CN115308914A - System and method for generating vortex light beam based on gradual change Fermat spiral seam - Google Patents
System and method for generating vortex light 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 gradient 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 a propagation path of the plane wave, the mask plate is provided with a rotationally symmetrical and superposed gradual-change Fermat spiral seam, and after the gradual-change Fermat spiral seam is irradiated by the plane wave, vortex beams with specific topological loads are generated on a given observation plane along the propagation direction; wherein the gradual change fermat spiral seam is based on a rotationally symmetrical superposition of a plurality of discrete pinholes and a continuous and equal width fermat spiral seam design. The method can generate the high-quality vortex light beam at a specific distance under the irradiation of the plane wave, the light intensity of the vortex light beam keeps a circular structure and is uniform in light intensity distribution, the method is simple and low in cost, and the method not only can be applied to optical communication, but also is suitable for the micro-nano optical field needing the high-quality vortex light beam.
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 a gradient Fermat spiral seam.
Background
A vortex beam refers to a special beam with a helical wave front and an annular light intensity distribution. A large feature of the vortex beam is that it has a helical phase factor: exp (i l θ), where θ is the angular coordinate vector in a polar coordinate system and l represents the topological charge of the vortex beam. Wherein each photon of the vortex beam carries
Orbital angular momentum of wherein
Representing a simplified planck constant. Because the vortex light beam carries orbital angular momentum, the method has wide application prospect in the aspects of super-resolution microscopic imaging, particle capture, optical data storage, nonlinear optics, quantum information processing, multi-path free space communication and the like. Therefore, the high-quality vortex generation method becomes extremely important and becomes a hot research point in the current optical field.
Methods of generating optical vortices have been extensively studied, mainly: computer holography, spiral phase plate, spatial light modulator, optical waveguide, and mode conversion. However, these methods require a long optical path, and modulate the phase of the light beam during transmission, thereby generating a vortex light beam. The methods can only generate macroscopic vortex beams, the optical path structure is complicated, the beam size is large, and the method is difficult to meet the increasing application requirements of the micro-nano optical related field. In recent years, research on generating vortex beams by using micro-nano structures has become a research hotspot in the field of light field regulation. Different from the traditional method for generating vortex beams, the vortex optical beam generator based on the micro-nano structure design has the advantages of small volume, convenience in use, integration, capability of realizing multiplexing and the like. The micro-nano structure for generating the vortex light beam has various forms, for example, the micro-nano structure is composed of nano antennas, nano spiral seams, concentric rings and other nano structures, and can generate the micro vortex light beam. The sizes of the structures are in micro-nano magnitude, so that the advantages of the micro-nano structure in the aspect of micro control of a light field are reflected. However, each approach has its own limitations. The optical purity of vortex generated by the nano spiral slit is very sensitive to dichroism and delay 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, constructing a novel micro-nano structure to generate a high-quality vortex beam is very important in practical applications.
The existing method for generating vortex light beams by using a spiral structure mainly comprises the following steps: the method comprises the following steps: spiral holograms are used to generate a vortex beam (Heckenberg N R, mcDuff R, smith CP, et al. Generation of optical phase by computer-generated holograms [ J ]. Optics letters,1992,17 (3): 221-223.) by superimposing and interfering a spherical wave with a vortex beam to obtain an interference pattern, recording the pattern with a film or substrate to form a spiral hologram, and finally irradiating the spiral hologram with a spherical wave to generate a vortex beam. 2: a Fermat spiral structure (1. Yang, yuanjie, et al. "Orbital-angular-molar-module selection by polarization systematic periodic superproposition of phase states to electronic vortex beams." Physical Review letters119 (9): 094802, 2017. Yang, yuanjie, et al. "Manipulation of annular-angular-molar using rows." Physical Review version 12 (6): 064007, 2019.) is assembled using a plurality of circular light-transmitting holes, and a hologram designed by this method consists of N number of pinholes distributed along the Fermat spiral. Plane waves are diffracted by pinholes which are distributed along the fermat spiral and are arranged in a rotational symmetry manner, and vortex beams with specific topological charges can be effectively generated in a plane at a distance z. The topological charge of the generated vortex beam is equal to the number of fermat spirals. 3: one or more helical structures with equal width are used to generate vortex beams in a specific transmission plane (Yang, yuanjie, et al, "analogue beam vortex beam: modulating organic and regular expression with probability" "Nanophotonics 3 (7): 677-682, 2018.), which changes the Fermat helical structure formed by a plurality of pinholes into the Fermat helical structure formed by a light-transmitting helical slit with equal width and continuous, so as to generate vortex beams in a specific transmission distance.
However, when the method is used for selecting the vortex light beam generated by the spiral hologram of the same type of processing technology, the halo light intensity of the method has strong fluctuation, the light spot is particularly uneven, and the halo shape is not circular. The Fermat spiral micro-nano structure constructed by a plurality of pinholes and equal-width Fermat spiral lines can be used for generating vortex light beams, but the vortex light beams generated by the two methods have low light intensity quality, light intensity fluctuation exists on the light rings, and when the topological load is small, the light rings of the vortex light beams have certain deformation and are not of a standard circular structure. The low-quality vortex light beam limits the application requirements of the vortex light beam in some precise micro-nano optical fields.
Disclosure of Invention
Therefore, the technical problem to be solved by the invention is to overcome the problems in the prior art, and provide a system and a method for generating vortex beams based on a gradient Fermat spiral seam, wherein the system and 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 is uniform in light intensity distribution, and the method is simple and low in cost, not only can be applied to optical communication, but also is suitable for the micro-nano optical field needing the high-quality vortex beams.
In order to solve the technical problem, the invention provides a system for generating vortex light beams based on a gradually-changed Fermat spiral seam, which comprises:
a plane wave generating module for generating a plane wave;
the mask plate is arranged on a propagation path of the plane wave, the mask plate is provided with a gradient Fermat spiral seam which is rotationally symmetrically superposed, and after the plane wave irradiates the gradient Fermat spiral seam, vortex light beams with specific topological loads are generated on a given observation plane along a propagation direction;
the gradual change Fermat spiral seam is designed based on a plurality of discrete pinholes which are rotationally symmetrically overlapped and a continuous Fermat spiral seam with the same width.
In one embodiment of the invention, the slot width of the gradual Fermat spiral slit gradually increases from the inside to the outside.
In one embodiment of the invention, the structure of the gradual Fermat spiral seam is determined by the number of spirals and the degree of rotation thereof.
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:
on a given observation plane along the propagation direction, the complex amplitude of a single wavelet generated for the s-th gradual fermat spiral seam is expressed as:
wherein λ is the wavelength of the plane wave, k is the wave number,
represents the transmittance function of the s-th gradually-changed Fermat spiral seam,
the radial and azimuthal coordinates on the plane of the graduated fermat spiral slot are indicated, (R, phi) the radial and azimuthal coordinates on the viewing plane, and z the transmission distance.
In one embodiment of the present invention, the transmittance function of the s-th gradual Fermat spiral seam is expressed as:
in the formula, r α Represents the radius size of each point of the gradual Fermat spiral seam from the central point under the azimuth angle of 0-2 pi, wherein alpha represents the azimuth angle, r 0 The initial radius of the gradually changed Fermat spiral seam is represented, the value of l is the value of the spiral number, d represents the width of the gradually changed Fermat spiral seam under different angles alpha, d 0 Is a constant value representing the length, A is a constant value representing the ratioA constant.
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 small waves by rotationally symmetric superposition on a given viewing surface is represented as:
in the formula (I), the compound is shown in the specification,
the complex amplitude of a single wavelet generated by the s-th gradually-changed Fermat spiral seam in the cylindrical polar coordinate system is represented, R and phi respectively represent 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 light beams based on the gradually-changed fermat spiral seam, which is realized by the system for generating vortex light beams based on the gradually-changed fermat spiral seam, and the method comprises the following steps:
designing a rotationally symmetrical and superposed gradient Fermat spiral seam, and generating vortex beams with specific topological charges on a given observation plane along a propagation direction after plane waves irradiate the gradient Fermat spiral seam;
the gradual change Fermat spiral seam is designed based on a plurality of discrete pinholes which are rotationally symmetrically overlapped and a continuous Fermat spiral seam with the same width.
In one embodiment of the invention, a method of generating a vortex beam of a specific topological charge in a given viewing plane along a propagation direction comprises:
on a given observation plane along the propagation direction, the complex amplitude of a single wavelet generated for the s-th gradual fermat spiral seam is expressed as:
wherein λ is the wavelength of the plane waveAnd k is the number of waves,
represents the transmittance function of the s-th gradually-changed Fermat spiral seam,
the radial and azimuthal coordinates on the plane of the graduated fermat spiral slot are indicated, (R, phi) the radial and azimuthal coordinates on the viewing plane, and z the transmission distance.
In one embodiment of the present invention, the transmittance function of the s-th gradual Fermat spiral seam is expressed as:
in the formula, r α Represents the radius of each point of the gradually changed Fermat spiral seam from the central point under the azimuth angle of 0-2 pi, wherein alpha represents the azimuth angle, r 0 Representing the initial radius of the gradual change Fermat spiral seam, the value of l is the value of the number of spirals, 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 value indicating the ratio.
In one embodiment of the invention, a method of 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 by rotationally symmetric superposition on a given viewing surface is represented as:
in the formula (I), the compound is shown in the specification,
the complex amplitude of a single wavelet generated by the s-th gradually-changed Fermat spiral seam in a cylindrical polar coordinate system is represented, R and phi respectively represent 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 light beam based on the gradient Fermat spiral seam can generate the high-quality vortex light beam at a specific distance under the irradiation of the plane wave, the light intensity of the vortex light beam keeps a circular structure and is uniform in light intensity distribution, the method is simple and low in cost, and the method not only can be applied to optical communication, but also is suitable for the micro-nano optical field needing the high-quality vortex light beam.
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In order that the present disclosure may be more readily and clearly understood, reference will now be made in detail to the present disclosure, examples of which are illustrated in the accompanying drawings.
Fig. 1 is a schematic diagram of a system for generating a vortex beam based on a gradual-change fermat spiral slit according to the present invention.
FIG. 2 is a schematic structural diagram of a gradient Fermat spiral seam when topological loads on a mask plate take different values.
Fig. 3 is a graph of the light intensity of the vortex beam generated by the present invention at the observation plane z =1m by illuminating the graded fermat spiral slit shown in fig. 2 with a plane wave having a wavelength λ =532.8 nm.
FIG. 4 shows the central intensity of the three patterns of masks and the vortex beams generated by the masks.
Detailed Description
The present invention is further described below in conjunction with the following figures and specific examples so that those skilled in the art may better understand the present invention and practice it, but the examples are not intended to limit the present invention.
Referring to fig. 1, fig. 1 is a schematic diagram of a system for generating a vortex beam based on a gradual-change fermat 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 a propagation path of the plane wave, the mask plate is provided with a gradient Fermat spiral seam which is rotationally symmetrically superposed, and after the plane wave irradiates the gradient Fermat spiral seam, vortex light beams with specific topological loads are generated on a given observation plane along a propagation direction; the gradual change Fermat spiral seam is designed based on a plurality of discrete pinholes which are rotationally symmetrically overlapped and a continuous Fermat spiral seam with the same width.
The invention designs a rotational symmetry superposed gradient Fermat spiral seam structure, the seam width of which is gradually increased from inside to outside, when the increasing degree of the seam width from thin to thick is more obvious, the quality of the obtained light beam is better, the structure of the gradient Fermat spiral seam is determined by the number of spirals and the degree of rotation thereof, wherein the degree of rotation refers to the azimuth angle covered by each spiral seam within a certain radius.
The system for generating the vortex light beam based on the gradient Fermat spiral seam can generate the high-quality vortex light beam at a specific distance under the irradiation of plane waves, the light intensity of the vortex light beam keeps a circular structure and is uniform in light intensity distribution, the system is simple in structure and low in cost, and the system can be applied to optical tweezers and optical communication and is suitable for micro-nano optical fields needing the high-quality vortex light beam, such as micro-nano optical encryption, micro-nano optical manipulation and the like.
Specifically, as shown in fig. 1, a high quality vortex beam of a specific topological charge l can be generated at a specific propagation distance z under the condition that a plane wave irradiates a gradient fermat spiral slit. The gradual-change Fermat spiral seam structure on the mask plate can be changed by designing the spiral number m and the rotation degree (referring to the azimuth angle covered by each spiral seam within a certain radius). Based on fresnel diffraction theory, the complex amplitude of a single wavelet generated for the s-th graduated spiral slit on a given observation plane along the propagation direction is expressed as:
where λ is the wavelength, k is the wavenumber,
the s-th gradient fermat spiral seam is shown as a transmittance function,
the radial and azimuthal coordinates on the plane of the graduated fermat spiral slot are indicated, (R, phi) the radial and azimuthal coordinates on the viewing plane, and z the transmission distance.
The transmittance function of the above-mentioned s-th gradually-changed fermat spiral seam can be expressed as:
in the formula r α The radius of each point of the Fermat spiral seam from the central point gradually changed under the azimuth angle of 0-2 pi is represented, wherein alpha represents the azimuth angle, the value interval is 0-2 pi, r 0 The initial radius of the gradual Fermat spiral seam is shown (i.e. the 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 λ is the wavelength of the plane wave. Importantly, the gradual change Fermat spiral seam is embodied in the way that the width of the slit is gradually increased from inside to outside, d in formula 2 represents the width of the gradual change Fermat spiral seam under different angles alpha, and d 0 Is a constant value representing the length, A is a constant representing the proportion (A changes along with the values of different topological loads l), and when the angle alpha is 0, the minimum width of the gradual change Fermat spiral seam is Api d 0 /2. With the increasing angle alpha, the radius and the width of the gradual Fermat spiral seam at the angle alpha correspondingly increase.
The total complex amplitude field produced by the rotationally symmetric superposition of m such wavelets is then represented as:
in the formula (I), the compound is shown in the specification,
representing the complex amplitude of a single wavelet generated by the s-th gradually-changed Fermat spiral seam in a cylindrical polar coordinate system, wherein R and phi respectively represent a radial coordinate and an azimuth coordinate on an observation plane, and z representsThe transmission distance.
In this embodiment, the wavelength λ =53.28nm of the incident plane wave, the distance z =1m from the observation plane to the gradually-changing fermat spiral slit mask plate, and the minimum radius r of the gradually-changing fermat spiral slit are selected 0 =1.4mm and d 0 =0.02mm. As shown in the schematic diagram 2 (a), when the topological loading is l =3, there are three rotationally symmetric gradually-changed fermat spiral seams, and a is 0.84; as shown in the schematic diagram 2 (b), when the topological load is l =4, there are four rotationally symmetric gradually-changed fermat spiral seams, and a is 0.75; as shown in the schematic diagram 2 (c), when the topological loading is l =5, there are five rotationally symmetric gradually-changed fermat spiral seams, and a is 0.68; as shown in the schematic diagram 2 (d), when the topological loading is l =6, there are three rotationally symmetric gradient fermat spiral slits, and a is 0.64.
Fig. 3 shows a graph of the intensity of the vortex beam generated by illuminating the graded fermat spiral slit shown in fig. 2 with a plane wave of wavelength λ =532.8mm and at the observation plane z =1 m. It can be seen from fig. 3 that the gradient fermat spiral slot of the present patent design can produce a high quality vortex beam.
In order to verify the high-quality effect of the vortex light beam generated by the method, the central light intensity of the vortex light beam generated based on the spiral hologram is shown in fig. 4 (a), the central light intensity of the vortex light beam generated based on the continuous equal-width fermat spiral seam is shown in fig. 4 (B), the central light intensity of the vortex light beam generated based on the gradual change fermat spiral seam is shown in fig. 4 (C), it can be seen from fig. 4 that the light ring shape of the vortex light beam generated by the method of fig. 4 (a) is petal-shaped and has poor light beam quality, the light intensity quality of the vortex light beam generated by the method of fig. 4 (B) is low, light intensity fluctuation exists on the light ring, when the topological load is small, the light ring of the vortex light beam has certain deformation and is not a standard circular structure, the quality of the vortex light beam generated by the method of fig. 4 (C) is obviously improved, 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 gradual change fermat spiral seam disclosed in the second embodiment of the present invention is introduced, and a method for generating a vortex beam based on a gradual change fermat spiral seam described below and a system for generating a vortex beam based on a gradual change fermat spiral seam described above may be referred to in correspondence.
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 the vortex beams based on the gradual change Fermat spiral seam, and the method comprises the following steps:
designing a rotationally symmetrical overlapped gradient Fermat spiral seam, and generating vortex light beams with specific topological charges on a given observation plane along a propagation direction after plane waves irradiate the gradient Fermat spiral seam;
the gradual change Fermat spiral seam is designed based on a plurality of discrete pinholes which are rotationally symmetrically overlapped and a continuous Fermat spiral seam with the same width.
In one embodiment of the invention, a method of generating a vortex beam of a specific topological charge in a given viewing plane along a propagation direction comprises:
on a given observation plane along the propagation direction, the complex amplitude of the single wavelet generated for the s-th graded fermat spiral seam is expressed as:
wherein λ is the wavelength of plane wave, k is the wave number,
represents the transmittance function of the s-th gradually-changed Fermat spiral seam,
the radial and azimuthal coordinates on the progressive fermat spiral slot plane are indicated, (R, phi) the radial and azimuthal coordinates on the viewing plane, and z the transmission distance.
In one embodiment of the present invention, the transmittance function of the s-th gradual Fermat spiral seam is expressed as:
in the formula, r α Represents the radius size of each point of the gradual Fermat spiral seam from the central point under the azimuth angle of 0-2 pi, wherein alpha represents the azimuth angle, r 0 The initial radius of the gradually changed Fermat spiral seam is represented, the value of l is the value of the spiral number, d represents the width of the gradually changed Fermat spiral seam under different angles alpha, d 0 Is a constant value indicating the length, and A is a constant value indicating the ratio.
In one embodiment of the invention, a method of generating a vortical beam of specific topological charges in a propagation direction at a given viewing plane comprises:
the total complex amplitude field produced by m small waves by rotationally symmetric superposition on a given viewing surface is represented as:
in the formula (I), the compound is shown in the specification,
the complex amplitude of a single wavelet generated by the s-th gradually-changed Fermat spiral seam in a cylindrical polar coordinate system is represented, R and phi respectively represent a radial coordinate and an azimuth coordinate on an observation plane, and z represents a transmission distance.
The method for generating the vortex light beam based on the gradient Fermat spiral seam can generate the high-quality vortex light beam at a specific distance under the irradiation of the plane wave, the light intensity keeps a circular structure and is uniform in light intensity distribution, the method is simple and low in cost, and the method not only can be applied to optical communication, but also is suitable for the micro-nano optical field needing the high-quality vortex light beam.
The method for generating a vortex beam based on the gradual-change fermat spiral seam of the embodiment is implemented based on the system for generating a vortex beam based on the gradual-change fermat spiral seam, and therefore, the specific implementation of the method can be found in the previous embodiment section of the system for generating a vortex beam based on the gradual-change fermat spiral seam, and therefore, the specific implementation can refer to the description of the corresponding partial embodiment and is not further described herein.
In addition, since the method for generating the vortex beam based on the gradual change fermat spiral seam of the embodiment is implemented based on the system for generating the vortex beam based on the gradual change fermat spiral seam, the function of the method corresponds to that of the system, and the description is omitted here.
As will be appreciated by one skilled in the art, 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 should be understood that the above examples are only for clarity of illustration and are not intended to limit the embodiments. Various other modifications and alterations will occur to those skilled in the art upon reading the foregoing description. And are neither required nor exhaustive of all embodiments. And obvious variations or modifications of the invention may be made without departing from the spirit or scope of the invention.
Claims (10)
1. A system for generating a vortex beam based on a gradual fermat spiral seam, comprising:
a plane wave generating module for generating a plane wave;
the mask plate is arranged on a propagation path of the plane wave, the mask plate is provided with a gradient Fermat spiral seam which is rotationally symmetrically superposed, and after the plane wave irradiates the gradient Fermat spiral seam, vortex light beams with specific topological loads are generated on a given observation plane along a propagation direction;
the gradual change Fermat spiral seam is designed based on a plurality of discrete pinholes which are rotationally symmetrically overlapped and a continuous Fermat spiral seam with the same width.
2. The system for generating a vortex beam based on a graded fermat spiral seam of claim 1, wherein: the slit width of the gradual change Fermat spiral seam is gradually increased from inside to outside.
3. The system for generating a vortex beam based on a graded fermat spiral slit of claim 1 or 2, wherein the structure of the graded fermat spiral slit is determined by the number of spirals and their degree of rotation.
4. The system for generating a vortex beam based on a graded fermat spiral slit of claim 2, wherein generating a vortex beam of a specific topological charge on a given observation plane along a propagation direction comprises:
on a given observation plane along the propagation direction, the complex amplitude of the single wavelet generated for the s-th graded fermat spiral seam is expressed as:
wherein λ is the wavelength of plane wave, k is the wave number,
represents the transmittance function of the s-th gradually-changed Fermat spiral seam,
representing the radial and azimuthal coordinates on the plane of the graduated fermat spiral seam,
representing the radial and azimuthal coordinates on the viewing plane and z represents the transmission distance.
5. The method for generating a vortex beam based on a graded fermat spiral slit of claim 4, wherein the transmittance function of the s-th graded fermat spiral slit is expressed as:
in the formula, r α Represents the radius size of each point of the gradual Fermat spiral seam from the central point under the azimuth angle of 0-2 pi, wherein alpha represents the azimuth angle, r 0 Representing the initial radius of the gradual Fermat spiral seam, the value of l is the number of spirals, d is the value at different angles alphaWidth of lower progressive Fermat spiral seam, d 0 Is a constant value representing the length, and A is a constant representing the proportionality.
6. The method of generating a vortex beam based on a graded fermat spiral slit of claim 5, wherein generating a vortex beam of a specific topological charge in a propagation direction at a given viewing plane comprises:
the total complex amplitude field produced by m small waves by rotationally symmetric superposition on a given viewing surface is represented as:
in the formula (I), the compound is shown in the specification,
the complex amplitude of a single wavelet generated by the s-th gradually-changed Fermat spiral seam in the cylindrical polar coordinate system is represented, R and phi respectively represent a radial coordinate and an azimuth coordinate on an observation plane, and z represents a transmission distance.
7. A method for generating a vortex beam based on a gradual-change fermat spiral slit, which is implemented by the system for generating the vortex beam based on the gradual-change fermat spiral slit according to any one of claims 1 to 6, and which comprises:
designing a rotationally symmetrical overlapped gradient Fermat spiral seam, and generating vortex light beams with specific topological charges on a given observation plane along a propagation direction after plane waves irradiate the gradient Fermat spiral seam;
the gradual change Fermat spiral seam is designed based on a plurality of discrete pinholes which are rotationally symmetrically overlapped and a continuous Fermat spiral seam with the same width.
8. The method for generating a vortex beam based on a graded fermat spiral slit of claim 7, wherein the method for generating a vortex beam of a specific topological charge on a given observation plane along a propagation direction comprises:
on a given observation plane along the propagation direction, the complex amplitude of a single wavelet generated for the s-th gradual fermat spiral seam is expressed as:
wherein λ is the wavelength of the plane wave, k is the wave number,
represents the transmittance function of the s-th gradually-changed Fermat spiral seam,
the radial and azimuthal coordinates on the progressive fermat spiral slot plane are indicated, (R, phi) the radial and azimuthal coordinates on the viewing plane, and z the transmission distance.
9. The method for generating a vortex beam based on a graded fermat spiral slit of claim 8, wherein the transmittance function of the s-th graded fermat spiral slit is expressed as:
in the formula, r α Represents the radius size of each point of the gradual Fermat spiral seam from the central point under the azimuth angle of 0-2 pi, wherein alpha represents the azimuth angle, r 0 Representing the initial radius of the gradual change Fermat spiral seam, the value of l is the value of the number of spirals, d represents the width of the gradual change Fermat spiral seam under different angles alpha, d 0 Is a constant value representing the length, and A is a constant representing the proportionality.
10. The method for generating a vortex beam based on a graded fermat spiral slit of claim 9, wherein the method for 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 small waves by rotationally symmetric superposition on a given viewing surface is represented as:
in the formula (I), the compound is shown in the specification,
the complex amplitude of a single wavelet generated by the s-th gradually-changed Fermat spiral seam in a cylindrical polar coordinate system is represented, R and phi respectively represent a radial coordinate and an azimuth coordinate on an observation plane, and z represents a transmission distance.
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| CN116699857A (en) * | 2023-08-04 | 2023-09-05 | 华中科技大学 | Vortex light beam sorting method based on Fermat spiral transformation and optical diffraction device |
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| CN109709682A (en) * | 2019-01-25 | 2019-05-03 | 电子科技大学 | A kind of device generating combined vortex light beam |
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| HAN WANG: "Vortex beam generation with variable topological charge based on a spiral slit" * |
| YUANJIE YANG: "Anomalous Bessel vortex beam: modulating orbital angular momentum with propagation" * |
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| CN116699857A (en) * | 2023-08-04 | 2023-09-05 | 华中科技大学 | Vortex light beam sorting method based on Fermat spiral transformation and optical diffraction device |
| CN116699857B (en) * | 2023-08-04 | 2023-10-24 | 华中科技大学 | Vortex light beam sorting method based on Fermat spiral transformation and optical diffraction device |
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