the characteristic that the spiral cone is limited by azimuth angle and radial coordinates;
performing binarization processing on the spiral cone phase function based on a preset binarization function to obtain a plurality of light transmission bands;
combining and constructing the plurality of light transmission bands based on a preset transmittance function to obtain a complete spiral cone-shaped zone plate;
wherein, the spiral cone phase function is:
；
wherein,rthe radial coordinate is represented by a graph of the radial coordinate,θindicating the azimuth angle of the beam,lthe number of topological charges is represented and,nrepresenting presets is a power function of (a) to (b),r 0 representing radial coordinatesrIs used for the normalization coefficient of (a),λindicating the wavelength of the incident light,frepresenting the focal length.
2. The method of constructing a spiral cone zone plate of claim 1, wherein the predetermined binarization function is:
；
wherein,krepresenting a preset intermediate parameter.
3. The method of constructing a spiral cone zone plate of claim 2, wherein the predetermined transmittance function is:
。
4. the method of claim 3, further comprising, after obtaining the plurality of light transmitting zones:
the preset transmittance function is improved to obtain a composite structure function;
and combining and constructing part of structures which can be rotationally overlapped in the plurality of light transmission bands based on the composite structure function to obtain the composite spiral cone-shaped zone plate.
5. The method of constructing a spiral cone zone plate of claim 4, wherein the composite structural function is:
；
where rem () represents the remainder,mis a positive integer.
6. The method of constructing a spiral cone zone plate of claim 1, wherein the azimuth angle has a value ranging from 0 to 2πThe exponentiation takes a fractional value from 0 to 1.
7. The method of constructing a spiral cone zone plate of any of claims 4-6, further comprising:
changing the value of the preset power function, and/or the value of the topological charge number, and/or the value of the preset intermediate parameter, so as to adjust the structure of the spiral cone-shaped zone plate, and/or adjust the structure of the composite spiral cone-shaped zone plate.
8. A spiral cone zone plate manufactured by the method of any one of claims 1-7.
9. The spiral cone zone plate of claim 8, consisting of a transparent portion of the spiral type and an opaque portion of the spiral type.
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