CN107621701B - Method and system for generating double-index Bessel Gaussian beam - Google Patents
Method and system for generating double-index Bessel Gaussian beam Download PDFInfo
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Abstract
The invention relates to a method and a system for generating a double-index Bessel Gaussian beam, which are designed for realizing superposition of a plurality of different transverse wave vectors and Bessel Gaussian beams with specific amplitudes. The invention firstly introduces a phase factor into a linear polarized Gaussian beam through a vortex phase plate to generate a Gaussian vortex beam; then, the Gaussian vortex beam passes through an amplitude spatial light modulator loaded with at least two annular amplitude holograms, and the light transmittance of the annular amplitude holograms is regulated so as to regulate the amplitude of the Gaussian vortex beam (double-index Bessel Gaussian beam) to generate a double-index Bessel Gaussian beam angular spectrum function; finally, a fourier transform is performed, producing a bi-exponential bessel gaussian beam. The double-index Bessel Gaussian beam superposition method has higher flexibility and simpler operation for generating the double-index Bessel Gaussian beam.
Description
Technical Field
The invention relates to a method and a system for generating a double-index Bessel Gaussian beam.
Background
Since Durnin proposed and experimentally produced a bessel beam, a great deal of work has been done to investigate this particular beam because of its two main properties, namely non-diffracting and self-repairing. These characteristics make Bessel beams of light useful in particle acceleration, medical imaging, material detection, optical micromanipulation, optical trapping, and other fields. Since an ideal Bessel beam has infinite radial direction and carries infinite energy, the ideal Bessel beam cannot be generated physically, so that only approximate Bessel beams can be generated in experiments, the approximate Bessel beams can have the main characteristics of the Bessel beams in quite far propagation distances, and the Bessel Gaussian beam is one of the Bessel beams and is easy to generate in experiments. Methods are also being continuously improved in experiments to improve the quality of the generation of bessel beams.
There are many methods for generating bessel beams, and focusing by using a lens after parallel light passes through a circular ring, so that zero-order bessel beams can be generated on the focal plane of the lens, which is the earliest method. With the progress of technology, a zero-order Bessel beam can be generated by parallel light passing through a prism, and a higher-order Bessel beam can also be generated by Laguerre Gaussian beam passing through the prism. Various Bessel beams may be generated later by combining holograms with spatial light modulators, and resonators, refractive systems, interferometers, diffractive phase elements, etc. may also be used to generate Bessel beams.
The method for realizing Bessel beam superposition is realized mainly by loading holograms by using a spatial light modulator. The single spatial light modulator achieves superposition of Bessel beams by directly converting an incident light field into a light field of multiple Bessel beam superposition by loading a circular phase hologram with one spatial light modulator (Vasiloeuu R, dudley A, khilo N, et al, generating superpositions of higher-order Bessel beams [ J ]. Optics express,2009,17 (26): 23389-23395.).
The dual spatial light modulator is used for realizing superposition of vector Bessel light beams, namely, by utilizing the property that the spatial light modulator only modulates light beams in the horizontal direction, firstly, a horizontal incident light field is made to enter a spatial light modulator loaded with a spiral-axis prism phase hologram to generate the Bessel light beams, then the light beams are divided into horizontal directions and vertical directions through a half-wave plate, then, the horizontal components of the vector Bessel light beams are modulated through a second spatial modulator, and finally, the two components of the vector Bessel light beams are superposed (FuS, zhang S, gao C.Bessel beams with spatial oscillating polarization [ J ]. Scientific Reports,2016,6).
The single spatial light modulator method can only realize superposition of Bessel beams with the same radial wave vector, and cannot control the amplitude of the Bessel beams.
Besides the two defects, the vector Bessel superposition method can only realize superposition of two Bessel beams, a plurality of Bessel beams cannot be realized, and the energy consumption utilization rate of light passing through the two spatial light modulators is greatly reduced.
In view of the above-mentioned drawbacks, the present inventors have actively studied and innovated to create a method and system for generating a bi-exponential bessel gaussian beam, which is more industrially valuable.
Disclosure of Invention
In order to solve the technical problems, the invention aims to provide a method and a system for generating a double-index Bessel Gaussian beam, which are used for realizing superposition of a plurality of different transverse wave vector Bessel Gaussian beams and performing amplitude control on the plurality of Bessel Gaussian beams.
To achieve the above object, the present invention provides a method for generating a dual-index bessel gaussian beam, comprising:
the method comprises the steps that firstly, a linear polarized Gaussian beam passes through a vortex phase plate, and a phase factor is introduced into the linear polarized Gaussian beam to generate a Gaussian vortex beam; then, the Gaussian vortex beam passes through an amplitude spatial light modulator loaded with at least two annular amplitude holograms, and the amplitude of the Gaussian vortex beam is regulated and controlled by regulating and controlling the light transmittance of the annular amplitude holograms, so that an angular spectrum function of the double-index Bessel Gaussian beam is generated; and finally, carrying out Fourier transformation on the Gaussian vortex beam subjected to amplitude regulation to generate a double-index Bessel Gaussian beam.
Further, before passing through the vortex phase plate, the Gaussian beam firstly passes through an attenuation sheet to adjust the light intensity of the Gaussian beam of the emergent fundamental mode, and then passes through a beam expander to expand the light spot size of the Gaussian beam and perform collimation treatment on the Gaussian beam.
Further, the double-exponential Bessel Gaussian beam is subjected to Fourier transform by a Fourier lens, and the distance between the Fourier lens and the amplitude spatial light modulator is f 0, wherein f0 Is the focal length of the fourier transform lens.
Further, the light intensity of the double-exponential bessel gaussian beam recorded at the fourier plane is also included.
Further, the analytical expression of the double-index Bessel Gaussian beam on the Fourier plane is as follows:
wherein r, theta is the radial and angular coordinates, k, on the light source face 0 =2pi/λ is wavenumber, λ is wavelength, ω g Representing the width of the gaussian envelope,angular aperture of Bessel beam, l is topological charge, p is radial index, J l Is a first class Bessel function of the first order;
coefficient C n The equation satisfied is:
is a Laguerre polynomial with angle indexes p and l respectively;
angular apertureThe equation is satisfied:
ω 0 a constant associated with the resulting bi-exponential bessel gaussian beam size; η (eta) n Is the root of the following set of equations:
equation set (4) has p+1 roots, one for each rootRepresenting the location of the radial intensity maxima of the ragel gaussian beam. Zeta type toy 1l Is the following equation
J l-1 (ξ)-J l+1 (ξ)＝0 (5)
A first root greater than zero;
the angular spectrum of a double-exponential bessel gaussian beam is the fourier transform of the double-exponential bessel gaussian beam:
wherein ,is the radial and angular coordinates in the polar coordinate system on the angular spectrum plane, f is a constant greater than zero
Bringing equation (1) into (2) yields the angular spectrum analytical expression for the double-exponential bessel gaussian beam:
wherein ω q ＝2f/k 0 ω g ，I l Is a first class of modified Bessel functions.
From equation (7), it can be seen that the double-exponential Bessel beam removes a common factorBesides, the amplitude expression and the phase of the variable can be separated in a distributed manner, namely, the amplitude and the phase of the variable can be independently regulated and controlled to obtain an angular spectrum distribution function corresponding to the formula (7); the amplitude distribution in equation (7) is:
the phase distribution is
Fourier transform lens after distance from lens f 0 At the position of the first part,the diagonal spectral function being subjected to a Fourier transform, i.e
Substituting the formula (7) into the formula (10) and integrating to obtain the following formula:
focal length f of lens 0 Equal to a constant f in the angular spectrum function, at a Fourier lens distance f 0 Where a bi-exponential bessel beam is generated.
To achieve the above object, the present invention provides a system for generating a dual-index bessel gaussian beam, comprising:
the device comprises a vortex phase plate, an amplitude spatial light modulator and a Fourier lens, wherein the vortex phase plate, the amplitude spatial light modulator and the Fourier lens are sequentially arranged along the transmission direction of polarized Gaussian beams, the amplitude spatial light modulator is used for loading at least two annular amplitude full-system graphs, and the Fourier lens is used for carrying out Fourier transform on double-index Bessel Gaussian beams output by the amplitude spatial light modulator.
Further, the vortex phase plate is a transparent plate with a fixed refractive index, an incident surface of the vortex phase plate is of a plane structure, an emergent surface of the vortex phase plate is of an irregular vortex surface structure with a rotation step, and the thickness of the vortex surface is increased along with the increase of the azimuth angle.
Further, the Fourier lens is located at a distance f from the amplitude spatial light modulator 0, wherein f0 Is the focal length of the fourier transform lens.
Further, a beam analyzer is provided at the fourier plane for recording the light intensity of the double-exponential bessel gaussian beam.
Further, the system also comprises a computer respectively connected with the amplitude spatial light modulator and the beam analyzer.
By means of the scheme, the method and the system for generating the double-index Bessel Gaussian beam have the following advantages:
gaussian beam of the inventionFirst, a gaussian vortex beam is generated through a vortex phase plate, and the gaussian vortex beam is passed through a hologram loaded with a plurality of annular amplitudes, generating a double-exponential bessel gaussian beam. The phase part of the angular spectrum function is adjusted through the vortex phase plate, and the amplitude function is regulated and controlled through adjusting the light transmittance of the amplitude hologram. The generated Bessel Gaussian superimposed beams are the superimposed Bessel Gaussian beams with different radial wave numbers, and the superimposed Bessel Gaussian beams can be superimposed simultaneously. And can also pass through coefficient C n Each control the amplitude of the superimposed light beam, and the operation is simple, and the energy utilization rate of the light source is high.
The foregoing description is only an overview of the present invention, and is intended to provide a better understanding of the present invention, as it is embodied in the following description, with reference to the preferred embodiments of the present invention and the accompanying drawings.
Drawings
FIG. 1 is a schematic diagram of a system for producing a dual-index Bessel Gaussian beam according to the invention; 1, a light source; 2. an attenuation sheet; 3. a beam expander; 4. a vortex phase plate; 5. a transmissive spatial light modulator; 6. a fourier lens; 7. a beam analyzer; 8 and 9, a computer;
FIG. 2 is a theoretical calculation of example 1 of the method of the present invention for producing a double-exponential Bessel Gaussian beam; (a) an angular spectrum of l=2, p=1; (b) an angular spectrum of l=1, p=1; (c) an angular spectrum of l=2, p=2; (d) a superimposed light field of l=2, p=1; (e) a superimposed light field of l=1, p=1; (f) a superimposed light field of l=2, p=2;
FIG. 3 is a graph of an experimental angular spectrum fit of example 1 of the method of the present invention for producing a double exponential Bessel Gaussian beam; (a) an angular spectrum of l=2, p=1; (b) an angular spectrum of l=1, p=1; (c) an angular spectrum of l=2, p=2; (d) an angular spectrum fit of l=2, p=1; (e) an angular spectrum fit of l=1, p=1; (f) an angular spectrum fit of l=2, p=2;
FIG. 4 is a superimposed light field imaging intensity fitting plot of example 1 of the method of the present invention for producing a double exponential Bessel Gaussian beam; (a) superimposed light field intensity of l=2, p=1; (b) superimposed light field intensity of l=1, p=1; (c) a superimposed light field intensity of l=2, p=2; (d) a superimposed light field intensity fit of l=2, p=1; (e) a superimposed light field intensity fit of l=1, p=1; (f) l=2, p=2.
Detailed Description
The following describes in further detail the embodiments of the present invention with reference to the drawings and examples. The following examples are illustrative of the invention and are not intended to limit the scope of the invention.
Example 1
As shown in fig. 1, the method of generating a double-exponential bessel gaussian beam according to the present embodiment is implemented by the following means,
light source: linearly polarized Gaussian beam with wavelength of 400nm-800nm
Vortex phase plate: the transparent plate with a fixed refractive index is provided with a regular plane structure at one end and an irregular vortex surface structure similar to a rotation step at the other end, and the thickness of the vortex surface is increased along with the increase of azimuth angle; the light intensity of the transmitted light beam is not changed basically, and the light intensity is mainly used for introducing a phase factor exp (il phi), wherein l is the topological charge number, phi is the azimuth angle with the center point of the phase plate as the origin, and the light intensity is a phase-only modulation tool;
transmissive amplitude spatial light modulator: for controlling the amplitude distribution and the magnitude of the angular spectrum function of the double-exponential Bessel beam, the light transmitted from the transmission type amplitude spatial light modulator is the angular spectrum function of the angular spectrum of the double-exponential Bessel Gaussian beam to be generated.
Fourier lens: after the transmissive spatial light modulator, the spatial light modulator is positioned at the front focal plane of the fourier lens. For fourier transforming the light beam passing through the spatial light modulator;
a beam analyzer, which is placed at the Fourier plane to shoot light intensity information;
and (3) a computer: and the device is respectively connected with the spatial light modulator and the light beam analysis instrument, controls the amplitude information of the spatial light modulator, and records and stores the light intensity of the light field overlapped by the Bessel Gaussian light beam obtained by shooting.
The method for generating the double-index Bessel Gaussian beam in the embodiment specifically comprises the following steps: the method comprises the steps that firstly, a linear polarized Gaussian beam passes through a vortex phase plate, and a phase factor is introduced into the linear polarized Gaussian beam to generate a Gaussian vortex beam; then, the Gaussian vortex beam passes through an amplitude spatial light modulator loaded with at least two annular amplitude holograms, and the amplitude of the Gaussian vortex beam is regulated and controlled by regulating and controlling the light transmittance of the annular amplitude holograms, so that a double-index Bessel Gaussian beam angular spectrum function is generated; finally, fourier transform is carried out to generate a double-index Bessel Gaussian beam
In this embodiment, the fourier transform is performed on the bi-exponential bessel gaussian beam by a fourier lens, where the distance from the fourier lens to the amplitude spatial light modulator is f 0, wherein f0 Is the focal length of the fourier transform lens.
In this embodiment, the generated bessel gaussian superimposed beam is a superposition of bessel gaussian beams having different radial wavenumbers, and the superposition of a plurality of bessel gaussian beams can be simultaneously realized. And can also pass through coefficient C n Each control the amplitude of the superimposed light beam, and the operation is simple, and the energy utilization rate of the light source is high.
Example 2
In the method for generating the double-index Bessel Gaussian beam in the embodiment, on the basis of embodiment 1, the Gaussian beam firstly passes through an attenuation sheet before passing through a vortex phase plate, the light intensity of the Gaussian beam in an emergent fundamental mode is adjusted, then the light spot size of the Gaussian beam is expanded through a beam expander, and the Gaussian beam is collimated.
In this embodiment, the light intensity of the double-exponential bessel gaussian beam recorded at the fourier plane is also included.
Example 3
As shown in fig. 1, the system for generating a dual-index bessel gaussian beam according to the present embodiment includes:
light source: a linear polarized Gaussian beam with the wavelength of 400nm-800nm;
the device comprises a vortex phase plate, a transmission type amplitude spatial light modulator and a Fourier lens which are sequentially arranged along the transmission direction of the polarized Gaussian beam.
Vortex phase plate: the transparent plate with a fixed refractive index is provided with a regular plane structure at one end and an irregular vortex surface structure similar to a rotation step at the other end, and the thickness of the vortex surface is increased along with the increase of azimuth angle; the light intensity of the transmitted light beam is not changed basically, and the light intensity is mainly used for introducing a phase factor exp (il phi), wherein l is the topological charge number, phi is the azimuth angle with the center point of the phase plate as the origin, and the light intensity is a phase-only modulation tool;
transmissive amplitude spatial light modulator: for controlling the amplitude distribution and the magnitude of the angular spectrum function of the double-exponential Bessel beam, the light transmitted from the transmission type amplitude spatial light modulator is the angular spectrum function of the angular spectrum of the double-exponential Bessel Gaussian beam to be generated.
Fourier lens: after the transmissive spatial light modulator, the spatial light modulator is positioned at the front focal plane of the fourier lens. For fourier transforming the light beam passing through the spatial light modulator.
And a beam analyzer, which is arranged at the Fourier plane and shoots the light intensity information.
Further comprising computers 8, 9: the computer 9 is connected with the air-transmission type amplitude spatial light modulator and controls the amplitude information of the spatial light modulator. The computer 8 is connected with a beam analysis instrument, and records and stores the light intensity of the light field overlapped by the Bessel Gaussian beam obtained by shooting.
As shown in fig. 2 to 4, a vortex beam is generated along a polarized gaussian beam by a vortex phase plate 4 having a spiral spatial structure that can generate different topological charges (i is an integer). The vortex beam is transmitted to a transmissive spatial light modulator 5 (model HDSLM85T, pixel size 1920×1080, pixel size 8.5 μm), the loading of information (angular spectrum of the light field to be generated) on the spatial light modulator is controlled by a computer 9, the outgoing light after the information loading is further passed through a fourier lens 6, the focal length of the fourier lens is 400mm, and the distance from the spatial light modulator is equal to the focal length.
In this embodiment, the vortex phase plate is used to adjust the phase part of the angular spectrum function, and the amplitude spatial light modulator is used to adjust and control the amplitude function, so as to realize the superposition of multiple different transverse wave vector Bessel Gaussian beams, and the amplitudes of the multiple Bessel Gaussian beams can be controlled, so that the double-index Bessel Gaussian beams with specific parameters are realized, the superposition flexibility is higher, and the operation is simpler.
Example 4
The system for generating a dual-index bessel gaussian beam according to this embodiment further includes, on the basis of embodiment 3, an attenuator 2 and a beam expander 3 disposed in front of the vortex phase plate in the transmission direction of the polarized gaussian beam. Attenuation sheet: for adjusting the intensity of the outgoing fundamental mode gaussian beam. Beam expander: the spot size of the gaussian beam is expanded and collimated.
The working principle of the method and the system for generating the double-index Bessel Gaussian beam is as follows;
(1) Bessel Gaussian superimposed light field description:
the analytical expression of the double-index Bessel Gaussian beam at the source field is as follows:
wherein r, theta is the radial and angular coordinates, k, on the light source face 0 =2pi/λ is wavenumber, λ is wavelength, ω g Representing the width of the gaussian envelope,angular aperture of Bessel beam, l is angular index (topological charge), p is radial index, J l Is a first class Bessel function of order l. Definition coefficient C n The equation is satisfied:
is a Laguerre polynomial with angle indexes p and l respectively; angle aperture->The equation is satisfied:
ω 0 a constant is associated with the resulting bi-exponential bessel gaussian beam size. η (eta) n Is the root of the following set of equations:
equation set (4) has p+1 roots, one for each rootRepresenting the location of the radial intensity maxima of the ragel gaussian beam. Zeta type toy 1l Is the following equation
J l-1 (ξ)-J l+1 (ξ)＝0 (5)
A first root greater than zero. When l=1, ζ 11 =1.84; when l=2, ζ 12 ＝3.05。
(2) Angular spectrum of double-index Bessel Gaussian beam
The angular spectrum of a double-exponential bessel gaussian beam is the fourier transform of the double-exponential bessel gaussian beam:
wherein Is the radial and angular coordinates in the polar coordinate system on the angular spectrum plane, f is a constant greater than zero, and brings equation (1) into (2), resulting in its analytical expression:
wherein ω q ＝2f/k 0 ω g ，I l Is a first class of modified Bessel functions.
From equation (7), it can be seen that the double-exponential Bessel beam removes a common factorBesides, the amplitude expression and the phase distribution can be separated into variables, namely, the amplitude and the phase of the variable can be independently regulated and controlled to obtain the angular spectrum distribution function corresponding to the formula (7), and the distribution property of the angular spectrum function can be not considered because the common factors are not changed. The amplitude distribution in equation (7) is:
the phase distribution is
In the proposed method for generating a bi-exponential bessel gaussian beam (see fig. 1), the phase part of the angular spectrum function is adjusted by a vortex phase plate [ formula (9) ], and the amplitude function is adjusted by an amplitude spatial light modulator [ formula (8) ], which is also the core method for generating the beam.
(3) Obtaining double-index Bessel Gaussian beam through Fourier transformation
The angular spectrum function corresponding to the double-index Bessel Gaussian beam is obtained through regulation and control of the vortex phase plate and the amplitude type spatial light modulator, and then the angular spectrum function is separated from the spatial light modulator f 0 A Fourier transform lens (focal length f of lens) 0 ) Thus, after distance from the lens f 0 Where equivalent to a Fourier transform of the diagonal spectral function, i.e
Substituting the formula (7) into the formula (10) and integrating to obtain the following formula:
comparing the formula (11) with the formula (1), knowing the focal length f of the lens 0 Equal to the constant f in the angular spectrum function, equation (11) degenerates to equation (1), i.e., at the Fourier lens distance f 0 Where a bi-exponential bessel beam is generated.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, and it should be noted that it is possible for those skilled in the art to make several improvements and modifications without departing from the technical principle of the present invention, and these improvements and modifications should also be regarded as the protection scope of the present invention.
Claims (8)
1. A method of producing a bi-exponential bessel gaussian beam, comprising:
the method comprises the steps that firstly, a linear polarized Gaussian beam passes through a vortex phase plate, and a phase factor is introduced into the linear polarized Gaussian beam to generate a Gaussian vortex beam; then, the Gaussian vortex beam passes through an amplitude spatial light modulator loaded with at least two annular amplitude holograms, and the amplitude of the Gaussian vortex beam is regulated and controlled by regulating and controlling the light transmittance of the annular amplitude holograms, so that an angular spectrum function of the double-index Bessel Gaussian beam is generated; and finally, carrying out Fourier transformation on the Gaussian vortex beam subjected to amplitude regulation to generate a double-index Bessel Gaussian beam.
2. The method of generating a bi-exponential bessel gaussian beam according to claim 1, wherein said gaussian beam is first passed through an attenuator before passing through a vortex phase plate, the intensity of the outgoing fundamental mode gaussian beam is adjusted, and then the spot size of said gaussian beam is expanded by a beam expander and said gaussian beam is collimated.
3. The method of generating a dual-exponential bessel gaussian beam according to claim 2, wherein said dual-exponential bessel gaussian beam is fourier transformed by a fourier lens, said fourier transform being transmittedThe mirror is at a distance f from the amplitude spatial light modulator 0, wherein f0 Is the focal length of the fourier transform lens.
4. The method of generating a bi-exponential bessel gaussian beam according to claim 1, further comprising recording the intensity of the bi-exponential bessel gaussian beam at the fourier plane.
5. The method of generating a dual-exponential bessel gaussian beam according to claim 1, wherein,
the analytical expression of the double-index Bessel Gaussian beam on the Fourier plane is as follows:
wherein r, theta is the radial and angular coordinates, k, on the light source face 0 =2pi/λ is wavenumber, λ is wavelength, ω g Representing the width of the gaussian envelope,angular aperture of Bessel beam, l is topological charge, p is radial index, J l Is a first class Bessel function of the first order;
coefficient C n The equation satisfied is:
is a Laguerre polynomial with angle indexes p and l respectively;
angular apertureThe equation is satisfied:
ω 0 a constant associated with the resulting bi-exponential bessel gaussian beam size; η (eta) n Is the root of the following set of equations:
equation set (4) has p+1 roots, one for each root(n=1,..p+1) represents the position of the maximum radial intensity value of the ragel gaussian beam, ζ 1l Is the following equation
J l-1 (ξ)-J l+1 (ξ)＝0 (5)
A first root greater than zero;
the angular spectrum of a double-exponential bessel gaussian beam is the fourier transform of the double-exponential bessel gaussian beam:
wherein ,is the radial and angular coordinates in the polar coordinate system on the angular spectrum plane, f is a constant greater than zero, and brings equation (1) into (2) to obtain the angular spectrum analysis expression of the double-index Bessel Gaussian beam:
wherein ω q ＝2f/k 0 ω g ，I l Is a first-order modified Bessel function;
from equation (7), it can be seen that the double-exponential Bessel beam removes a common factorBesides, the amplitude expression and the phase of the variable can be separated in a distributed manner, namely, the amplitude and the phase of the variable can be independently regulated and controlled to obtain an angular spectrum distribution function corresponding to the formula (7); the amplitude distribution in equation (7) is:
the phase distribution is
Fourier transform lens after distance from lens f 0 Where the diagonal spectral function is Fourier transformed, i.e
Substituting the formula (7) into the formula (10) and integrating to obtain the following formula:
focal length f of lens 0 Equal to a constant f in the angular spectrum function, at a Fourier lens distance f 0 Where a bi-exponential bessel beam is generated.
6. A system for producing a bi-exponential bessel gaussian beam, comprising:
the Fourier lens is used for carrying out Fourier transformation on the double-index Bessel Gaussian beams output by the amplitude spatial light modulator;
the vortex phase plate is a transparent plate with a fixed refractive index, an incident surface of the vortex phase plate is of a planar structure, an emergent surface of the vortex phase plate is of an irregular vortex surface structure with a rotating step, and the thickness of the vortex surface is increased along with the increase of an azimuth angle;
the distance between the Fourier lens and the amplitude spatial light modulator is f 0, wherein f0 Is the focal length of the fourier transform lens.
7. The system for generating a bi-exponential bessel gaussian beam according to claim 6, further comprising a beam analyzer disposed at the fourier plane for recording the intensity of the bi-exponential bessel gaussian beam.
8. The system for generating a dual-exponential bessel gaussian beam according to claim 6, further comprising a computer connected to said amplitude spatial light modulator and said beam analyzer, respectively.
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Citations (14)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP0026959A1 (en) * | 1979-10-08 | 1981-04-15 | Leuven Research & Development V.Z.W. | System for generating digital signals corresponding to selectable functions |
| JPH10153750A (en) * | 1996-11-25 | 1998-06-09 | Sumitomo Electric Ind Ltd | Laser beam shaping optical parts |
| CN101251655A (en) * | 2008-03-21 | 2008-08-27 | 北京理工大学 | Apparatus for implementing orbit angular momentum state super position and modulation |
| CN102043177A (en) * | 2009-10-13 | 2011-05-04 | 鲁东大学 | Radial logarithm spiral phase plate (SPP) |
| CN102547074A (en) * | 2012-01-04 | 2012-07-04 | 西安电子科技大学 | Surfacelet domain BKF model Bayes video denoising method |
| CN102981277A (en) * | 2012-12-12 | 2013-03-20 | 苏州大学 | System and method for generating radial Bessel-Gaussian beam |
| WO2013056211A2 (en) * | 2011-10-13 | 2013-04-18 | H. Lee Moffitt Cancer Center & Research Institute, Inc. | Telomerase reverse transcriptase deficience as diagnostic marker of myelodysplastic syndrome |
| CN203101733U (en) * | 2012-12-12 | 2013-07-31 | 苏州大学 | System for generating radial Bessel-Gauss beams |
| CN103777248A (en) * | 2014-02-08 | 2014-05-07 | 中国科学院电子学研究所 | TEM one-dimensional forward modeling method applicable to irregular transmitting loop |
| CN103792663A (en) * | 2014-01-17 | 2014-05-14 | 北京空间机电研究所 | Optical system generating screw type Bessel beams and generating method |
| EP2949117A1 (en) * | 2013-01-25 | 2015-12-02 | The Trustees Of Columbia University In The City Of New York | Depth of field 3d imaging slm microscope |
| CN106200020A (en) * | 2016-07-07 | 2016-12-07 | 苏州大学 | The control method of luminous power suffered by a kind of radial anisotropic nano wire |
| CN107065046A (en) * | 2017-06-28 | 2017-08-18 | 河南科技大学 | A kind of Bessel-Gaussian beam mask plate based on Mittag Leffler functions |
| CN207457617U (en) * | 2017-09-07 | 2018-06-05 | 苏州大学 | The system for generating double index Bessel-Gaussian beams |
Family Cites Families (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7418016B2 (en) * | 2003-02-13 | 2008-08-26 | Avago Technologies Ecbu Ip (Singapore) Pte. Ltd. | Method and apparatus for modifying the spread of a laser beam |
| FR2974638B1 (en) * | 2011-04-26 | 2013-11-29 | Meggitt France | LIGHT ENERGY TRANSMISSION DEVICE AND TRANSMISSION METHOD THEREOF |
| US10795144B2 (en) * | 2014-12-06 | 2020-10-06 | Howard Hughes Medical Institute | Microscopy with structured plane illumination and point accumulation for imaging and nanoscale topography |
-
2017
- 2017-09-07 CN CN201710802047.3A patent/CN107621701B/en active Active
Patent Citations (14)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP0026959A1 (en) * | 1979-10-08 | 1981-04-15 | Leuven Research & Development V.Z.W. | System for generating digital signals corresponding to selectable functions |
| JPH10153750A (en) * | 1996-11-25 | 1998-06-09 | Sumitomo Electric Ind Ltd | Laser beam shaping optical parts |
| CN101251655A (en) * | 2008-03-21 | 2008-08-27 | 北京理工大学 | Apparatus for implementing orbit angular momentum state super position and modulation |
| CN102043177A (en) * | 2009-10-13 | 2011-05-04 | 鲁东大学 | Radial logarithm spiral phase plate (SPP) |
| WO2013056211A2 (en) * | 2011-10-13 | 2013-04-18 | H. Lee Moffitt Cancer Center & Research Institute, Inc. | Telomerase reverse transcriptase deficience as diagnostic marker of myelodysplastic syndrome |
| CN102547074A (en) * | 2012-01-04 | 2012-07-04 | 西安电子科技大学 | Surfacelet domain BKF model Bayes video denoising method |
| CN102981277A (en) * | 2012-12-12 | 2013-03-20 | 苏州大学 | System and method for generating radial Bessel-Gaussian beam |
| CN203101733U (en) * | 2012-12-12 | 2013-07-31 | 苏州大学 | System for generating radial Bessel-Gauss beams |
| EP2949117A1 (en) * | 2013-01-25 | 2015-12-02 | The Trustees Of Columbia University In The City Of New York | Depth of field 3d imaging slm microscope |
| CN103792663A (en) * | 2014-01-17 | 2014-05-14 | 北京空间机电研究所 | Optical system generating screw type Bessel beams and generating method |
| CN103777248A (en) * | 2014-02-08 | 2014-05-07 | 中国科学院电子学研究所 | TEM one-dimensional forward modeling method applicable to irregular transmitting loop |
| CN106200020A (en) * | 2016-07-07 | 2016-12-07 | 苏州大学 | The control method of luminous power suffered by a kind of radial anisotropic nano wire |
| CN107065046A (en) * | 2017-06-28 | 2017-08-18 | 河南科技大学 | A kind of Bessel-Gaussian beam mask plate based on Mittag Leffler functions |
| CN207457617U (en) * | 2017-09-07 | 2018-06-05 | 苏州大学 | The system for generating double index Bessel-Gaussian beams |
Non-Patent Citations (1)
| Title |
|---|
| Pillay, S等.Analysis of the propagation characteristics of circular step-index fibre with new sheath helix boundary condition.JOURNAL OF ELECTROMAGNETIC WAVES AND APPLICATIONS.2014, 第28卷 ( 第4期 ),第420-429页. * |
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