CN107238933B - Method and system for generating a local fractional order Bessel vortex beam - Google Patents
Method and system for generating a local fractional order Bessel vortex beam Download PDFInfo
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Abstract
The invention relates to a method and a system for generating a partial fractional order Bessel vortex beam, which are designed for obtaining a vortex beam with a topological charge number which continuously changes along with the distance and changes along with the wavelength on a transmission direction axis. The light beam passes through a spiral slit structure, wherein the spiral slit structure is an optical piece which is provided with a light-transmitting and notched spiral slit and is opaque to the rest parts except the spiral slit. And generating vortex light beams with the topological charge number changing continuously along with the transmission distance in the transmission direction and the topological charge number changing along with the wavelength in the transmission direction after the spiral slit structure. Such longitudinal manipulation techniques of the present invention can address many of the challenges faced in telemetry and data communications and even data encryption.
Description
Technical Field
The invention relates to a method and system for generating a local fractional order Bessel vortex beam.
Background
A vortex beam is a beam with a spiral phase distribution with a phase factor exp [ il theta ] in its expression, each photon in the beam carrying an orbital angular momentum of l, where l is called the topological charge number. Because the vortex beam has orbital angular momentum l, the carried orbital angular momentum can be transferred to the particles to drive the particles to rotate, and the capture and translation of micron and submicron particles can be realized, so that the tool is visually called an optical wrench. In addition, the vortex beam has a wide application prospect in information coding, and information can be coded and transmitted by utilizing the orbital angular momentum of the vortex beam. This novel coding scheme has many unique advantages: (1) The value of the topological charge number l can be an integer, zero or even a fraction, so that the method has higher coding capability. (2) has higher confidentiality. Therefore, the method has great significance for measuring the topological charge number of the vortex beam. Based on the characteristics, the vortex beam has a wide application prospect in the aspects of driving particles to rotate, encoding information, biomedicine and transmitting optical information.
The current research on vortex beams is mainly limited to vortex beams of integer orders, but has important significance on research on vortex beams of fractional orders. The vortex beam has stronger coding capability because of fractional order value; this is important for atomic optics and quantum information optics. Different from the circularly symmetric light intensity distribution of the integer-order vortex beam, the bright ring of the fractional-order vortex beam is provided with a notch, and the method has more application in the aspect of the manipulation of microparticles.
Bessel beams are one of the most commonly used vortex beam models in vortex beams due to their special non-diffraction and self-healing properties. The generation and propagation characteristics of fractional order bessel vortex beams have been widely studied both theoretically and experimentally so far.
The method for generating the fractional order vortex beam comprises the following steps: spiral phase plate method, axicon conversion method, spatial light modulator generation method, laguerre Gaussian weighted superposition method, etc.
Spiral phase plate method [ Oemrawsingh S S R, eliel E R, woerdman J P, et al half-integral spiral phase plates for optical wavelengths [ J ]. Journal of Optics A: pure and Applied Optics,2004,6 (5): S288 ], which utilizes a spiral phase plate to introduce a certain amount of dislocation into a light wave having a smooth wavefront to generate wavefront dislocations, and a fractional order vortex beam is generated by passing such a spiral phase plate.
The axicon conversion method [ Scott G, mcArdle n. Effect generation of nearly diffraction-free beams using an axicon [ J ]. Optical Engineering,1992,31 (12): 2640-2643 ] was mainly made for the generation of bessel's undiffracted light beam, and was an evolution of the spiral phase plate method described above. The base film Gaussian beam passes through a fractional order spiral phase plate to generate fractional vortex beam, and then passes through an axicon to generate non-diffraction beam fractional order Bessel vortex beam.
The spatial light modulator [ S.H.Tao, W.M.Lee, and x.c. yuan, "Dynamic optical manipulation with a higher-order fractional Bessel beam generated from a spatial light modulator," opt. Lett.28 (20), 1867-1869 (2003) ] is to load phase information onto the phase spatial light modulator to obtain the desired fractional order vortex beam. The method is different from the holographic grating in that the method synchronously loads the graph on the computer to the spatial light modulator to generate the hologram, and the process of manufacturing the holographic grating is omitted.
Laguerre Gaussian weighted overlap methodJ B,O’Holleran K,Preece D,et al.Light beams with fractional orbital angular momentum and their vortex structure[J].Optics Express,2008,16(2):993-1006.]The required fractional order can be formed by weighted superposition of several integer Laguerre Gaussian beams, but the actual fractional resolution is not strictly obtained, but other modes can be omitted according to the weighting coefficients.
These methods all have certain drawbacks, and when vortex beams with different topological charges are required, the spiral phase plate or information loaded on the spatial light modulator is required to be changed each time or analysis solution is calculated to obtain the required beam. The topological charge number of the fractional order vortex beam generated by the method of the spiral phase plate is related to the manufacture of the spiral phase plate. Through a certain spiral phase plate, the topological charge number with a certain fixed fraction is provided. The axicon conversion method is an upgrade of the spiral phase plate, the defect is similar to the spiral phase plate, the spatial light modulator is actually similar to the holographic grating, and the defect is that a vortex beam with a specific fraction needs to be obtained, and the phase information needs to be changed once. The fractional order beam produced by the Laguerre Gaussian weighted overlap-add method is not actually an exact analytical solution, but rather an approximation.
In view of the above-mentioned drawbacks, the present inventors have actively studied and innovated to create a method and system for generating a locally fractional order bessel vortex beam, which is more industrially useful.
Disclosure of Invention
In order to solve the technical problems, the invention aims to provide a method and a system for generating a partial fractional order Bessel vortex beam, which can not only obtain a vortex beam with a topological charge number continuously changing along with a transmission distance in a transmission direction, but also obtain a vortex beam with a topological charge number changing along with a wavelength.
To achieve the above object, the present invention provides a method for generating a partial fractional order bessel vortex beam, comprising:
performing beam expansion treatment on the light beam; the beam after beam expansion passes through a spiral slit structure, and a vortex beam with the topological charge number changing continuously along with the transmission distance in the transmission direction and the topological charge number changing along with the wavelength in the transmission direction is generated after the spiral slit structure;
wherein the spiral slit structure is an optical piece provided with a light-transmitting and notch spiral slit and the rest parts except the spiral slit are not light-transmitting, and the radius of the light-transmitting and notch spiral slit meets the following formula
In the formula, r 0 The radius of the smallest radius of the spiral slit of the light transmission gap is, alpha is the included angle between other points of the spiral light transmission slit and the point of the smallest radius, and N is a fixed value.
Specifically, the value of N should satisfy n=l×z×λ, where λ is the wavelength of the light source, z is the distance between the observation plane and the spiral slit structure, and l is the topological load size l to be acquired.
In particular, it also includes setting up the spot shape at different distances from the spiral slit structure at the observation plane behind the spiral slit structure to confirm whether a continuously varying topological load is obtained.
Further, the spiral slit structure is formed by loading a light-transmitting, notched spiral slit and a light-impermeable portion on a transmissive spatial light modulator.
To achieve the above object, the present invention provides a system for generating a partial fractional order bessel vortex beam, comprising:
the beam expander is used for expanding the light beam, and the spot size of the light beam after the beam expansion treatment can cover the spiral slit;
the spiral slit structure is used for generating vortex light beams with the topological charge number changing continuously along with the transmission distance in the transmission direction and the topological charge number changing along with the wavelength in the transmission direction after the light beams subjected to beam expansion pass through the spiral slit structure; the spiral slit structure is an optical piece provided with a light-transmitting and notch spiral slit, and the rest parts except the spiral slit are not light-transmitting, and the radius of the light-transmitting and notch spiral slit meets the following formula
In the formula, r 0 The radius of the smallest radius of the spiral slit of the light transmission gap is, alpha is the included angle between other points of the spiral light transmission slit and the point of the smallest radius, and N is a fixed value.
Further, the device also comprises a digital sensor arranged on the observation plane behind the spiral slit structure, wherein the digital sensor is used for recording the light spot shapes at different distances from the spiral slit structure and confirming whether the continuously-changed topological load is obtained.
Further, the digital sensor is arranged at a transmission distance z=1 m, z=1.14m, z=1.34 m, z=1.56 m, z=1.89 m from the spiral slit structure to record vortex beams with topological charges of m=2, m=1.17, m=1.5, m=1.3, and m=1, respectively.
Preferably, the transmissive spatial light modulator is loaded with light transmissive, notched spiral slits and opaque portions to form the spiral slit structure.
By means of the scheme, the method and the system for generating the partial fractional order Bessel vortex beam have at least the following advantages:
when a plane wave is incident on a screen, the increment of angles of two similar points on the incident wave along the slit is delta alpha (r) respectively α ,α)，(r α +Δα, α+Δα), the phase difference between the points (0, z) arriving at the viewing plane after different distances is Δθ=2ρΔρλ, where Δρ=ρ α +Δα-ρ α The phase shift across the slit is constant if Δρ=lλΔα/2π. Can only getTo obtain a vortex beam with a topological charge of l on an observation plane, the topological charge number of the center of the generated vortex beam on the propagation distance is inversely proportional to the distance. Therefore, the invention not only can obtain the vortex beam with the topological charge number changing continuously along with the transmission distance in the transmission direction, but also can obtain the vortex beam with the topological charge number changing along with the wavelength.
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 generating a partial fractional order Bessel vortex beam in accordance with the present invention; wherein: 1. a laser; 2. a beam expander; 3. a transmissive spatial light modulator; 4. a wavefront sensor;
FIG. 2 is a slit block diagram of a method and system of generating a partial fractional order Bessel vortex beam in accordance with the present invention;
FIG. 3 is a schematic diagram of the method and system of the present invention for generating a partial fractional order Bessel vortex beam and the spiral slit and parameters actually loaded onto a transmissive spatial light modulator; the black plane is the added spiral slit, and the gray plane is the observation plane.
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.
Description: the topological charge number of the vortex beam in the transmission process is conservative, and the invention aims at the change of the topological charge number in a local area on the central axis. Thus, the change of the topological load number with the transmission distance is referred to as the change of the local area on the central axis, which is called local fractional order.
The invention aims at the continuous change of the topological charge number on the distance of the center of the transmission shaft, which means that the corresponding topological charge number can be obtained by only changing the distance for the required topological charge number. And retains its non-diffracting properties. And the wavelength can be changed to obtain the desired number of topological charges.
Example 1
The system for generating a local fractional order Bessel vortex beam according to the present embodiment comprises:
a laser 1, wherein the laser is a 100mw solid-state laser, and the emitted laser wavelength is 532nm;
the beam expander 2 is used for expanding the laser beam emitted by the laser, and the size of the light spot after the beam expansion is required to be larger than that of the spiral slit;
spiral slit structure 3: the spiral slit structure is shown in figure 1, white is slit, transparent, black is opaque, and its radius is required to meet the formulaWherein r is 0 The method is characterized in that the radius of the spiral slit at the position with the smallest radius is a radius, alpha is an included angle between other points on the spiral slit and the point with the smallest radius, N is a fixed value, and in practical application, the value of N needs to consider the wavelength lambda of a light source, the range of the distance z between an expected observation plane and the spiral slit structure and the range of the topological load size l to be obtained, and finally N=l×z×lambda is met; r is (r) 0 The relation with N needs to be satisfied->
In the present embodiment, let r 0 α is the angle between the other points on a spiral slit and the point where the radius is smallest, let l=2, z=4000/lmm, since let the wavelength λ be 532 nm.
Example 2
The system for generating the partial fractional order bessel vortex beam in the embodiment further comprises a digital sensor, namely an electronic coupling element, on the basis of embodiment 1, for recording the spot shapes at different distances and confirming whether the continuously-changed topological load is obtained. When the expanded light passes through the spiral slit structure, a vortex beam with topological charges of m=2, m=1.17, m=1.5, m=1.3 and m=1 can be observed at transmission distances of z=1, z=1.14m, z=1.34 m, z=1.56 m and z=1.89 m respectively. Wherein the phase of the swirling beam can be measured by a wavefront sensor.
Example 3
The method for generating the partial fractional order Bessel vortex beam comprises the following steps:
performing beam expansion treatment on the light beam;
the beam after beam expansion passes through a spiral slit structure, and a vortex beam with the topological charge number changing continuously along with the transmission distance in the transmission direction and the topological charge number changing along with the wavelength in the transmission direction is generated after the spiral slit structure;
wherein the spiral slit structure is an optical piece provided with a light-transmitting and notch spiral slit and the rest parts except the spiral slit are not light-transmitting, and the radius of the light-transmitting and notch spiral slit meets the following formula
In the formula, r 0 The radius of the smallest radius of the spiral slit of the light transmission gap is, alpha is the included angle between other points of the spiral light transmission slit and the point of the smallest radius, and N is a fixed value. In practical application, the value of N needs to be considered in terms of the wavelength λ of the light source, the range of the distance z between the observation plane and the spiral slit structure, and the range of the topological load size l to be obtained, where n=l×z×λ, where λ is the wavelength of the light source, z is the distance between the observation plane and the spiral slit structure, and l is the topological load size l to be obtained. r is (r) 0 The relation with N needs to be satisfied
In this embodiment, the method further includes setting, on an observation plane behind the spiral slit structure, spot shapes recorded at different distances from the spiral slit structure to confirm whether continuously variable topology load is obtained. The specific recording distance can be specifically set according to actual needs.
The working principle of each embodiment is as follows:
the zero order bessel beam can be considered the fourier transform of a circular slit, so the first observation of the bessel beam is by placing a circular slit in the focal plane of a convex lens. When the monochromatic plane wave is incident on the screen with the annular slit, the emitted wave can pass through the annular ring and then carry out the same phase transfer at the same distance in the propagation direction. This is why a bright spot is obtained at the very center of the spot, i.e. it is the zero-order bessel beam. However, if the annular slit is destroyed and becomes a spiral slit, the emitted wave is transferred from different positions on the spiral slit by the axial field of the observation plane. That is, a continuous phase shift is generated along the spiral slit, and a phase singularity can be seen on the optical axis.
Constructing a slit, wherein r α And alpha is a radius and an angle, respectively, r 0 Is the initial radius of the spiral slit. ρ α Is the point (r) α Alpha, 0) to the viewing plane (0, z). When a plane wave is incident on the screen, the increment of the angle of two similar points along the slit on the incident wave is delta alpha, (r) respectively α ,α)，(r α +Δα, α+Δα), the phase difference between the points (0, z) arriving at the viewing plane after different distances is Δθ=2ρΔρλ, where Δρ=ρ α +Δα-ρ α Phase shift across the slit if Δρ=lλΔα/2piIs constant. This means that the closed loop of the phase wavefront in the viewing plane on the axis is 2pi.l. That is, there is an optical vortex in the viewing plane and +.>For topological charge number, to obtain spiral phase, a spiral slit is constructed, and the mathematical expression is:
in this way, a vortex beam with a topological load of l can be obtained on the observation plane, and in addition, after the product of the expression lz is fixed, the l at the center gradually decreases with the increase of the propagation distance. I.e. the topological charge number of the center of the generated vortex beam in terms of propagation distance is inversely proportional to the distance.
When the gap of the spiral slit is much smaller than the radius, the spiral slit may be regarded as a ring slit to some extent. Thus, the vortex beam can be approximated as a Bessel vortex beam. In the Fresnel approximation, the complex amplitude of the diffracted beam after propagation of the z-distance can be obtained from the following diffraction equation
Where T (x, y) is the aperture function of the spiral slit.
The light intensity and phase change of the vortex beam transmitted along with the distance can be simulated by the expression. The experimental demonstration can be carried out by loading the expression of the spiral slit on the spatial light modulator after the program simulation drawing.
The value of the topological charge number can be an integer, zero or even a fraction, so that the method has higher coding capability. And thus also has higher confidentiality. Therefore, the method has great significance for measuring the topological charge number of the vortex beam. Based on the characteristics, the vortex beam has a wide application prospect in the aspects of driving particles to rotate, encoding information, biomedicine and transmitting optical information. The invention not only can obtain the vortex beam with the topological charge number changing continuously along with the distance on the transmission direction axis, but also can obtain the vortex beam with the topological charge number changing along with the wavelength. Such longitudinal steering techniques can address many challenges faced in telemetry and data communications and even data encryption.
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 (4)
1. A method of generating a local fractional order bessel vortex beam comprising:
performing beam expansion treatment on the light beam; the beam after beam expansion passes through a spiral slit structure, and a vortex beam with the topological charge number changing continuously along with the transmission distance in the transmission direction and the topological charge number changing along with the wavelength in the transmission direction is generated after the spiral slit structure;
wherein the spiral slit structure is an optical piece provided with a light-transmitting and notch spiral slit and the rest parts except the spiral slit are not light-transmitting, and the radius of the light-transmitting and notch spiral slit meets the following formula
In the formula, r 0 The radius of the smallest radius part of the spiral slit of the light transmission gap is that alpha is an included angle between other points of the spiral light transmission slit and the point of the smallest radius part, and N is a fixed value;
the value of N should be n=l×z×λ, where λ is the wavelength of the light source, z is the distance between the observation plane and the spiral slit structure, and l is the topological load size l to be obtained.
2. The method of generating a partial fractional order bessel vortex beam of claim 1 further comprising setting spot shapes recorded at different distances from the spiral slit structure at a viewing plane behind the spiral slit structure to confirm whether a continuously varying topological charge is obtained.
3. The method of generating a partial fractional order bessel vortex beam of claim 1 wherein the spiral slit structure is formed by loading a transmissive, notched spiral slit and an opaque portion on a transmissive spatial light modulator.
4. A system for generating a locally fractional order bessel vortex beam, comprising:
the beam expander is used for expanding the light beam, and the spot size of the light beam after the beam expansion treatment can cover the spiral slit;
the spiral slit structure is used for generating vortex light beams with the topological charge number changing continuously along with the transmission distance in the transmission direction and the topological charge number changing along with the wavelength in the transmission direction after the light beams subjected to beam expansion pass through the spiral slit structure; the spiral slit structure is an optical piece provided with a light-transmitting and notch spiral slit, and the rest parts except the spiral slit are not light-transmitting, and the radius of the light-transmitting and notch spiral slit meets the following formula
In the formula, r 0 The radius of the smallest radius part of the spiral slit of the light transmission gap is that alpha is an included angle between other points of the spiral light transmission slit and the point of the smallest radius part, and N is a fixed value;
the digital sensor is used for recording the light spot shapes at different distances from the spiral slit structure and determining whether continuously-changed topological load is obtained or not;
the digital sensor is arranged at a transmission distance z=1 m, z=1.14m, z=1.34 m, z=1.56 m and z=1.89 m from the spiral slit structure, and records vortex beams with topological charges of m=2, m=1.17, m=1.5, m=1.3 and m=1 respectively;
the transmission type spatial light modulator is loaded with a spiral slit with light transmission and notch and a light-tight part to form the spiral slit structure.
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| CN109870890B (en) * | 2019-01-11 | 2020-06-26 | 中国科学院西安光学精密机械研究所 | Integer order vortex light beam phase mask plate with fractional order vortex contour and light path system |
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| CN114994930B (en) * | 2022-06-13 | 2024-01-19 | 中国计量大学 | Vortex light beam generator based on multi-circle spiral nano groove structure |
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