CN115308914B - System and method for generating vortex beam based on gradual change Fermat spiral seam - Google Patents
System and method for generating vortex beam based on gradual change Fermat spiral seam Download PDFInfo
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Abstract
The invention relates to a system for generating vortex beams based on a gradual change Fermat spiral seam, which comprises a plane wave generating module and a mask plate, wherein the plane wave generating module is used for generating plane waves; the mask plate is arranged on the propagation path of the plane wave, a gradual change Fermat spiral seam which is rotationally symmetrical and overlapped is arranged on the mask plate, and vortex beams with specific topological charges are generated on a given observation plane along the propagation direction after the gradual change Fermat spiral seam is irradiated by the plane wave; wherein the progressive fischer helical seam is based on a rotationally symmetrically superimposed discrete plurality of pinholes and a continuous and equally wide fischer helical seam design. The method can generate high-quality vortex beams at a specific distance under the irradiation of plane waves, the light intensity of the vortex beams keeps a circular structure and the light intensity distribution is uniform, is simple and low in cost, can be applied to optical communication, and is suitable for micro-nano optical fields requiring high-quality vortex beams.
Description
Technical Field
The invention relates to the technical field of optical systems, in particular to a system and a method for generating vortex beams based on gradual change Fermat spiral joints.
Background
Vortex beam refers to a special beam with a spiral wavefront and an annular light intensity distribution. A big feature of the vortex beam is that it has a spiral phase factor: exp (i l θ), where θ is the angular coordinate vector in the polar coordinate system and l represents the topological charge of the vortex beam. Wherein each photon of the swirling beam carriesIs the orbital angular momentum of>Representing a simplified planck constant. The vortex light beam carries orbital angular momentum, so that the vortex light beam has wide application prospects in the aspects of super-resolution microscopic imaging, particle capture, optical data storage, nonlinear optics, quantum information processing, multipath free space communication and the like. Because ofThis high quality method of vortex generation becomes extremely important and a big research hotspot in the current optical field.
Methods for generating optical vortices have been widely studied, mainly: computer-generated hologram, spiral phase plate, spatial light modulator, optical waveguide, mode conversion, and the like. However, these methods require a long optical path, modulating the phase of the beam during transmission, thereby producing a swirling beam. The methods can only generate macroscopic vortex beams, the light path structure is complex, the beam size is large, and the application requirements of the increasingly-grown micro-nano optical related fields are difficult to deal with. In recent years, research on generating vortex beams by utilizing a micro-nano structure has become a research hotspot in the field of light field regulation. Unlike traditional vortex beam generating method, the vortex beam generator based on micro-nano structure design has the advantages of small volume, convenient use, integration, multiplexing realization and the like. The micro-nano structure for generating the vortex beam has various forms, for example, the micro-nano structure is composed of a nano antenna, a nano spiral slit, a concentric ring and the like, and can generate the vortex beam under the microcosmic state. The sizes of the structures are all on the micro-nano level, which also shows the superiority of the micro-nano structure in the aspect of light field micro-control. However, each method has its own limitations. The vortex light purity generated by the nanometer spiral seam is very sensitive to dichroism and retardation of materials and structures, so that the generated vortex light beams have the defects of low light intensity quality, uneven light intensity distribution and the like. Therefore, it is important in practical applications to construct new micro-nano structures to produce high quality vortex beams.
The existing methods for generating vortex beams by using a spiral structure mainly comprise the following steps: method 1: vortex beams are generated by using spiral holograms (Heckenberg N R, mcDuff R, smith CP, et al generation of optical phase singularities by computer-generated holograms [ J ]. Optics letters,1992,17 (3): 221-223.), by overlapping spherical waves with the vortex beams to obtain interference patterns, recording the patterns with a film or a base plate to form a spiral hologram, and finally irradiating the spiral hologram with a spherical wave to generate the vortex beams. 2: the hologram designed by the method consists of N pinholes distributed along the Fermat spiral, and the combination of a plurality of circular light holes is utilized to form a Fermat spiral structure (1.Yang,Yuanjie,et al. "orbit-angular-momentum mode selection by rotationally symmetric superposition of chiral states with application to electron vortex beams." Physical ReviewLetters119 (9): 094802,2017;2.Yang,Yuanjie,et al. "Manipulation of Orbital-angular-momentum spectrum using pinhole plates." Physical Review Applied (6): 064007,2019.). Plane waves diffract through pinholes distributed along the fermat's spiral and rotationally symmetrically arranged, effectively creating a vortex beam with a specific topological charge in the plane of distance z. The number of topological charges of the generated vortex beam is equal to the number of Fermat spiral lines. 3: the vortex beam is generated at a specific transmission plane by using one or more spiral structures with equal width, and the first method is based on the first method, and the Fermat spiral structure formed by a plurality of pinholes is changed into the Fermat spiral structure formed by continuous light transmission spiral slits with equal width, so that the vortex beam is generated at a specific transmission distance.
However, when the vortex beam generated by the spiral hologram of the same processing technology is selected, the light intensity fluctuation of the light ring is strong, the light spot is particularly uneven, and the shape of the light ring is not circular. The Fermat spiral micro-nano structure constructed by utilizing a plurality of pinholes and an equal width Fermat spiral line can be used for generating vortex beams, but the light intensity quality of the vortex beams generated by the two methods is lower, the light intensity fluctuation exists on the light ring, and when the topological load is smaller, the light ring of the vortex beams has certain deformation and is not in a standard circular structure. This low quality vortex beam limits its application requirements in some precision micro-nano optics fields.
Disclosure of Invention
Therefore, the technical problem to be solved by the invention is to overcome the problems existing in the prior art, and a system and a method for generating vortex beams based on gradual change Fermat spiral joints are provided, which can generate high-quality vortex beams at a specific distance under the irradiation of plane waves, the light intensity of the vortex beams keeps a circular structure and the light intensity distribution is uniform, and the method is simple and low in cost, can be applied to important applications in optical communication, and is suitable for micro-nano optical fields requiring high-quality vortex beams.
In order to solve the above technical problems, the present invention provides a system for generating vortex beam based on gradual change Fermat spiral slit, comprising:
a plane wave generating module for generating a plane wave;
the mask plate is arranged on the propagation path of the plane wave, a gradual change Fermat spiral seam which is rotationally symmetrical and overlapped is arranged on the mask plate, and vortex light beams with specific topological charges are generated on a given observation plane along the propagation direction after the gradual change Fermat spiral seam is irradiated by the plane wave;
wherein the progressive fischer spiral seam is based on a rotationally symmetrically superimposed discrete plurality of pinholes and a continuous and equally wide fischer spiral seam design.
In one embodiment of the present invention, the slit width of the graded fermat spiral slit increases gradually from inside to outside.
In one embodiment of the invention, the configuration of the graduated fermat helical seam is determined by the number of helices and their degree of rotation.
In one embodiment of the invention, generating a vortex beam of a specific topological charge in a given viewing plane along a propagation direction comprises:
the complex amplitude of a single wavelet generated for the s-th progressive fischer spiral slit at a given observation plane along the propagation direction is expressed as:
where lambda is the wavelength of the plane wave, k is the wave number,represents the transmittance function of the s-th graded Fermat spiral slit,>representing radial and azimuthal coordinates on the progressive fermat's spiral seam plane, (R, phi) representing radial and azimuthal coordinates on the viewing plane, z representing the transmission distance.
In one embodiment of the present invention, the transmittance function of the s-th graded Fischer-Tropsch spiral slit is expressed as:
wherein r is α Representing the radius of each point of the progressive Fermat spiral seam from the center point at an azimuth angle of 0-2 pi, where alpha represents azimuth angle, r 0 The initial radius of the gradual change Fermat spiral seam is represented, the value of l takes the value of the spiral number, d represents the width of the gradual change Fermat spiral seam under different angles alpha, d 0 Is a constant value indicating the length, and a is a constant indicating the proportionality.
In one embodiment of the invention, generating a vortex beam of a specific topological charge in a given viewing plane along a propagation direction comprises:
the total complex amplitude field produced by m wavelets on a given viewing surface by rotationally symmetric superposition is expressed as:
in the method, in the process of the invention,the complex amplitude of a single wavelet generated by an s-th gradual change Fermat spiral seam in a cylindrical polar coordinate system is represented, R, phi respectively represents a radial coordinate and an azimuth coordinate on an observation plane, and z represents a transmission distance.
In addition, the invention also provides a method for generating vortex beams based on the gradual change Fermat spiral seam, which is realized by the system for generating vortex beams based on the gradual change Fermat spiral seam, and the method comprises the following steps:
designing a gradual change Fermat spiral seam which is rotationally symmetrical and overlapped, and generating vortex light beams with specific topological charges on a given observation plane along the propagation direction after the gradual change Fermat spiral seam is irradiated by plane waves;
wherein the progressive fischer spiral seam is based on a rotationally symmetrically superimposed discrete plurality of pinholes and a continuous and equally wide fischer spiral seam design.
In one embodiment of the invention, a method of generating a vortex beam of a specific topology charge in a given viewing plane along a propagation direction includes:
the complex amplitude of a single wavelet generated for the s-th progressive fischer spiral slit at a given observation plane along the propagation direction is expressed as:
where lambda is the wavelength of the plane wave, k is the wave number,represents the transmittance function of the s-th graded Fermat spiral slit,>representing radial and azimuthal coordinates on the progressive fermat's spiral seam plane, (R, phi) representing radial and azimuthal coordinates on the viewing plane, z representing the transmission distance.
In one embodiment of the present invention, the transmittance function of the s-th graded Fischer-Tropsch spiral slit is expressed as:
wherein r is α Representing the radius of each point of the progressive Fermat spiral seam from the center point at an azimuth angle of 0-2 pi, where alpha represents azimuth angle, r 0 The initial radius of the gradual change Fermat spiral seam is represented, and the l value is taken as the spiralThe value of the number of turns, d, represents the width of the progressive Fermat spiral at different angles α, d 0 Is a constant value indicating the length, and a is a constant indicating the proportionality.
In one embodiment of the invention, a method of generating a vortex beam of a specific topology charge in a given viewing plane along a propagation direction includes:
the total complex amplitude field produced by m wavelets on a given viewing surface by rotationally symmetric superposition is expressed as:
in the method, in the process of the invention,the complex amplitude of a single wavelet generated by an s-th gradual change Fermat spiral seam in a cylindrical polar coordinate system is represented, R, phi respectively represents a radial coordinate and an azimuth coordinate on an observation plane, and z represents a transmission distance.
Compared with the prior art, the technical scheme of the invention has the following advantages:
the system and the method for generating the vortex beam based on the gradual change Fermat spiral seam can generate the vortex beam with high quality at a specific distance under the irradiation of plane waves, the light intensity of the vortex beam keeps a circular structure, the light intensity distribution is uniform, the method is simple and low in cost, and the method not only can be applied to optical communication, but also is suitable for micro-nano optical fields requiring the vortex beam with high quality.
Drawings
In order that the invention may be more readily understood, a more particular description of the invention will be rendered by reference to specific embodiments thereof that are illustrated in the appended drawings.
Fig. 1 is a schematic diagram of a system for generating a vortex beam based on a progressive fischer spiral seam according to the present invention.
Fig. 2 is a schematic structural diagram of a gradual change fermat spiral slit when topological charges on a mask plate take different values.
Fig. 3 is a graph of the intensity of a swirling beam produced at the observation plane z=1m by illuminating the progressive fermat spiral slit shown in fig. 2 with a plane wave having a wavelength λ=532.8 nm in accordance with the present invention.
Fig. 4 shows the center light intensity of the mask plate and the vortex beam generated by the mask plate in three modes.
Detailed Description
The present invention will be further described with reference to the accompanying drawings and specific examples, which are not intended to be limiting, so that those skilled in the art will better understand the invention and practice it.
Referring to fig. 1, fig. 1 is a schematic diagram of a system for generating vortex beams based on a progressive fischer spiral slit according to the present invention, which includes:
a plane wave generating module for generating a plane wave;
the mask plate is arranged on the propagation path of the plane wave, a gradual change Fermat spiral seam which is rotationally symmetrical and overlapped is arranged on the mask plate, and vortex light beams with specific topological charges are generated on a given observation plane along the propagation direction after the gradual change Fermat spiral seam is irradiated by the plane wave; wherein the progressive fischer spiral seam is based on a rotationally symmetrically superimposed discrete plurality of pinholes and a continuous and equally wide fischer spiral seam design.
The invention designs a gradual change Fermat spiral slit structure with rotationally symmetrical superposition, the slit width of which gradually increases from inside to outside, when the degree of increase of the slit width from thin to thick is more obvious, the quality of the obtained light beam is better, the gradual change Fermat spiral slit structure is determined by the number of spirals and the rotation degree thereof, wherein the rotation degree refers to the azimuth angle covered by each spiral slit in a certain radius.
The system for generating the vortex beam based on the gradual change Fermat spiral seam can generate the vortex beam with high quality at a specific distance under the irradiation of plane waves, has the advantages of keeping a circular structure of light intensity and uniform light intensity distribution, has a simple structure and low cost, can be applied to optical tweezers and optical communication, and is suitable for micro-nano optical fields needing the vortex beam with high quality, such as micro-nano optical encryption, micro-nano optical manipulation and the like.
In particular, as shown in fig. 1, a high quality vortex beam of a specific topological charge can be produced at a specific propagation distance z under the condition that a plane wave irradiates a gradual fermat spiral slit. The gradual fermat spiral seam structure on the mask plate can be changed by designing the number of spirals m and their degree of rotation (referring to the azimuth covered by each spiral seam within a certain radius). Based on fresnel diffraction theory, on a given observation plane along the propagation direction, the complex amplitude of a single wavelet generated for the s-th graded spiral slit is expressed as:
where lambda is the wavelength, k is the wavenumber,the s-th gradual change Fermat spiral seam transmittance function is shown,representing radial and azimuthal coordinates on the progressive fermat's spiral seam plane, (R, phi) representing radial and azimuthal coordinates on the viewing plane, z representing the transmission distance.
The transmittance function of the s-th gradual change Fermat spiral seam can be expressed as follows:
wherein r is α The radius of each point of the gradually-changed Fermat spiral seam from the center point under the azimuth angle of 0-2 pi is represented, wherein alpha represents the azimuth angle, and the value interval is 0-2 pi, r 0 The initial radius of the gradual Fermat spiral seam is shown (i.e. angle a takes 0), the value of l takes the value of the number of spirals, i.e. l-m, z is the transmission distance and lambda is the wavelength of the plane wave. Importantly, the gradual Fermat spiral seam is characterized in that the width of the slit gradually increases from inside to outside, and d in the formula 2 represents gradual Fermat spiral at different angles alphaWidth of slit d 0 Is a constant value representing the length, A is a constant representing the proportionality (A changes with the values of different topological charges), and when the angle alpha is 0, the minimum width of the gradual Fermat spiral seam is A pi d 0 /2. As the angle α increases, the radius and width of the progressive fischer-tropsch spiral seam at the angle α correspondingly increases.
Then the total complex amplitude field produced by the rotationally symmetric superposition of m such wavelets is denoted as:
in the method, in the process of the invention,the complex amplitude of a single wavelet generated by an s-th gradual change Fermat spiral seam in a cylindrical polar coordinate system is represented, R, phi respectively represents a radial coordinate and an azimuth coordinate on an observation plane, and z represents a transmission distance.
In this embodiment, the wavelength λ= 53.28nm of the incident plane wave is selected, the distance z=1m of the progressive fischer spiral slit mask plate from the observation plane is selected, and the minimum radius r of the progressive fischer spiral slit is selected 0 =1.4 mm and d 0 =0.02 mm. As shown in the schematic fig. 2 (a), when the topology load takes l=3, there are three gradual fermat spiral seams with rotational symmetry, and a takes 0.84; as shown in the schematic diagram 2 (b), when the topology load takes l=4, there are four gradual fermat spiral slits with rotational symmetry, and a takes 0.75; as shown in the schematic diagram 2 (c), when the topology load takes l=5, there are five gradual fermat spiral slits with rotational symmetry, and a takes 0.68; as shown in the schematic diagram 2 (d), when the topology load takes l=6, there are three gradual fermat spiral slits with rotational symmetry, and a takes 0.64.
Fig. 3 shows the intensity profile of a swirling beam produced at the observation plane z=1m by illuminating the progressive fermat spiral slit shown in fig. 2 with a plane wave of wavelength λ=532.8 mm. It can be seen from fig. 3 that the progressive fermat spiral seam of the present patent design can produce a high quality vortex beam.
In order to verify the high quality effect of the vortex beam generated by the present invention, fig. 4 (a) shows the central light intensity of the vortex beam generated based on the spiral hologram, fig. 4 (B) shows the central light intensity of the vortex beam generated based on the continuous and uniform width of the fischer spiral slit, fig. 4 (C) shows the central light intensity of the vortex beam generated based on the gradual change fischer spiral slit, as can be seen from fig. 4, the shape of the light ring of the vortex beam generated by the method of fig. 4 (a) is petal-shaped, the light beam quality is poor, the light intensity quality of the vortex beam generated by the method of fig. 4 (B) is low, the light intensity fluctuation exists on the light ring, and when the topology load is small, the light ring of the vortex beam has a certain deformation, which is not a standard circular structure, the quality of the vortex beam generated by the method of fig. 4 (C) has a relatively obvious improvement, and the light intensity structure maintains a circular structure and is uniformly distributed.
In the following, a method for generating a vortex beam based on a graded fermat spiral slit according to a second embodiment of the present invention is described, and a method for generating a vortex beam based on a graded fermat spiral slit described below and a system for generating a vortex beam based on a graded fermat spiral slit described above may be referred to correspondingly.
The embodiment of the invention also provides a method for generating vortex beams based on the gradual change Fermat spiral seam, which is realized by the system for generating vortex beams based on the gradual change Fermat spiral seam, and comprises the following steps:
designing a gradual change Fermat spiral seam which is rotationally symmetrical and overlapped, and generating vortex light beams with specific topological charges on a given observation plane along the propagation direction after the gradual change Fermat spiral seam is irradiated by plane waves;
wherein the progressive fischer spiral seam is based on a rotationally symmetrically superimposed discrete plurality of pinholes and a continuous and equally wide fischer spiral seam design.
In one embodiment of the invention, a method of generating a vortex beam of a specific topology charge in a given viewing plane along a propagation direction includes:
the complex amplitude of a single wavelet generated for the s-th progressive fischer spiral slit at a given observation plane along the propagation direction is expressed as:
where lambda is the wavelength of the plane wave, k is the wave number,represents the transmittance function of the s-th graded Fermat spiral slit,>representing radial and azimuthal coordinates on the progressive fermat's spiral seam plane, (R, phi) representing radial and azimuthal coordinates on the viewing plane, z representing the transmission distance.
In one embodiment of the present invention, the transmittance function of the s-th graded Fischer-Tropsch spiral slit is expressed as:
wherein r is α Representing the radius of each point of the progressive Fermat spiral seam from the center point at an azimuth angle of 0-2 pi, where alpha represents azimuth angle, r 0 The initial radius of the gradual change Fermat spiral seam is represented, the value of l takes the value of the spiral number, d represents the width of the gradual change Fermat spiral seam under different angles alpha, d 0 Is a constant value indicating the length, and a is a constant indicating the proportionality.
In one embodiment of the invention, a method of generating a vortex beam of a specific topology charge in a given viewing plane along a propagation direction includes:
the total complex amplitude field produced by m wavelets on a given viewing surface by rotationally symmetric superposition is expressed as:
in the method, in the process of the invention,the complex amplitude of a single wavelet generated by an s-th gradual change Fermat spiral seam in a cylindrical polar coordinate system is represented, R, phi respectively represents a radial coordinate and an azimuth coordinate on an observation plane, and z represents a transmission distance.
The method for generating the vortex beam based on the gradual change Fermat spiral seam can generate the vortex beam with high quality at a specific distance under the irradiation of plane waves, the light intensity of the vortex beam keeps a circular structure and the light intensity distribution is uniform, and the method is simple and low in cost, can be applied to optical communication, and is suitable for micro-nano optical fields requiring the vortex beam with high quality.
The method for generating the vortex beam based on the gradual change Fermat spiral slit according to the present embodiment is implemented based on the system for generating the vortex beam based on the gradual change Fermat spiral slit, so that the embodiment of the method can be seen from the part of the embodiment of the system for generating the vortex beam based on the gradual change Fermat spiral slit in the foregoing, and therefore, the detailed description of the embodiment of the system for generating the vortex beam based on the gradual change Fermat spiral slit will be referred to the description of the corresponding embodiments of the respective parts, and will not be further described herein.
In addition, since the method for generating the vortex beam based on the gradual change fermat spiral slit according to the present embodiment is implemented based on the system for generating the vortex beam based on the gradual change fermat spiral slit, the function thereof corresponds to the function of the system described above, and the description thereof is omitted herein.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It is apparent that the above examples are given by way of illustration only and are not limiting of the embodiments. Other variations and modifications of the present invention will be apparent to those of ordinary skill in the art in light of the foregoing description. It is not necessary here nor is it exhaustive of all embodiments. And obvious variations or modifications thereof are contemplated as falling within the scope of the present invention.
Claims (9)
1. A system for generating a vortex beam based on a progressive fischer-tropsch spiral seam, comprising:
a plane wave generating module for generating a plane wave;
the mask plate is arranged on the propagation path of the plane wave, a gradual change Fermat spiral seam which is rotationally symmetrical and overlapped is arranged on the mask plate, and vortex light beams with specific topological charges are generated on a given observation plane along the propagation direction after the gradual change Fermat spiral seam is irradiated by the plane wave;
wherein the gradual change Fermat spiral seam is designed based on a plurality of discrete pinholes and continuous and equal width Fermat spiral seams which are overlapped in a rotation symmetry way;
the slit width of the gradual Fermat spiral slit gradually increases from inside to outside.
2. The progressive fischer-tropsch spiral slit based vortex beam generating system of claim 1 wherein the structure of the progressive fischer-tropsch spiral slit is determined by the number of spirals and their degree of rotation.
3. The progressive fermat spiral seam based vortex beam generating system of claim 1 wherein generating a vortex beam of a specific topological charge in a given viewing plane along a propagation direction comprises:
the complex amplitude of a single wavelet generated for the s-th progressive fischer spiral slit at a given observation plane along the propagation direction is expressed as:
where lambda is the wavelength of the plane wave, k is the wave number,represents the transmittance function of the s-th gradual change Fermat spiral seam,representing radial and azimuthal coordinates on the progressive fermat's spiral seam plane, (R, phi) representing radial and azimuthal coordinates on the viewing plane, z representing the transmission distance.
4. A system for generating a vortex beam based on a progressive fischer spiral seam as in claim 3 wherein the transmittance function of the s-th progressive fischer spiral seam is expressed as:
wherein r is α Representing the radius of each point of the progressive Fermat spiral seam from the center point at an azimuth angle of 0-2 pi, where alpha represents azimuth angle, r 0 The initial radius of the gradual change Fermat spiral seam is represented, the value of l takes the value of the spiral number, d represents the width of the gradual change Fermat spiral seam under different angles alpha, d 0 Is a constant value indicating the length, and a is a constant indicating the proportionality.
5. The progressive fischer-tropsch spiral seam based vortex beam generating system of claim 4 wherein generating a vortex beam of a specific topology charge in a given viewing plane along a propagation direction comprises:
the total complex amplitude field produced by m wavelets on a given viewing surface by rotationally symmetric superposition is expressed as:
in the method, in the process of the invention,the complex amplitude of a single wavelet generated by an s-th gradual change Fermat spiral seam in a cylindrical polar coordinate system is represented, R, phi respectively represents a radial coordinate and an azimuth coordinate on an observation plane, and z represents a transmission distance.
6. A method of generating a vortex beam based on a graduated fermat spiral slit, the method being implemented by a graduated fermat spiral slit based vortex beam generating system as claimed in any one of claims 1 to 5, the method comprising:
designing a gradual change Fermat spiral seam which is rotationally symmetrical and overlapped, and generating vortex light beams with specific topological charges on a given observation plane along the propagation direction after the gradual change Fermat spiral seam is irradiated by plane waves;
wherein the gradual change Fermat spiral seam is designed based on a plurality of discrete pinholes and continuous and equal width Fermat spiral seams which are overlapped in a rotation symmetry way;
the slit width of the gradual Fermat spiral slit gradually increases from inside to outside.
7. The method of generating a vortex beam based on a graded fermat spiral seam of claim 6 wherein the method of generating a vortex beam of a specific topological charge in a given viewing plane along the propagation direction comprises:
the complex amplitude of a single wavelet generated for the s-th progressive fischer spiral slit at a given observation plane along the propagation direction is expressed as:
where lambda is the wavelength of the plane wave, k is the wave number,represents the transmittance function of the s-th gradual change Fermat spiral seam,representing radial and azimuthal coordinates on the progressive fermat's spiral seam plane, (R, phi) representing radial and azimuthal coordinates on the viewing plane, z representing the transmission distance.
8. The method of generating a vortex beam based on a graded fischer spiral slit of claim 7, wherein the transmittance function of the s-th graded fischer spiral slit is expressed as:
wherein r is α Representing the radius of each point of the progressive Fermat spiral seam from the center point at an azimuth angle of 0-2 pi, where alpha represents azimuth angle, r 0 The initial radius of the gradual change Fermat spiral seam is represented, the value of l takes the value of the spiral number, d represents the width of the gradual change Fermat spiral seam under different angles alpha, d 0 Is a constant value indicating the length, and a is a constant indicating the proportionality.
9. The method of generating a vortex beam based on a graded fermat spiral seam of claim 8 wherein the method of generating a vortex beam of a specific topological charge in a given viewing plane along the propagation direction comprises:
the total complex amplitude field produced by m wavelets on a given viewing surface by rotationally symmetric superposition is expressed as:
in the method, in the process of the invention,the complex amplitude of a single wavelet generated by an s-th gradual change Fermat spiral seam in a cylindrical polar coordinate system is represented, R, phi respectively represents a radial coordinate and an azimuth coordinate on an observation plane, and z represents a transmission distance.
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