Method and system for improving the sudden self-focusing ability of a circular airy beam

Abstract

The application discloses a method and system for improving the sudden self-focusing ability of a circular Airy beam, and relates to the technical field of beam transmission and control. The method comprises the following steps: determining the transmission direction of the circular Airy beam by acquiring the circular Airy beam transmitted in free space and establishing a space orthogonal coordinate system; determining the light intensity distribution of the circular Airy beam on a focal plane and an initial plane and the on-axis light field of the circular Airy beam according to the light field integral form of the circular Airy beam on any observation plane; and determining the intensity contrast according to the light intensity distribution and the on-axis light field. Under the condition of a given exponential decay factor, the dimensionless radius of the main ring in the circular Airy beam is changed, a first curve graph is drawn according to the on-axis light field, the optimal dimensionless radius is determined according to the first curve graph and the intensity contrast, and finally the strongest sudden self-focusing ability of the circular Airy beam is obtained according to the optimal dimensionless radius. The application realizes the improvement of the sudden self-focusing ability of the circular Airy beam.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of light beam transmission and control, in particular to a method and system for improving the self-focusing ability of a circular Airy beam. BACKGROUND

[0002] Self-focusing refers to the fact that the light intensity of a light beam remains at a low level before reaching the focal point when the light beam is transmitted in free space without any auxiliary optical components, and the light intensity suddenly increases by tens or even hundreds of times at the moment of reaching the focal point. The concept of self-focusing was first proposed in the study of the transmission characteristics of radially symmetric Airy beams.

[0003] The self-focusing ability of a light beam is described by the intensity contrast ratio, which is the ratio of the light intensity peak on the focal plane to the light intensity peak on the initial plane. The focal length of a light beam is defined as the distance between the focal plane and the initial plane. Soon after, this phenomenon of self-focusing was experimentally verified. This led to a surge of research on the self-focusing characteristics of circular Airy beams. Researchers have tried various methods to improve the self-focusing ability of Airy beams, such as modifying the circular Airy beam, blocking the circular Airy beam on the initial plane, extending to partially coherent circular Airy beams, introducing optical vortices into the circular Airy beam, introducing chirp into the circular Airy beam, and designing an array of Airy beams. At the same time, researchers have continuously expanded the application scenarios of self-focusing, and self-focusing has been applied to medical treatment, optical trapping, photon bullets, atomic manipulation, multi-photon polymerization, terahertz emission, optical communication, optical manipulation, dynamic imaging, image transmission, and food safety detection.

[0004] So far, the potential of the self-focusing ability of circular Airy beams has been fully tapped. In this context, how to further improve the self-focusing ability of circular Airy beams has become a problem to be solved. SUMMARY

[0005] The purpose of the present application is to provide a method and system for improving the self-focusing ability of a circular Airy beam to solve the problem of further improving the self-focusing ability of a circular Airy beam.

[0006] To achieve the above-mentioned purpose, the present application provides the following solutions:

[0007] A method for improving the self-focusing ability of a circular Airy beam, comprising:

[0008] obtaining the light beam parameters of a circular Airy beam transmitted in free space; the light beam parameters include light intensity control parameters, an exponential decay factor, the radius of a main ring, a scale factor, and an Airy function;

[0009] determining the light field of the circular Airy beam on the initial plane according to the light beam parameters;

[0010] The light field is dimensionless, and a dimensionless light field is obtained;

[0011] According to the dimensionless light field, a light field integral form of the circular Airy beam in free space transmission is determined by using the Collins integral formula;

[0012] A space rectangular coordinate system is established with the direction of the circular Airy beam transmission as the z-axis, and the x-axis and y-axis are divided in the plane perpendicular to the z-axis;

[0013] Based on the space rectangular coordinate system, a plurality of observation planes are divided according to different values of the z-axis coordinate; the observation planes include an initial plane and a focal plane; the observation plane of z=0 is taken as the initial plane, and the observation plane corresponding to the peak value of the light intensity of the on-axis light field of the circular Airy beam is taken as the focal plane, and z is the coordinate of the z-axis in the space rectangular coordinate system;

[0014] According to the light field integral form, the light intensity distribution of the circular Airy beam on any observation plane in free space transmission and the on-axis light field of the circular Airy beam are determined;

[0015] According to the on-axis light field, the light intensity peak value on the focal plane is determined;

[0016] According to the light intensity distribution on the initial plane, the light intensity peak value on the initial plane is determined;

[0017] According to the light intensity peak value on the focal plane and the light intensity peak value on the initial plane, the intensity contrast is determined;

[0018] Under the condition of a given exponential decay factor, the dimensionless radius of the main ring in the circular Airy beam is changed, and a first curve graph is drawn according to the on-axis light field; the first curve graph is a curve graph of the intensity contrast with respect to the dimensionless radius;

[0019] According to the first curve graph and the intensity contrast, an optimal dimensionless radius is determined;

[0020] According to the optimal dimensionless radius, the strongest sudden self-focusing ability of the circular Airy beam is obtained.

[0021] Optionally, according to the beam parameter, the light field of the circular Airy beam on the initial plane is determined, specifically including:

[0022] The light field of the circular Airy beam on the initial plane is determined by using the formula

[0023] Wherein, U(r, 0) is the expression of the light field of the circular Airy beam on the initial plane, z=0 in the initial plane, r represents the radial coordinate, r=(x 2 +y 2 )​1 / 2 , x is a coordinate of an x-axis in a spatial rectangular coordinate system, y is a coordinate of a y-axis in the spatial rectangular coordinate system, A is a light intensity control parameter, A ensures that a light intensity peak value of the circular Airy beam on the initial plane is always 1, a is an exponential attenuation factor, r0 is a radius of the main ring, w0 is a scale factor, and Ai(·) is an Airy function.

[0024] Optionally, the light field is subjected to dimensionless processing to obtain a dimensionless light field, specifically including:

[0025] The dimensionless light field is obtained by using a formula U1(r, 0) = Aexp[a(R0-s r )]Ai(R0-s r );

[0026] wherein U1(r, 0) is an expression of the dimensionless light field of the circular Airy beam on the initial plane, R0 = r0 / w0, R0 is a dimensionless radius of the main ring, s r =r / w0, s r is a dimensionless radial coordinate, r0 is a radius of the main ring, w0 is a scale factor, r is a radial coordinate, a is an exponential attenuation factor, A is a light intensity control parameter, and Ai(·) is an Airy function.

[0027] Optionally, according to the dimensionless light field, a light field integral form of the circular Airy beam in free space transmission is determined by using a Collins integral formula, specifically including:

[0028] The light field integral form of the circular Airy beam in free space transmission is determined by using a formula ;

[0029] wherein U(r, z) is an integral expression of the light field of the circular Airy beam in free space transmission, i represents an imaginary unit, z0 is a Rayleigh distance, w0 is a scale factor, k represents a wave number, k = 2π / λ, λ is a wavelength of the circular Airy beam, J0(·) is a zero-order first kind Bessel function, τ is an integral variable, A is a light intensity control parameter, a is an exponential attenuation factor, R0 is a dimensionless radius of the main ring, s r is a dimensionless radial coordinate, and Ai(·) is an Airy function.

[0030] Optionally, according to the light field integral form, a light intensity distribution of the circular Airy beam on any observation plane in free space transmission and an on-axis light field of the circular Airy beam are determined, specifically including:

[0031] The on-axis light field of the circular Airy beam is obtained by using a formula ;

[0032] Wherein, U(0, z) is a simplified expression of the on-axis light field of the circular Airy beam, i represents an imaginary unit, z0 is a Rayleigh distance, w0 is a scale factor, k represents a wave number, k = 2π / λ, λ is a wavelength of the circular Airy beam, τ is an integral variable, A is a light intensity control parameter, a is an exponential attenuation factor, R0 is a dimensionless radius of the main ring, and Ai(·) is an Airy function.

[0033] Optionally, under the condition of a given exponential attenuation factor, the dimensionless radius of the main ring in the circular Airy beam is changed, a first curve graph is drawn according to the on-axis light field, and then the method further comprises:

[0034] Under the condition of a given exponential attenuation factor, a second curve graph is drawn according to the on-axis light field by changing the dimensionless radius of the main ring of the circular Airy beam; the second curve graph is a curve graph of a focal length of the circular Airy beam relative to the dimensionless radius;

[0035] The optimal focal length of the circular Airy beam is determined according to the second curve graph and the optimal dimensionless radius value.

[0036] To achieve the above object, the present application further provides the following scheme:

[0037] A system for improving the sudden self-focusing ability of a circular Airy beam, comprising:

[0038] A beam parameter acquisition module is configured to acquire beam parameters of a circular Airy beam transmitted in free space; the beam parameters include a light intensity control parameter, an exponential attenuation factor, a radius of a main ring, a scale factor, and an Airy function.

[0039] A light field determination module is configured to determine a light field of the circular Airy beam on an initial plane according to the beam parameters.

[0040] A light field dimensionless processing module is configured to perform dimensionless processing on the light field to obtain a dimensionless light field.

[0041] A light field integral form determination module is configured to determine an integral form of the light field of the circular Airy beam transmitted in free space according to the dimensionless light field by using a Collins integral formula.

[0042] A coordinate system establishment module is configured to establish a space rectangular coordinate system by taking a transmission direction of the circular Airy beam as a z-axis and dividing an x-axis and a y-axis in a plane perpendicular to the z-axis.

[0043] a plane determination module configured to divide, based on the rectangular coordinate system, a plurality of observation planes according to different values of the z-axis longitudinal coordinate; the observation planes include an initial plane and a focal plane; the observation plane with z=0 is taken as the initial plane, and the observation plane corresponding to the peak value of the light intensity of the light field on the optical axis of the circular Airy beam is taken as the focal plane, and z is the coordinate of the z-axis in the rectangular coordinate system;

[0044] a light intensity distribution determination module configured to determine the light intensity distribution of the circular Airy beam on any observation plane in free space transmission according to the light field integral form;

[0045] an on-axis light field determination module configured to determine the on-axis light field of the circular Airy beam according to the light field integral form;

[0046] a light intensity peak value determination module configured to determine the light intensity peak value on the focal plane according to the on-axis light field, and determine the light intensity peak value on the initial plane according to the light intensity distribution on the initial plane;

[0047] an intensity contrast determination module configured to determine the intensity contrast according to the light intensity peak value on the focal plane and the light intensity peak value on the initial plane;

[0048] a first curve graph determination module configured to change the dimensionless radius of the main ring of the circular Airy beam under the condition of a given exponential decay factor, and draw a first curve graph according to the on-axis light field; the first curve graph is a curve graph of the intensity contrast versus the dimensionless radius;

[0049] an optimal dimensionless radius value determination module configured to determine an optimal dimensionless radius according to the first curve graph and the intensity contrast;

[0050] a strongest sudden self-focusing ability determination module configured to obtain the strongest sudden self-focusing ability of the circular Airy beam according to the optimal dimensionless radius.

[0051] Optionally, the method further comprises:

[0052] a second curve graph determination module configured to change the dimensionless radius of the main ring of the circular Airy beam under the condition of a given exponential decay factor, and draw a second curve graph according to the on-axis light field; the second curve graph is a curve graph of the focal length of the circular Airy beam versus the dimensionless radius;

[0053] an optimal focal length determination module configured to determine an optimal focal length of the circular Airy beam according to the second curve graph and the optimal dimensionless radius value.

[0054] Optionally, the method further comprises a solid-state laser;

[0055] the solid-state laser is configured to generate a fundamental mode Gaussian beam.

[0056] Optionally, further comprising: a phase spatial light modulator, a circular aperture and a Fourier lens;

[0057] The phase spatial light modulator is configured to perform phase modulation on the fundamental mode Gaussian beam to obtain modulated light.

[0058] The circular aperture is configured to screen the first diffraction order of the modulated light.

[0059] The Fourier lens is configured to perform Fourier transform on the light corresponding to the first diffraction order in the modulated light to obtain the circular Airy beam at the focal length of the Fourier lens.

[0060] According to the specific embodiments of the present application, the following technical effects are disclosed:

[0061] The method and system for improving the sudden self-focusing ability of the circular Airy beam provided by the present application determine the transmission direction of the circular Airy beam by obtaining the circular Airy beam transmitted in free space and establishing a spatial rectangular coordinate system, determine the light intensity distribution of the circular Airy beam on the focal plane and the initial plane and the on-axis light field of the circular Airy beam according to the light field integral form of the circular Airy beam on any observation plane, and determine the intensity contrast according to the light intensity distribution and the on-axis light field. Under the condition of a given exponential decay factor, by changing the dimensionless radius of the main ring in the circular Airy beam, a first curve graph is drawn according to the on-axis light field, the optimal dimensionless radius is determined according to the first curve graph and the intensity contrast, and finally the strongest sudden self-focusing ability of the circular Airy beam is obtained according to the optimal dimensionless radius. The present application realizes the improvement of the sudden self-focusing ability of the circular Airy beam. BRIEF DESCRIPTION OF DRAWINGS

[0062] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0063] Figure 1 The flowchart of the method for improving the sudden self-focusing ability of the circular Airy beam provided by the present application;

[0064] Figure 2 The curve graph provided by the present application; Figure 2 (a) The curve graph of the intensity contrast versus the dimensionless radius provided by the present application; Figure 2 (b) The curve graph of the focal length versus the dimensionless radius provided by the present application;

[0065] Figure 3Intensity distribution of the dimensionless radius 5 circular Airy beam provided by the present application on different observation planes in free space; Figure 3 (a) Intensity distribution of the dimensionless radius 5 circular Airy beam provided by the present application on the z=0 observation plane in free space; Figure 3 (b) Intensity distribution of the dimensionless radius 5 circular Airy beam provided by the present application on the z=0.577m observation plane in free space; Figure 3 (c) Intensity distribution of the dimensionless radius 5 circular Airy beam provided by the present application on the z=0.961m observation plane in free space; Figure 3 (d) Intensity distribution of the dimensionless radius 5 circular Airy beam provided by the present application on the z=1.081m observation plane in free space;

[0066] Figure 4 Intensity distribution of the dimensionless radius 15.6 circular Airy beam provided by the present application on different observation planes in free space; Figure 4 (a) Intensity distribution of the dimensionless radius 15.6 circular Airy beam provided by the present application on the z=0 observation plane in free space; Figure 4 (b) Intensity distribution of the dimensionless radius 15.6 circular Airy beam provided by the present application on the z=0.577m observation plane in free space; Figure 4 (c) Intensity distribution of the dimensionless radius 15.6 circular Airy beam provided by the present application on the z=0.961m observation plane in free space; Figure 4 (d) Intensity distribution of the dimensionless radius 15.6 circular Airy beam provided by the present application on the z=1.081m observation plane in free space;

[0067] Figure 5 Intensity distribution of the dimensionless radius 20 circular Airy beam provided by the present application on different observation planes in free space; Figure 5 (a) Intensity distribution of the dimensionless radius 20 circular Airy beam provided by the present application on the z=0 observation plane in free space; Figure 5 (b) Intensity distribution of the dimensionless radius 20 circular Airy beam provided by the present application on the z=0.577m observation plane in free space; Figure 5 (c) Intensity distribution of the dimensionless radius 20 circular Airy beam provided by the present application on the z=0.961m observation plane in free space; Figure 5 (d) Intensity distribution of the dimensionless radius 20 circular Airy beam provided by the present application on the z=1.081m observation plane in free space;

[0068] Figure 6The structural diagram of the system for improving the sudden self-focusing ability of the circular Airy beam provided by the application. DETAILED DESCRIPTION

[0069] The technical solutions in the embodiments of the application will be clearly and completely described below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are only part of the embodiments of the application, rather than all the embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the application.

[0070] The application aims to provide a method and a system for improving the sudden self-focusing ability of a circular Airy beam. The method comprises the following steps: obtaining a circular Airy beam transmitted in free space and establishing a spatial rectangular coordinate system to determine the transmission direction of the circular Airy beam; determining the light intensity distribution of the circular Airy beam on a focal plane and an initial plane and the on-axis light field of the circular Airy beam according to the light field integral form of the circular Airy beam on any observation plane; and determining the intensity contrast according to the light intensity distribution and the on-axis light field. Under the condition of a given exponential decay factor, the dimensionless radius of the main ring in the circular Airy beam is changed, a first curve graph is drawn according to the on-axis light field, the optimal dimensionless radius is determined according to the first curve graph and the intensity contrast, and finally the strongest sudden self-focusing ability of the circular Airy beam is obtained according to the optimal dimensionless radius. The application realizes the improvement of the sudden self-focusing ability of the circular Airy beam.

[0071] In order to make the above-mentioned objects, features and advantages of the application more obvious and easy to understand, the application will be further described in detail below with reference to the drawings and specific embodiments.

[0072] Embodiment one

[0073] As shown in the accompanying drawings, Figure 1 The application provides a method for improving the sudden self-focusing ability of a circular Airy beam, which specifically comprises the following steps:

[0074] Step 101: obtaining the beam parameters of a circular Airy beam transmitted in free space; the beam parameters include light intensity control parameters, an exponential decay factor, the radius of a main ring, a scale factor and an Airy function.

[0075] Specifically, the obtaining process of the circular Airy beam transmitted in free space is as follows:

[0076] A solid-state laser generates a fundamental mode Gaussian beam. The generated fundamental mode Gaussian beam is expanded and split, and then is incident to a phase-type spatial light modulator for phase modulation. The modulated light reflected from the spatial light modulator is first filtered by a circular diaphragm to obtain the first diffraction order, and then is subjected to Fourier transform by a Fourier lens. The circular Airy beam can be obtained at the focal length of the Fourier lens, and the beam parameters are controlled by the program uploaded to the spatial light modulator.

[0077] Step 102: determining the light field of the circular Airy beam on the initial plane according to the beam parameters.

[0078] Specifically comprising:

[0079] The formula is used to determine the light field of the circular Airy beam on the initial plane.

[0080] Wherein, U(r, 0) is the expression of the light field of the circular Airy beam on the initial plane, z=0 in the initial plane, r represents the radial coordinate, r=(x 2 +y 2 ) 1 / 2 ; x is the coordinate of the x-axis in the rectangular coordinate system, y is the coordinate of the y-axis in the rectangular coordinate system, A is the light intensity control parameter, A ensures that the peak value of the light intensity of the circular Airy beam on the initial plane is always 1, a is the exponential decay factor, r0 is the radius of the main ring, w0 is the scale factor, and Ai(·) is the Airy function.

[0081] Step 103: performing dimensionless processing on the light field to obtain a dimensionless light field.

[0082] Specifically comprising:

[0083] The formula U1(r, 0)=Aexp[a(R0-s r )]Ai(R0-s r ) is used to obtain the dimensionless light field.

[0084] Wherein, U1(r, 0) is the expression of the dimensionless light field of the circular Airy beam on the initial plane, R0=r0 / w0, R0 is the dimensionless radius of the main ring, s r =r / w0, s r is the dimensionless radial coordinate, r0 is the radius of the main ring, w0 is the scale factor, r is the radial coordinate, a is the exponential decay factor, A is the light intensity control parameter, and Ai(·) is the Airy function.

[0085] Step 104: according to the dimensionless light field, the integral form of the light field of the circular Airy beam in free space transmission is determined by using the Collins integral formula.

[0086] The Collins integral formula is:

[0087]

[0088] Wherein, U(r, z) is the integral expression of the light field of the circular Airy beam in free space transmission, i represents the imaginary unit, k is the wave number, k=2π / λ, and λ is the wavelength of the circular Airy beam.​ is the angular coordinate, r' and is the integral variable.

[0089] The dimensionless light field expression of the circular Airy beam on the initial plane z = 0 is substituted into the above formula, and the formula The integral expression of the light field of the circular Airy beam on any observation plane z can be obtained:

[0090]

[0091] wherein U(r, z) is the integral expression of the light field of the circular Airy beam in free space transmission, i represents an imaginary unit, z0 is a Rayleigh distance, w0 is a scale factor, k represents a wave number, k = 2p / l, l is a wavelength of the circular Airy beam, J0(·) is a zero-order first kind Bessel function, t is an integral variable, A is a light intensity control parameter, a is an exponential attenuation factor, R0 is a dimensionless radius of the main ring, s r is a dimensionless radial coordinate, and Ai(·) is an Airy function.

[0092] Step 105: A spatial rectangular coordinate system is established with the direction of the circular Airy beam transmission as the z-axis, and the x-axis and the y-axis are divided in a plane perpendicular to the z-axis.

[0093] Step 106: Based on the spatial rectangular coordinate system, the z-axis coordinate is divided into multiple observation planes according to different values; the observation planes include an initial plane and a focal plane; the observation plane of z = 0 is taken as the initial plane, and the observation plane corresponding to the peak value of the light intensity of the on-axis light field of the circular Airy beam is taken as the focal plane, and z is the coordinate of the z-axis in the spatial rectangular coordinate system.

[0094] Step 107: The light intensity distribution of the circular Airy beam on any observation plane in free space transmission and the on-axis light field of the circular Airy beam are determined according to the integral form of the light field.

[0095] For the on-axis point of the transmission axis, the integral expression of the light field can be further simplified as:

[0096]

[0097] wherein U(0, z) is the simplified expression of the on-axis light field of the circular Airy beam, i represents an imaginary unit, z0 is a Rayleigh distance, w0 is a scale factor, k represents a wave number, k = 2p / l, l is a wavelength of the circular Airy beam, t is an integral variable, A is a light intensity control parameter, a is an exponential attenuation factor, R0 is a dimensionless radius of the main ring, and Ai(·) is an Airy function.

[0098] The on-axis light intensity of the circular Airy beam is:

[0099] I(0,z)=|U(0,z)| 2 .

[0100] wherein I(0,z) is the light intensity of the circular Airy beam at the on-axis position z.

[0101] Step 108: determining the light intensity peak (I fp ) on the focal plane according to the on-axis light field.

[0102] Step 109: determining the light intensity peak (I 0p ) on the initial plane according to the light intensity distribution on the initial plane.

[0103] Step 110: determining the intensity contrast according to the light intensity peak on the focal plane and the light intensity peak on the initial plane.

[0104] Specifically, the sudden self-focusing ability of the circular Airy beam is described by the intensity contrast I fp / I 0p .

[0105] Step 111: changing the dimensionless radius of the main ring in the circular Airy beam under the condition of a given exponential decay factor, and drawing a first curve and a second curve according to the on-axis light field; the first curve is a curve of the intensity contrast versus the dimensionless radius, and the second curve is a curve of the focal length of the circular Airy beam versus the dimensionless radius.

[0106] Specifically, since the circular Airy beam has circular symmetry on the initial plane z=0, the focal point must appear on the axis, and the plane with the peak on-axis light intensity is the focal plane. Since the light intensity peak I 0p on the initial plane is 1, the on-axis light intensity peak I fp reflects the sudden self-focusing ability. By searching for the maximum value in I(0,z)=|U(0,z)| 2 , I fp and the corresponding focal length (z f ) can be found, wherein the focal length z f of the circular Airy beam is defined as the distance between the focal plane and the initial plane.

[0107] Step 112: determining the optimal dimensionless radius according to the first curve and the intensity contrast.

[0108] Step 113: obtaining the strongest sudden self-focusing ability of the circular Airy beam according to the optimal dimensionless radius.

[0109] The optimal focal length of the circular Airy beam can also be determined according to the second curve and the optimal non-dimensional radius value.

[0110] According to the given focal position spot image, the formula in step 104 is used to give the spot image of the circular Airy beam at the focal position under three conditions that R0 is less than, equal to and greater than the optimal non-dimensional radius value respectively, and the correctness of step 112 is verified by comparing and analyzing the sudden self-focusing ability.

[0111] The method of the embodiment of the application is simple and effective, and when the non-dimensional radius takes the optimal non-dimensional radius value, the sudden self-focusing ability of the circular Airy beam reaches the strongest under the condition of a given exponential attenuation factor.

[0112] The sudden self-focusing ability of the circular Airy beam is analyzed in detail as follows: the characteristic parameters of the circular Airy beam are selected as follows: a = 0.05, w0 = 0.1 mm, and λ = 532 nm. Figure 2 The (a) part of the figure gives the intensity contrast I fp / I 0p versus the non-dimensional radius R0, that is, the first curve, Figure 2 The (b) part of the figure gives the focal length z f versus the non-dimensional radius R0, that is, the second curve. Figure 2 In the figure, the dotted line is added for convenience of illustration, when the non-dimensional radius R0 increases from zero to 15.6, the intensity contrast I fp / I 0p is always increasing, when the non-dimensional radius R0 further increases from 15.6, the intensity contrast I fp / I 0p decreases, and the focal length z f increases with the increase of the non-dimensional radius R0, when R0 = 15.6, the intensity contrast I fp / I 0p takes the maximum value 155.86, and the corresponding focal length z f = 0.961 m. Therefore, R0 = 15.6 is called the optimal non-dimensional radius value, and at this time, the sudden self-focusing ability of the circular Airy beam is the strongest.

[0113] Figures 3 to 5 The intensity distribution diagrams of the circular Airy beams with R0 = 5, R0 = 15.6 and R0 = 20 respectively in different observation planes in free space. Figures 3 to 5The intensity distributions of the (a) part-(d) part correspond to the free space z=0 observation plane, z=0.577m observation plane, z=0.961m observation plane and z=1.081m observation plane respectively. Among them, the z=0.577m observation plane, z=0.961m observation plane and z=1.081m observation plane are the focal planes of the circular Airy beams with R0=5, R0=15.6 and R0=20 respectively. In the initial plane z=0, the intensity pattern of the circular Airy beam is composed of a series of concentric rings, and the hollow area increases with the increase of R0. In the z=0.577m observation plane, the circular Airy beam with R0=5 is just self-focused, and its sudden self-focusing ability is 87.44, while the circular Airy beams with R0=15.6 and R0=20 have not yet self-focused, and the light intensity peaks of the circular Airy beams with R0=15.6 and R0=20 are only 1.16 and 0.99 respectively. In the z=0.961m observation plane, the circular Airy beam with R0=15.6 is just self-focused, and its sudden self-focusing ability is 155.86, while the circular Airy beam with R0=20 has not yet self-focused, and its light intensity peak is 1.74; the light intensity peak of the circular Airy beam with R0=5 is 5.4. In the z=1.081m observation plane, the circular Airy beam with R0=20 is just self-focused, and its sudden self-focusing ability is 149.11, while the circular Airy beams with R0=5 and R0=15.6 have not yet self-focused, and their light intensity peaks are 1.63 and 17.26 respectively.

[0114] In summary, when R0 is less than the optimal dimensionless radius value and R0 is greater than the optimal dimensionless radius value, the sudden self-focusing ability of the circular Airy beam is weaker than that when R0 is equal to the optimal dimensionless radius value. Therefore, in terms of sudden self-focusing ability, the optimal dimensionless radius value is the best choice for R0.

[0115] In practical applications, the method for improving the sudden self-focusing ability of the circular Airy beam given in the above embodiment can be applied to medical treatment, optical trapping, photon bullets, atomic manipulation, multi-photon polymerization, terahertz emission, optical communication, optical manipulation, dynamic imaging, image transmission and food safety detection.

[0116] The application of the method of the present embodiment will be specifically described below taking a medical treatment system as an example. In medical treatment, the circular Airy beam is used as a laser scalpel, and the lesion site is used as the focal position. According to the required focal intensity, the exponential decay factor a and the optimal dimensionless radius R0 of the main ring of the circular Airy beam are determined. Then, according to the specific lesion position, the scale factor w0 is selected. The focal length of the circular Airy beam is calculated as follows: f =2kw0(w0r p ) 1 / 2 , wherein r pThe first light intensity extreme peak counted from inside to outside on the initial plane z=0 of the circular Airy beam. It ensures that the light intensity of the circular Airy beam remains at a low level before reaching the lesion, avoids strong interaction between the circular Airy beam and the biological tissue before reaching the lesion, thereby minimizing the burn of the biological tissue through which the circular Airy beam passes, and the circular Airy beam self-focuses at the lesion, so that the light intensity is high enough to remove the lesion and achieve minimally invasive treatment.

[0117] Embodiment two

[0118] The application provides a system for improving the sudden self-focusing ability of a circular Airy beam, and specifically comprises the following steps of:

[0119] The light beam parameter acquisition module 601 is configured to acquire the light beam parameters of the circular Airy beam transmitted in free space; the light beam parameters include light intensity control parameters, an exponential decay factor, the radius of the main ring, a scale factor and an Airy function.

[0120] The light field determination module 602 is configured to determine the light field of the circular Airy beam on the initial plane according to the light beam parameters.

[0121] The light field dimensionless module 603 is configured to perform dimensionless processing on the light field to obtain a dimensionless light field.

[0122] The light field integral form determination module 604 is configured to determine the integral form of the light field of the circular Airy beam transmitted in free space by using the Collins integral formula according to the dimensionless light field.

[0123] The coordinate system establishment module 605 is configured to establish a space rectangular coordinate system by taking the transmission direction of the circular Airy beam as the z-axis and dividing the plane perpendicular to the z-axis into the x-axis and the y-axis.

[0124] The plane determination module 606 is configured to divide the space rectangular coordinate system into multiple observation planes according to different values of the z-axis longitudinal coordinate; the observation planes include an initial plane and a focal plane; the observation plane of z=0 is taken as the initial plane, and the observation plane corresponding to the peak value of the light intensity of the light field on the optical axis of the circular Airy beam is taken as the focal plane, and z is the coordinate of the z-axis in the space rectangular coordinate system.

[0125] The light intensity distribution determination module 607 is configured to determine the light intensity distribution of the circular Airy beam transmitted in free space on any observation plane according to the integral form of the light field.

[0126] The on-axis light field determination module 608 is configured to determine the on-axis light field of the circular Airy beam according to the integral form of the light field.

[0127] The light intensity peak determination module 609 is configured to determine a light intensity peak on the focal plane according to the on-axis light field, and determine a light intensity peak on the initial plane according to the light intensity distribution on the initial plane.

[0128] The intensity contrast determination module 610 is configured to determine an intensity contrast according to the light intensity peak on the focal plane and the light intensity peak on the initial plane.

[0129] The first curve graph determination module 611 is configured to change a dimensionless radius of a main ring in the circular Airy beam under the condition of a given exponential decay factor, and draw a first curve graph according to the on-axis light field; the first curve graph is a curve graph of the intensity contrast relative to the dimensionless radius.

[0130] The optimal dimensionless radius value determination module 612 is configured to determine an optimal dimensionless radius according to the first curve graph and the intensity contrast.

[0131] The strongest sudden self-focusing ability determination module 613 is configured to obtain a strongest sudden self-focusing ability of the circular Airy beam according to the optimal dimensionless radius.

[0132] The system for improving the sudden self-focusing ability of the circular Airy beam further comprises a second curve graph determination module, an optimal focal length determination module, a solid-state laser, a phase-type spatial light modulator, a circular aperture and a Fourier lens.

[0133] The second curve graph determination module is configured to change the dimensionless radius of the main ring of the circular Airy beam under the condition of a given exponential decay factor, and draw a second curve graph according to the on-axis light field; the second curve graph is a curve graph of a focal length of the circular Airy beam relative to the dimensionless radius.

[0134] The optimal focal length determination module is configured to determine an optimal focal length of the circular Airy beam according to the second curve graph and the optimal dimensionless radius value.

[0135] The solid-state laser is configured to generate a fundamental mode Gaussian beam.

[0136] The phase-type spatial light modulator is configured to perform phase modulation on the fundamental mode Gaussian beam to obtain modulated light.

[0137] The circular aperture is configured to screen a first diffraction order of the modulated light.

[0138] The Fourier lens is configured to perform Fourier transform on light corresponding to the first diffraction order in the modulated light, and obtain the circular Airy beam at a focal length of the Fourier lens.

[0139] The various embodiments described in this specification are presented for the purpose of illustrating the principles of the present application and its best mode of operation. Each of the embodiments described in this specification has been provided for the purpose of illustration only and the various embodiments are not intended to limit the present application in any way unless otherwise specifically indicated. The same parts and / or features of the various embodiments described in this specification can be referenced using the same reference numerals for the ease of understanding of the present application.

[0140] The principles and implementations of the present application have been described in the above embodiments, which are only used to help understand the method of the present application and its core idea. Meanwhile, for those skilled in the art, the specific implementation and application range of the present application can be changed according to the idea of the present application. In summary, the content of the specification should not be understood as a limitation of the present application.

Claims

1. A method for improving the sudden self-focusing ability of a circular Airy beam, characterized in that, The method comprises the following steps: obtaining the beam parameters of the circular Airy beam transmitted in free space; the beam parameters include light intensity control parameters, exponential attenuation factors, the radius of the main ring, scale factors and Airy functions; determining the light field of the circular Airy beam on an initial plane according to the beam parameters; dimensionless processing the light field to obtain a dimensionless light field; determining the integral form of the light field of the circular Airy beam in free space transmission according to the dimensionless light field by using the Collins integral formula; establishing a space rectangular coordinate system with the direction of the circular Airy beam transmission as the z-axis and the plane perpendicular to the z-axis as the x-axis and the y-axis; dividing the z-axis coordinate into multiple observation planes based on the space rectangular coordinate system; the observation planes include an initial plane and a focal plane; the observation plane with z=0 is taken as the initial plane, and the observation plane corresponding to the peak value of the light intensity of the light field on the optical axis of the circular Airy beam is taken as the focal plane, and z is the coordinate of the z-axis in the space rectangular coordinate system; determining the light intensity distribution of the circular Airy beam on any observation plane in free space transmission and the on-axis light field of the circular Airy beam according to the integral form of the light field; determining the light intensity peak value on the focal plane according to the on-axis light field; determining the light intensity peak value on the initial plane according to the light intensity distribution on the initial plane; determining the intensity contrast according to the light intensity peak value on the focal plane and the light intensity peak value on the initial plane; under the condition of a given exponential attenuation factor, changing the dimensionless radius of the main ring of the circular Airy beam, and drawing a first curve according to the on-axis light field; the first curve is a curve of the intensity contrast with respect to the dimensionless radius; determining the optimal dimensionless radius according to the first curve and the intensity contrast; obtaining the strongest sudden self-focusing ability of the circular Airy beam according to the optimal dimensionless radius.

2. The method of claim 1, wherein the method is performed by a computer system. The method for determining the light field of the circular Airy beam on an initial plane according to the beam parameters specifically comprises the following steps: Using the formula determining the light field of the circular Airy beam on the initial plane; wherein U(r, 0) is an expression of the light field of the circular Airy beam on the initial plane, in which z = 0, r represents a radial coordinate, r = (x 2 +y 2 ) 1 / 2 , x is a coordinate of an x-axis in a rectangular coordinate system, y is a coordinate of a y-axis in the rectangular coordinate system, A is a light intensity control parameter, A ensures that a light intensity peak value of the circular Airy beam on the initial plane is always 1, a is an exponential decay factor, r0 is a radius of the main ring, w0 is a scale factor, and Ai(·) is an Airy function.

3. The method of claim 1, wherein the method is performed by a computer system. dimensionless processing the light field to obtain a dimensionless light field; The dimensionless optical field is obtained using the formula U1(r, 0) = Aexp[a(R0-s r )]Ai(R0-s r ) where U1(r, 0) is the dimensionless light field expression of the circular Airy beam on the initial plane, R0 = r0 / w0, R0 is the dimensionless radius of the main ring, s r = r / w0, s r is the dimensionless radial coordinate, r0 is the radius of the main ring, w0 is the scale factor, r is the radial coordinate, a is the exponential decay factor, A is the light intensity control parameter, Ai(·) is the Airy function.

4. The method of claim 1, wherein the method is performed by a computer system. determining the integral form of the light field of the circular Airy beam in free space transmission according to the dimensionless light field by using the Collins integral formula; The light field integral form of the circular Airy beam in free space transmission is determined by the formula The light field integral form of the circular Airy beam in free space transmission is determined by the formula Wherein, U(r, z) is an integral expression of the light field of the circular Airy beam in free space transmission, i represents an imaginary unit, z0 is a Rayleigh distance, w0 is a scale factor, k represents a wave number, k = 2pi / lambda, lambda is a wavelength of the circular Airy beam, J0(·) is a zero-order first kind Bessel function, tau is an integral variable, A is a light intensity control parameter, a is an exponential attenuation factor, R0 is a dimensionless radius of the main ring, s r is a dimensionless radial coordinate, Ai(·) is an Airy function.

5. The method of claim 1, wherein the method is performed by a computer system. determining the light intensity distribution of the circular Airy beam on any observation plane in free space transmission and the on-axis light field of the circular Airy beam according to the integral form of the light field; The on-axis light field of the circular Airy beam is obtained by using the formula E (r, 0) = E0J0 (kr) wherein U(0, z) is a simplified expression of the on-axis light field of the circular Airy beam, i represents an imaginary unit, and z0is a Rayleigh range, w0is a scale factor, k represents a wave number, k = 2π / λ, λ is a wavelength of the circular Airy beam, τ is an integral variable, A is a light intensity control parameter, a is an exponential attenuation factor, R0is a dimensionless radius of the main ring, and Ai(·) is an Airy function.

6. The method of claim 1, wherein the method is performed by a computer system. under the condition of a given exponential attenuation factor, changing the dimensionless radius of the main ring of the circular Airy beam, and drawing a first curve according to the on-axis light field; the first curve is a curve of the intensity contrast with respect to the dimensionless radius; under the condition of a given exponential attenuation factor, changing the dimensionless radius of the main ring of the circular Airy beam, and drawing a second curve according to the on-axis light field; the second curve is a curve of the focal length of the circular Airy beam with respect to the dimensionless radius; determining the optimal focal length of the circular Airy beam according to the second curve and the optimal dimensionless radius value.

7. A system for improving the sudden self-focusing capability of a circular Airy beam, characterized in that, The method comprises the following steps: a beam parameter acquisition module is configured to obtain the beam parameters of the circular Airy beam transmitted in free space; The light beam parameters include light intensity control parameters, an exponential decay factor, a radius of a main ring, a scale factor, and an airy function; a light field determination module configured to determine a light field of the circular airy light beam on an initial plane according to the light beam parameters; a light field dimensionless processing module configured to perform dimensionless processing on the light field to obtain a dimensionless light field; a light field integral form determination module configured to determine a light field integral form of the circular airy light beam in free space transmission according to the dimensionless light field by using a Collins integral formula; a coordinate system establishment module configured to establish a space rectangular coordinate system with a direction of transmission of the circular airy light beam as a z-axis, and with an x-axis and a y-axis divided in a plane perpendicular to the z-axis; a plane determination module configured to divide, based on the space rectangular coordinate system, a plurality of observation planes according to different values of a z-axis ordinate; the observation planes include an initial plane and a focal plane; the observation plane with z = 0 is taken as the initial plane, and the observation plane corresponding to a peak value of light intensity of the light field on the optical axis of the circular airy light beam is taken as the focal plane, and z is a coordinate of the z-axis in the space rectangular coordinate system; a light intensity distribution determination module configured to determine a light intensity distribution of the circular airy light beam on any observation plane in free space transmission according to the light field integral form; an on-axis light field determination module configured to determine an on-axis light field of the circular airy light beam according to the light field integral form; a light intensity peak value determination module configured to determine a light intensity peak value on the focal plane according to the on-axis light field, and determine a light intensity peak value on the initial plane according to the light intensity distribution on the initial plane; an intensity contrast determination module configured to determine an intensity contrast according to the light intensity peak value on the focal plane and the light intensity peak value on the initial plane; a first curve graph determination module configured to change a dimensionless radius of a main ring in the circular airy light beam under a condition that an exponential decay factor is given, and draw a first curve graph according to the on-axis light field; the first curve graph is a graph of the intensity contrast with respect to the dimensionless radius; an optimal dimensionless radius value determination module configured to determine an optimal dimensionless radius according to the first curve graph and the intensity contrast; a light beam strongest sudden self-focusing ability determination module configured to obtain a strongest sudden self-focusing ability of the circular airy light beam according to the optimal dimensionless radius.

8. The system for increasing the ability of sudden self-focusing of a circular Airy beam according to claim 7, characterized in that, Further comprising: a second curve graph determination module configured to change the dimensionless radius of the main ring of the circular airy light beam under a condition that the exponential decay factor is given, and draw a second curve graph according to the on-axis light field; the second curve graph is a graph of a focal length of the circular airy light beam with respect to the dimensionless radius; an optimal focal length determination module configured to determine an optimal focal length of the circular airy light beam according to the second curve graph and the optimal dimensionless radius value.

9. The system for increasing the ability of sudden self-focusing of a circular Airy beam according to claim 8, characterized in that, Further comprising: a solid laser; the solid laser is configured to generate a fundamental mode Gaussian light beam.

10. The system for increasing the ability of sudden self-focusing of a circular Airy beam according to claim 9, characterized in that, Further comprising: a phase-type spatial light modulator, a circular diaphragm, and a Fourier lens; the phase-type spatial light modulator is configured to perform phase modulation on the fundamental mode Gaussian light beam to obtain a modulated light; the circular diaphragm is configured to screen a first diffraction order of the modulated light; The Fourier lens is used for Fourier transform of light corresponding to a first diffraction order of the modulated light, and the circular Airy beam is obtained at a focal length of the Fourier lens.

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