CN117472143A - Vortex beam-based integer decomposition method and system - Google Patents

Vortex beam-based integer decomposition method and system Download PDF

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Publication number
CN117472143A
CN117472143A CN202311412468.7A CN202311412468A CN117472143A CN 117472143 A CN117472143 A CN 117472143A CN 202311412468 A CN202311412468 A CN 202311412468A CN 117472143 A CN117472143 A CN 117472143A
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factor
integer
vortex
thin lens
light intensity
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Inventor
王金鑫
张敬仁
刘欣
马普娟
彭啸峰
曾军
梁春豪
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Shandong Normal University
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Shandong Normal University
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    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G—PHYSICS
    • G03—PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03H—HOLOGRAPHIC PROCESSES OR APPARATUS
    • G03H1/00—Holographic processes or apparatus using light, infrared or ultraviolet waves for obtaining holograms or for obtaining an image from them; Details peculiar thereto
    • G03H1/22—Processes or apparatus for obtaining an optical image from holograms
    • G03H1/2294—Addressing the hologram to an active spatial light modulator
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06E—OPTICAL COMPUTING DEVICES; COMPUTING DEVICES USING OTHER RADIATIONS WITH SIMILAR PROPERTIES
    • G06E3/00—Devices not provided for in group G06E1/00, e.g. for processing analogue or hybrid data
    • G06E3/001—Analogue devices in which mathematical operations are carried out with the aid of optical or electro-optical elements
    • G06E3/005—Analogue devices in which mathematical operations are carried out with the aid of optical or electro-optical elements using electro-optical or opto-electronic means
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations

Abstract

The invention belongs to the technical field of integer decomposition, and particularly relates to an integer decomposition method and system based on vortex beams, wherein the method comprises the following steps: setting an integer to be decomposed as a mode index of a vortex beam, and adjusting the azimuth angle of a pinhole in the digital micro lens array device according to a factor to be tried; sequentially irradiating the digital micro-lens array device and the first thin lens with vortex light beams, and shooting a light intensity distribution diagram at the back focal plane of the first thin lens by using a CCD camera; normalizing the light intensity distribution map to obtain a normalized optical axis light intensity value; and judging whether the factor to be tried is the factor of the integer to be decomposed or not according to the optical axis light intensity value. The invention judges whether the factor to be tried is the factor of the integer to be decomposed or not through the optical axis light intensity value, and can rapidly identify the factor and the non-factor of the integer.

Description

Vortex beam-based integer decomposition method and system
Technical Field
The invention belongs to the technical field of integer decomposition, and particularly relates to an integer decomposition method and system based on vortex beams.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
Integer decomposition originates from mathematics, but has attracted a great deal of interest to physicists, who have studied the relationship between theory of numbers and complex physical systems. Integer decomposition, especially large numbers, is still a tricky problem at present, but this difficulty tends to create high security based on information coding, cryptography, all-optical machine learning and other applications. To date, various methods have been developed to achieve integer decomposition, including quantum algorithms, quantum annealing, variational algorithms, and gaussian summation. While gauss and a wide variety of applications exist in different ways, including optical talbot effects, bose-einstein condensation, nuclear magnetic resonance techniques, cold atoms, interferometers, and the like. Purely classical optical methods mainly include the optical talbot effect and optical interferometry.
In practice, the optical talbot effect is distorted by optical diffraction due to the finite energy, which places an upper limit on the number of to-be-decomposed. Pearcard et al achieved factorization of the maximum 27 in free space propagation. For optical interferometry, the gaussian sum is typically achieved using multiple sources, one of which produces one of the gaussian sums. This technique places extremely high demands on the precise position or phase control of the multiple light sources, especially for large integer decompositions.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention provides an integer decomposition method and system based on vortex beams.
To achieve the above object, one or more embodiments of the present invention provide the following technical solutions:
the first aspect of the invention provides an integer decomposition method based on vortex beams, which comprises the following steps:
setting an integer to be decomposed as a mode index of a vortex beam, and adjusting the azimuth angle of a pinhole in the digital micro lens array device according to a factor to be tried;
sequentially irradiating the digital micro-lens array device and the first thin lens with vortex light beams, and shooting a light intensity distribution diagram at the back focal plane of the first thin lens by using a CCD camera;
normalizing the light intensity distribution map to obtain a normalized optical axis light intensity value;
and judging whether the factor to be tried is the factor of the integer to be decomposed or not according to the optical axis light intensity value.
A second aspect of the present invention provides an integer decomposition system based on vortex beams, comprising:
the vortex beam generation module is used for vortex beams with mode indexes being integers to be decomposed;
the light intensity distribution map acquisition module is used for shooting the light intensity distribution map at the back focal plane of the first thin lens by using a CCD camera after the vortex light beam irradiates the digital micro lens array device and the first thin lens in sequence;
the normalization processing module is used for carrying out normalization processing on the light intensity distribution map to obtain a normalized optical axis light intensity value;
and the judging module is used for judging whether the factor to be tried is the factor of the integer to be decomposed or not according to the optical axis light intensity value.
The one or more of the above technical solutions have the following beneficial effects:
the invention sets the mode index of vortex beam to be decomposed, uses the pinhole position in pinhole sieve to determine the size of trial factor, the vortex beam is focused to the back focal plane by lens after modulated by pinhole sieve, and the factor and non-factor are distinguished by measuring the light intensity value on the axis. The technology is simple and quick, and is expected to be applied to information coding, cryptography and the like.
Additional aspects of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention.
Fig. 1 is a flow chart of a method of a first embodiment.
Fig. 2 is a pinhole profile of the first embodiment.
Fig. 3 (a), (b), and (c) are light intensity distribution diagrams photographed at different trial factors p of the first embodiment, respectively.
Fig. 4 (a) and (b) are graphs of the factorization results of the pattern indexes l=30 and l=50 of the first embodiment, respectively.
In the figure, 1, a laser, 2, a liquid crystal spatial light modulator, 3, a second thin lens, 4, a pinhole plate, 5, a third thin lens, 6, a digital microlens array device, 7, a first thin lens, 8 and a CCD camera.
Detailed Description
Example 1
As shown in fig. 1, this embodiment discloses an integer decomposition method based on vortex beam, including:
step 1, setting an integer to be decomposed as a mode index of a vortex beam, and adjusting the azimuth angle of a pinhole in a digital micro-lens array device according to a factor to be tried;
step 2, sequentially irradiating the digital micro lens array device and the first thin lens with vortex beams, and shooting a light intensity distribution diagram at the back focal plane of the first thin lens by using a CCD camera;
step 3, carrying out normalization processing on the optical intensity distribution diagram to obtain a normalized optical axis light intensity value;
and step 4, judging whether the factor to be tried is the factor of the integer to be decomposed or not according to the optical axis light intensity value.
The invention sets the integer to be decomposed as the mode index l of the incident vortex beam, and the factor to be tried is selected as the parameter p for determining the pinhole position. True when p is lAt positive factors, then the intensity value on the optical axis may be maximized. If we normalize the on-axis intensity value, it is achieved that the on-axis intensity value is 1 only if p is a factor of l. In order to realize the large-scale distinction between the factor and the non-factor, the number of pinholes in the invention needs to satisfySo that all non-factors are compressed to the threshold +.>The following is given.
In step 1, a hologram of a vortex beam is loaded into a liquid crystal spatial light modulator through a digital holographic technology, a laser emits a completely coherent beam to irradiate the liquid crystal spatial light modulator, and the emergent beam of the liquid crystal spatial light modulator passes through a 4f imaging system to obtain the vortex beam.
The 4f imaging system includes: a second thin lens, a pinhole plate, and a third thin lens; the liquid crystal spatial light modulator is arranged at the front focal plane of the second thin lens, and the pinhole plate is arranged at the rear focal plane of the second thin lens and is arranged at the front focal plane of the third thin lens; the digital microlens array device is placed at the back focal plane of the third thin lens and at the front focal plane of the first thin lens, and the CCD camera is placed at the back focal plane of the first thin lens.
The +1 or-1 diffraction beam emitted by the 4f imaging system is the required vortex beam. The +1 or-1 order beam may be filtered out by a 4f imaging system with a spectral facet placed in the pinhole. The factor p to be tried can be determined by designing a needle mesh sieve;
the perforated screen is shown in fig. 2, where white is clear and black is opaque. The transmittance function of the pinhole sieve is a binary system function and can be realized by using a digital micro-lens array device. Therefore, the generated vortex beam irradiates the digital micro lens array device, loads a digital pinhole sieve, focuses to a back focal plane through a thin lens, and performs shooting measurement by using a CCD camera. The size of the try factor p can be changed continuously by programming the digital microlens array device in MATLAB to change the needle mesh screen of the digital microlens array device continuously.
In step 2, specifically, the method includes:
first, assuming that a lager-gaussian beam with a radial index of 0 is used as the vortex light field, the electric field can be described as:
where l is the mode index, ω, of the vortex beam 0 Is the beam waist size of the light beam,is the cylindrical coordinates at the light source.
To achieve integer decomposition, the transmittance function for a pinhole screen is set as:
wherein M represents the number of pinholes,representing the initial phase, delta is a Delta function and p is the azimuth angle that determines the pinhole. In view of the practical situation, the Delta function will be replaced in the experiment by a circular hole of diameter d. Wherein r is m ＝r 0 +m 2 P.d denotes the offset of the mth pinhole from the center.
The vortex beam is focused by a thin lens with the focal length f after being shielded and modulated by a pinhole screen. Wherein the pinhole screen is placed on the front focal plane of the thin lens, and the electric field at the back focal plane can be calculated by using the kohlrabi diffraction integral formula:
wherein the method comprises the steps of
Bringing equations (1) and (2) into (3) yields:
let r be 0 >>m 2 And/p.d, the light intensity value on the optical axis can be simplified as:
wherein the method comprises the steps ofIndicating the angle of the mth pinhole around the center.
Function ofCan be simplified into:
the above formula is Gaussian sum formula, whenIs->When the factor, or p, is a factor of l, then each of the gaussian terms is equal to 1, so the sum is equal to 1. Otherwise function->The value oscillates rapidly and the value is very small.
In step 3, normalizing the optical intensity distribution map to obtain a normalized optical axis optical intensity value, including: the CCD shoots a gray level image of the measured light intensity, the matlab reads the image and converts the image into a matrix, and the matrix is divided by the maximum value of the matrix, so that the normalization processing of the light intensity can be realized.
In step 4, determining whether the factor to be tried is a factor of an integer to be decomposed according to the optical axis light intensity value includes: if the optical axis light intensity value is 1, the factor to be tried is the factor of the integer to be decomposed, otherwise, the factor to be tried is the non-factor of the integer to be decomposed.
In this embodiment, the pinhole screen parameters of the digital microlens array device are set as follows: the wavelength λ=532 nm, the focal length of all three thin lenses is f=400 mm, the diameter d=0.04 mm of the circular hole, the first pinhole is offset from the optical axis by a distance: r is (r) 0 =6 mm, and the number of pinholes m=7.
As shown in fig. 3 (a), (b), and (c), for the number l=30 to be decomposed, the light intensity distribution at the focal plane with different trial factors p is shown with a cross symbol indicating the center position of the optical axis.
When p=5 and p=10, i.e., the factor of l, the normalized optical axis light intensity value is 1. And p=4, is not a factor of l, and the light intensity value on the optical axis is not 1. The resolution can be made simply and quickly by the magnitude of the light intensity value on the optical axis only.
As shown in (a) and (b) in fig. 4, when integers l=30 and l=53 are to be decomposed, wherein the error bars represent absolute differences between theoretical results and experimental results, the results show that the light intensity values on the optical axes (in terms ofRepresentation) are all at threshold ∈>The factors above, but not l, are all at threshold +.>The following.
Example two
The embodiment discloses an integer decomposition system based on vortex light beam, including:
the vortex beam generation module is used for vortex beams with mode indexes being integers to be decomposed;
the light intensity distribution map acquisition module is used for shooting the light intensity distribution map at the back focal plane of the first thin lens by using a CCD camera after the vortex light beam irradiates the digital micro lens array device and the first thin lens in sequence;
the normalization processing module is used for carrying out normalization processing on the light intensity distribution map to obtain a normalized optical axis light intensity value;
and the judging module is used for judging whether the factor to be tried is the factor of the integer to be decomposed or not according to the optical axis light intensity value.
Further, the vortex beam generating module includes: a laser, a liquid crystal spatial light modulator, and a 4f imaging system;
the hologram of the vortex beam is loaded into a liquid crystal spatial light modulator through a digital holographic technology, the liquid crystal spatial light modulator is irradiated by the completely coherent beam emitted by the laser, and the vortex beam is obtained by the emitted beam of the liquid crystal spatial light modulator through a 4f imaging system.
Further, the 4f imaging system includes: a second thin lens, a pinhole plate, and a third thin lens; the liquid crystal spatial light modulator is arranged at the front focal plane of the second thin lens, and the pinhole plate is arranged at the rear focal plane of the second thin lens and is arranged at the front focal plane of the third thin lens;
the emergent beam of the liquid crystal spatial light modulator sequentially passes through the second thin lens, the pinhole plate and the third thin lens and then is filtered out to obtain a +1 or-1 diffraction beam, namely a vortex beam.
Further, judging whether the factor to be tried is the factor of the integer to be decomposed according to the optical axis light intensity value, including: if the optical axis light intensity value is 1, the factor to be tried is the factor of the integer to be decomposed, otherwise, the factor to be tried is the non-factor of the integer to be decomposed.
It will be appreciated by those skilled in the art that the modules or steps of the invention described above may be implemented by general-purpose computer means, alternatively they may be implemented by program code executable by computing means, whereby they may be stored in storage means for execution by computing means, or they may be made into individual integrated circuit modules separately, or a plurality of modules or steps in them may be made into a single integrated circuit module. The present invention is not limited to any specific combination of hardware and software.
While the foregoing description of the embodiments of the present invention has been presented in conjunction with the drawings, it should be understood that it is not intended to limit the scope of the invention, but rather, it is intended to cover all modifications or variations within the scope of the invention as defined by the claims of the present invention.

Claims (10)

1. An integer decomposition method based on vortex beams, comprising:
setting an integer to be decomposed as a mode index of a vortex beam, and adjusting the azimuth angle of a pinhole in the digital micro lens array device according to a factor to be tried;
sequentially irradiating the digital micro-lens array device and the first thin lens with vortex light beams, and shooting a light intensity distribution diagram at the back focal plane of the first thin lens by using a CCD camera;
normalizing the light intensity distribution map to obtain a normalized optical axis light intensity value;
and judging whether the factor to be tried is the factor of the integer to be decomposed or not according to the optical axis light intensity value.
2. The integer decomposition method based on vortex beam as claimed in claim 1, wherein the relation between the number M of pinholes in the digital microlens array device and the mode index l of vortex beam is:
3. the method of integer decomposition based on vortex beam as claimed in claim 1, wherein said determining whether the factor to be tried is the factor of the integer to be decomposed based on the optical axis light intensity value comprises: if the optical axis light intensity value is 1, the factor to be tried is the factor of the integer to be decomposed, otherwise, the factor to be tried is the non-factor of the integer to be decomposed.
4. The integer decomposition method based on vortex beams according to claim 1, wherein a hologram of the vortex beams is loaded into a liquid crystal spatial light modulator by a digital holographic technology, a laser emits a completely coherent beam to irradiate the liquid crystal spatial light modulator, and the emergent beam of the liquid crystal spatial light modulator passes through a 4f imaging system to obtain the vortex beams.
5. The vortex beam based integer factorization method of claim 4 wherein the 4f imaging system comprises: a second thin lens, a pinhole plate, and a third thin lens; the liquid crystal spatial light modulator is arranged at the front focal plane of the second thin lens, and the pinhole plate is arranged at the rear focal plane of the second thin lens and is arranged at the front focal plane of the third thin lens;
the emergent beam of the liquid crystal spatial light modulator sequentially passes through the second thin lens, the pinhole plate and the third thin lens and then is filtered out to obtain a +1 or-1 diffraction beam, namely a vortex beam.
6. An integer decomposition system based on a vortex beam, comprising:
the vortex beam generation module is used for vortex beams with mode indexes being integers to be decomposed;
the light intensity distribution map acquisition module is used for shooting the light intensity distribution map at the back focal plane of the first thin lens by using a CCD camera after the vortex light beam irradiates the digital micro lens array device and the first thin lens in sequence;
the normalization processing module is used for carrying out normalization processing on the light intensity distribution map to obtain a normalized optical axis light intensity value;
and the judging module is used for judging whether the factor to be tried is the factor of the integer to be decomposed or not according to the optical axis light intensity value.
7. The vortex beam based integer factorization system of claim 6 wherein the vortex beam generation module comprises: a laser, a liquid crystal spatial light modulator, and a 4f imaging system;
the hologram of the vortex beam is loaded into a liquid crystal spatial light modulator through a digital holographic technology, the liquid crystal spatial light modulator is irradiated by the completely coherent beam emitted by the laser, and the vortex beam is obtained by the emitted beam of the liquid crystal spatial light modulator through a 4f imaging system.
8. The vortex beam based integer factorization system of claim 7 wherein the 4f imaging system comprises: a second thin lens, a pinhole plate, and a third thin lens; the liquid crystal spatial light modulator is arranged at the front focal plane of the second thin lens, and the pinhole plate is arranged at the rear focal plane of the second thin lens and is arranged at the front focal plane of the third thin lens;
the emergent beam of the liquid crystal spatial light modulator sequentially passes through the second thin lens, the pinhole plate and the third thin lens and then is filtered out to obtain a +1 or-1 diffraction beam, namely a vortex beam.
9. The vortex beam based integer factorization system of claim 6 wherein the number of pinholes M in the digital microlens array device is related to the mode index of the vortex beam, i:
10. the vortex beam based integer factorization system of claim 6 wherein the determining whether the factor to be tried is a factor of the integer to be factored based on the optical axis intensity value comprises: if the optical axis light intensity value is 1, the factor to be tried is the factor of the integer to be decomposed, otherwise, the factor to be tried is the non-factor of the integer to be decomposed.
CN202311412468.7A 2023-10-27 2023-10-27 Vortex beam-based integer decomposition method and system Pending CN117472143A (en)

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