CN105445943B - A kind of generation device and production method of fractional order perfection vortex beams - Google Patents
A kind of generation device and production method of fractional order perfection vortex beams Download PDFInfo
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Abstract
A kind of generation device and production method of fractional order perfection vortex beams, described device include a continuous-wave laser；It sends the direction of advance of light beam and is equipped with speculum, and the light beam direction of advance reflected through speculum is equipped with pinhole filter, convex lens I, the polarizer and beam-dividing cube；Reflected light direction of advance after beam-dividing cube is equipped with reflective spatial light modulator, and the light beam after its reflection passes through is equipped with analyzer, aperture, convex lens II and CCD camera through beam-dividing cube, its direction of advance；The method is, using computer generation containing axicon lens transmittance function and the plot of light intensity of fractional order vortex beams and plane wave interference, to write reflective spatial light modulator；Continuous-wave laser power supply is opened, light is reflected in the device, and after collimation, diffraction reconstruction etc., generates fractional order perfection vortex beams；The present invention can realize parameter can the fractional order perfection vortex beams that freely regulate and control of real-time online, can be widely applied to the fields such as the manipulation of particulate light, optic test.
Description
Technical Field
The invention relates to the field of particle light manipulation and optical testing, in particular to a device and a method for generating a fractional order perfect vortex light beam.
Background
Vortex beams have wide application in optically trapping, manipulating small particles, and the like. Becomes a very important research hotspot in the field of information optics in recent years. In 2004, the theoretical basis of fractional order optical vortices is comprehensively set forth by an M.V. Berry system for the first time [ J Opt a-Pure Appl Op, 2004, 62: 259 ]; subsequently, fractional order vortex beams were experimentally validated [ New J Phys, 2004, 61: 71 ]. Fractional order vortex beams, which can carry more information and provide finer particle manipulation, are a hot topic of competitive research by many researchers in the field of vortex optics.
At present, a plurality of methods for generating vortex beams mainly include a mode conversion method, a spiral phase plate method, a computer generated hologram method based on a spatial light modulator and the like. The bright ring radius of the vortex light beam generated by the methods is increased along with the increase of the topological load, and the characteristic makes the vortex light beam difficult to be coupled into the same optical fiber on a large scale. In 2013, Andrey s. Ostrovsky et al proposed the concept of a perfect vortex whose bright ring radius was independent of the topological charge value [ opt. lett. 38, 5342013 ], but this method produced additional stray light rings with perfect vortex beams. In 2015, Pravin value et al obtained an integer order perfect vortex without additional halo [ opt. lett., 40, 5972015 ] by fourier transforming a bessel-gaussian beam. Recently, the invention 'two-dimensional code phase grating for generating perfect vortex array' (publication No. 104808272a, published as 2015.07.29) describes a two-dimensional code phase grating for generating perfect vortex, and a plurality of perfect vortex arrays carrying different topological loads can be simultaneously generated on a fourier transform surface of the two-dimensional code phase grating through modulation of the two-dimensional code phase grating. However, the vortex beams generated by all the schemes are integer-order perfect vortices, and how to generate fractional-order perfect vortex beams is an urgent problem in the field.
Disclosure of Invention
The invention aims to solve the technical problems and provides a device and a method for generating a fractional order perfect vortex light beam, which can realize the fractional order perfect vortex light beam with real-time online free regulation and control of parameters.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a fractional order perfect vortex beam generating device comprises a continuous wave laser; the continuous wave laser is provided with a reflector in the advancing direction of a light beam, and the light beam after being reflected by the reflector is sequentially provided with a pinhole filter, a convex lens I, a polarizer and a beam splitting cube in the advancing direction; the light beam after passing through the beam splitting cube is divided into two beams, wherein one beam is reflected light, and the other beam is transmitted light; a reflective spatial light modulator is arranged in the forward direction of reflected light, and after light beams generated after being reflected by the reflective spatial light modulator pass through the beam splitting cube, an analyzer, a small-hole diaphragm, a convex lens II and a CCD camera are sequentially arranged in the forward direction of the reflective spatial light modulator;
the reflective spatial light modulator and the CCD camera are respectively connected with a computer; the distance between the pinhole filter and the convex lens I is the focal length of the convex lens I; the reflective spatial light modulator is arranged on the front focal plane of the convex lens II; the CCD camera is arranged on the back focal plane of the convex lens II.
The method for generating the fractional order perfect vortex beam by using the fractional order perfect vortex beam generating device comprises the following steps of:
generating a light intensity graph containing a cone lens transmittance function and interference of fractional order vortex light beams and plane waves by using a computer; the specific process is as follows:
the electric field of the plane wave is represented as:
wherein E is0The intensity of the amplitude is represented by,krepresents wave number, z represents propagation distance;
the electric field of a vortex beam perpendicularly incident on the axicon lens is expressed as:
wherein,is a constant of the amplitude of the wave,is the radius of the beam waist,mtaking a fraction for the topological charge number;jis an imaginary number unit；
The complex amplitude transmittance function of the axicon is:
in the formula,nis the refractive index of the material of the axicon,athe cone angle of the conical lens is the included angle between the conical surface of the conical lens and the bottom plane;kin terms of the wave number, the number of waves,Ris the cone lens pupil radius;
after passing through the cone lens, the vortex light beam interferes with the plane wave, and the complex amplitude distribution is as follows:
；
combining with the computer holographic technique, the complex amplitude E is calculated by a computer1Writing the light intensity pattern into the reflective spatial light modulator;
turning on a power supply of the continuous wave laser, reflecting a light beam emitted by the continuous wave laser by a reflector, entering a pinhole filter, collimating by a convex lens I, converting the collimated light beam into linearly polarized light by a polarizer, and irradiating the linearly polarized light on a beam splitting cube; the light beam after passing through the beam splitting cube is split into two beams, one beam is reflected light, and the other beam is transmitted light; the reflected light beam irradiates on the reflective spatial light modulator;
step four, the light beam irradiated on the reflective spatial light modulator is used for diffracting and reproducing the fractional-order Bessel-Gaussian light beam; the Bessel-Gaussian beam reproduced by diffraction passes through a beam splitting cube, an analyzer and a small-hole diaphragm and then irradiates on a convex lens II to perform Fourier transform to generate a fractional perfect vortex beam;
fifthly, after the fractional order perfect vortex light beam is imaged in a CCD camera, the image enters a computer for subsequent analysis;
step six,According to the analysis result of the computer, the radius of the bright ring of the generated perfect vortex light beam is not changed along with the change of the fractional order topological charge value m; by adjusting the refractive index of the material of the axicon lens in the first stepnOr angle of taperaThe radius of the bright ring of the perfect vortex beam of the fractional order can be adjusted.
Has the advantages that: compared with the prior art, the device and the method for generating the fractional order perfect vortex light beam can realize the fractional order perfect vortex light beam with real-time online free regulation and control of parameters; the device has the advantages of simple principle, low cost, real-time online adjustment of parameters and easy operation; can be widely applied to the fields of particle light manipulation, optical test and the like.
Drawings
FIG. 1 is an apparatus schematic of the fractional order perfect vortex beam generating apparatus of the present invention; the labels in the figure are: 100. the device comprises a laser 110, a reflector 120, a pinhole filter 130, convex lenses I and 131, convex lenses II and 141, a polarizer 142, an analyzer 150, a beam splitting cube 200, a reflective spatial light modulator 210, a pinhole diaphragm 300, a CCD camera 400 and a computer;
FIG. 2 is a set of fractional order perfect vortex beam intensity plots recorded by a computer.
Detailed Description
As shown in the figure, a fractional order perfect vortex beam generating device comprises a continuous wave laser 100; the continuous wave laser 100 is provided with a reflector 110 in the forward direction of a light beam, and the forward direction of the light beam reflected by the reflector 110 is sequentially provided with a pinhole filter 120, a convex lens I130, a polarizer 141 and a beam splitting cube 150; the light beam passing through the beam splitting cube 150 is split into two beams, wherein one beam is reflected light and the other beam is transmitted light; the reflecting spatial light modulator 200 is arranged in the advancing direction of the reflected light, and the analyzer 142, the small-hole diaphragm 210, the convex lens II131 and the CCD camera 300 are sequentially arranged in the advancing direction of the light beam generated after the light beam is reflected by the reflecting spatial light modulator 200 after passing through the beam splitting cube 150;
the reflective spatial light modulator 200 and the CCD camera 300 are respectively connected with a computer 400; the distance between the pinhole filter 120 and the convex lens I130 is the focal length of the convex lens I130; the reflective spatial light modulator 200 is arranged on the front focal plane of the convex lens II 131; the CCD camera 300 is arranged on the back focal plane of the convex lens II 131.
The method for generating the fractional order perfect vortex beam by using the fractional order perfect vortex beam generating device comprises the following steps of:
step one, generating a light intensity map containing a cone lens transmittance function and interference of fractional order vortex light beams and plane waves by using a computer 400; the specific process is as follows:
the electric field of the plane wave is represented as:
wherein E is0The intensity of the amplitude is represented by,krepresents wave number, z represents propagation distance;
the electric field of a vortex beam perpendicularly incident on the axicon lens is expressed as:
wherein,is a constant of the amplitude of the wave,is the radius of the beam waist,mtaking a fraction for the topological charge number;jis an imaginary unit;
the complex amplitude transmittance function of the axicon is:
in the formula,nis the refractive index of the material of the axicon,athe cone angle of the conical lens is the included angle between the conical surface of the conical lens and the bottom plane;kin terms of the wave number, the number of waves,Ris the cone lens pupil radius;
after passing through the cone lens, the vortex light beam interferes with the plane wave, and the complex amplitude distribution is as follows:
；
step two, combining the computer 400 to calculate the complex amplitude E1The intensity map of (a) is written into the reflective spatial light modulator 200;
step three, turning on a power supply of the continuous wave laser 100, enabling the light beam emitted by the continuous wave laser 100 to enter a pinhole filter 120 after being reflected by a reflector 110, then collimating the light beam by a convex lens I130, converting the collimated light beam into linearly polarized light by a polarizer 141, and irradiating the linearly polarized light on a beam splitting cube 150; the light beam passing through the beam splitting cube 150 is split into two beams, one is reflected light, and the other is transmitted light; the reflected beam is illuminated on the reflective spatial light modulator 200;
step four, the light beam irradiated on the reflective spatial light modulator 200 is used for diffracting and reproducing the fractional order Bessel-Gaussian light beam; the Bessel-Gaussian beam reproduced by diffraction passes through the beam splitting cube 150, the analyzer 142 and the small-aperture diaphragm 210, and then is irradiated on the convex lens II131 for Fourier transform to generate a fractional order perfect vortex beam;
step five, after the fractional order perfect vortex light beam is imaged in the CCD camera, the image enters the computer 400 for subsequent analysis;
sixthly, according to the analysis result of the computer, the radius of the bright ring of the generated perfect vortex light beam is not changed along with the change of the fractional order topological charge value m; by adjusting the refractive index of the material of the axicon lens in the first stepnOr angle of taperaThe radius of the bright ring of the perfect vortex beam of the fractional order can be adjusted.
Examples
As shown in FIG. 1, an apparatus for generating a fractional order perfect vortex beam includes a continuous wave laser 100, in this embodiment, the continuous wave laser 100 selects a He-Ne laser having a wavelength of 632.8nm and a power of 3 mW; the light beam emitted by the continuous wave laser 100 is reflected by the reflector 110 and enters the spatial filter 120, then is collimated by the convex lens I130, and the collimated light beam is changed into linearly polarized light by the polarizer 141 and irradiates the beam splitting cube 150; after passing through the beam splitting cube 150, the reflected light impinges on the reflective spatial light modulator 200;
the light beam passing through the beam splitting cube 150 is split into two beams, one is reflected light, and the other is transmitted light; the reflected light irradiates on the reflective spatial light modulator 200, and is reflected by the reflective spatial light modulator 200 to generate a fractional order Bessel-Gaussian beam, the fractional order Bessel-Gaussian beam passes through the beam splitting cube 150 and the analyzer 142 and then irradiates on the small aperture diaphragm 210, the fractional order Bessel-Gaussian beam passing through the small aperture diaphragm 210 is Fourier transformed by the convex lens II131 to generate a fractional order perfect vortex beam, and the fractional order perfect vortex beam is imaged in the CCD camera 300; then stored in the computer 400 for analysis;
the distance between the spatial filter 120 and the convex lens I130 is the focal length of the convex lens I130; the reflective spatial light modulator 200 is arranged on the front focal plane of the convex lens II 131; the CCD camera 300 is arranged on the back focal plane of the convex lens II 131; the reflective spatial light modulator 200 and the CCD camera 300 are respectively connected with a computer 400;
the reflective spatial light modulator 200 is used for generating a fractional order Bessel-Gaussian beam; the polarizer 141 and the analyzer 142 are used for adjusting the beam quality of the vortex beam; the aperture 210 is used for selecting the first order diffracted beam of the light field diffracted by the reflective spatial light modulator 200; the convex lens II131 has the function of carrying out Fourier transform on the fractional order Bessel-Gaussian beam.
A method for generating a fractional order perfect vortex beam comprises the following specific steps:
step one, generating a cone lens transmittance function and a light intensity graph of interference of fractional order vortex light beams and plane waves by using a computer 400, and specifically comprising the following steps of:
the electric field of the plane wave is represented as:
wherein E is0The intensity of the amplitude is represented by,krepresenting wave number and z representing propagation distance.
The electric field of a vortex beam perpendicularly incident on the axicon lens is expressed as:
wherein,is a constant of the amplitude of the wave,is the radius of the beam waist,mthe number of topological charges, taking the fraction,jis an imaginary unit;
the complex amplitude transmittance of the axicon lens is as follows:
in the formula,nis the refractive index of the material of the axicon,athe cone angle of the conical lens is the included angle between the conical surface of the conical lens and the bottom plane;kin terms of the wave number, the number of waves,Ris the cone lens pupil radius;
after passing through the cone lens, the vortex light beam interferes with the plane wave, and the complex amplitude distribution is as follows:
step two, combining the computer 400 to calculate the complex amplitude E1The intensity map of (a) is written into the reflective spatial light modulator 200;
step three, turning on a power supply of the continuous wave laser 100, enabling the light beam emitted by the continuous wave laser 100 to enter a pinhole filter 120 after being reflected by a total reflection mirror 110, then collimating the light beam by a convex lens I130, converting the collimated light beam into linearly polarized light after passing through a polarizer 141, and irradiating the linearly polarized light beam on a beam splitting cube 150; the light beam passing through the beam splitting cube 150 is split into two beams, one is reflected light, and the other is transmitted light; the reflected beam is illuminated on the reflective spatial light modulator 200;
step four, the light beam irradiated on the reflective spatial light modulator 200 is used for diffracting and reproducing the fractional order Bessel-Gaussian light beam; the Bessel-Gaussian beam reproduced by diffraction passes through the beam splitting cube 150, the analyzer 142 and the small-aperture diaphragm 210, and then irradiates on the convex lens II131 to perform Fourier transform to generate a fractional order perfect vortex beam;
step five, after the fractional order perfect vortex light beam is imaged in the CCD camera 300, the image is stored in the computer 400 for subsequent analysis;
step eight, FIG. 2 is a group of fractional order perfect vortex beam intensity graphs recorded by a computer, wherein the topological charge value m = 2.1-3.0, and the interval is 0.1 order; from the figure2, the change of the gap of the bright ring of the vortex light beam can be seen, and the generated fractional order perfect vortex light beam is very ideal; in addition, the refractive index of the cone lens material in the first step is adjustednOr angle of taperaThe radius of the bright ring of the perfect vortex beam of the fractional order can be adjusted. The device and the method can generate the fractional order perfect vortex light beam, and have the advantages of simple principle, simple structure, online regulation and control and easy operation.
Claims (1)
1. A device used in the method comprises a continuous wave laser (100), a reflector (110) is arranged in the advancing direction of a light beam emitted by the continuous wave laser (100), and a pinhole filter (120), a convex lens I (130), a polarizer (141) and a beam splitting cube (150) are sequentially arranged in the advancing direction of the light beam reflected by the reflector (110); the light beam passing through the beam splitting cube (150) is split into two beams, wherein one beam is reflected light, and the other beam is transmitted light; a reflective spatial light modulator (200) is arranged in the forward direction of reflected light, and after a light beam generated after being reflected by the reflective spatial light modulator (200) passes through a beam splitting cube (150), an analyzer (142), a small-hole diaphragm (210), a convex lens II (131) and a CCD camera (300) are sequentially arranged in the forward direction of the light beam; the reflective spatial light modulator (200) and the CCD camera (300) are respectively connected with a computer (400); the distance between the pinhole filter (120) and the convex lens I (130) is the focal length of the convex lens I (130); the reflective spatial light modulator (200) is arranged on the front focal plane of the convex lens II (131); the CCD camera (300) is arranged on the back focal plane of the convex lens II (131);
the method is characterized in that: the method comprises the following steps:
generating a light intensity map containing a cone lens transmittance function and interference of fractional order vortex light beams and plane waves by using a computer (400); the specific process is as follows:
the electric field of the plane wave is represented as:
Ep＝E0exp(-ikz)
wherein E is0Representing amplitude intensity, k representing wave number, z representing propagation distance;
the electric field of a vortex beam perpendicularly incident on the axicon lens is expressed as:
wherein A is0Is an amplitude constant, w0Taking the fraction as the waist radius and m as the topological charge number; j is an imaginary unit;
the complex amplitude transmittance function of the axicon is:
<mrow> <mi>t</mi> <mrow> <mo>(</mo> <mi>r</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>exp</mi> <mo>&lsqb;</mo> <mo>-</mo> <mi>j</mi> <mi>k</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>r</mi> <mi>&alpha;</mi> <mo>&rsqb;</mo> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mo>(</mo> <mi>r</mi> <mo>&le;</mo> <mi>R</mi> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>0</mn> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mo>(</mo> <mi>r</mi> <mo>></mo> <mi>R</mi> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
wherein n is the refractive index of the cone lens material, α is the cone angle of the cone lens, namely the included angle between the cone surface and the bottom plane of the cone lens, k is the wave number, and R is the pupil radius of the cone lens;
after passing through the cone lens, the vortex light beam interferes with the plane wave, and the complex amplitude distribution is as follows:
combining with the computer holographic technique, the complex amplitude E is calculated by a computer (400)1Writing the intensity map of (a) into the reflective spatial light modulator (200);
turning on a power supply of the continuous wave laser (100), enabling light beams emitted by the continuous wave laser (100) to enter a pinhole filter (120) after being reflected by a reflector (110), then collimating the light beams through a convex lens I (130), converting the collimated light beams into linearly polarized light after passing through a polarizer (141), and irradiating the linearly polarized light on a beam splitting cube (150); the light beam passing through the beam splitting cube (150) is split into two beams, one beam is reflected light, and the other beam is transmitted light; the reflected light beam is irradiated on a reflective spatial light modulator (200);
fourthly, the light beam irradiated on the reflective spatial light modulator (200) is used for diffracting and reproducing the fractional-order Bessel-Gaussian light beam; the diffraction-reproduced Bessel-Gaussian beam passes through a beam splitting cube (150), an analyzer (142) and a small aperture diaphragm (210), and then irradiates on a convex lens II (131) to perform Fourier transform to generate a fractional order perfect vortex beam;
fifthly, after the fractional order perfect vortex light beam is imaged in a CCD camera, the image enters a computer (400) for subsequent analysis;
and sixthly, according to the analysis result of the computer, the radius of the bright ring of the generated perfect vortex light beam is not changed along with the change of the fractional order topological charge value m, and the radius of the bright ring of the fractional order perfect vortex light beam can be adjusted by adjusting the refractive index n of the cone lens material or the value of the cone angle α in the step one.
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| CN103954367B (en) * | 2014-04-18 | 2016-08-31 | 河南科技大学 | A kind of device measuring fractional order optical eddy topology charge values and measuring method thereof |
| CN103983367B (en) * | 2014-04-30 | 2017-01-25 | 河南科技大学 | Fractional vortex beam topological charge value measuring method based on light intensity analysis |
| CN104635344B (en) * | 2015-02-28 | 2017-02-22 | 河南科技大学 | Bessel light beam generating device with adjustable parameters and production method of bessel beam generating device |
| CN105115607B (en) * | 2015-08-10 | 2017-12-01 | 河南科技大学 | Utilize the device and method for intersecting two-slit interference measurement vortex beams topology charge values |
| CN105043543B (en) * | 2015-08-27 | 2017-04-05 | 河南科技大学 | A kind of manufacture method of the super Rayleigh speckle field of controllable |
| CN205594238U (en) * | 2015-12-24 | 2016-09-21 | 河南科技大学 | Device for generating perfect vortex light beam of fractional order |
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