Apparatus and method for generating and controlling digital airy-like beams

Abstract

The application provides a device and method for generating and controlling digital Airy-like beams, which comprises a light source, a first reflection system, a thin lens system (a first thin lens and a second thin lens), a phase modulation system (a first spatial light modulator and a second spatial light modulator), a second reflection system and an observation system; the light source is used for generating circularly polarized laser, and the circularly polarized laser sequentially passes through the first reflection system, the first thin lens, the first spatial light modulator, the second thin lens, the second spatial light modulator and the second reflection system to generate an Airy-like beam; the first reflection system and the second reflection system are used for calibrating incident light, the first thin lens is used for inversely Fourier transforming incident light, the second thin lens is used for Fourier transforming incident light, the first spatial light modulator and the second spatial light modulator are respectively used for performing cubic phase modulation on incident light waves, and the observation system is used for capturing the intensity distribution of the generated Airy-like beam.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of optical technology, in particular to a kind of generation and control device and method of digitalized airy-like light beam. BACKGROUND

[0002] As a kind of spatial structure light field with special phase structure and polarization state, airy beam can realize approximate non-diffraction and attenuation within a certain transmission distance, it has three characteristics, namely non-diffraction, self-acceleration and self-repairing.The non-diffraction characteristic determines that airy can carry huge energy.The self-acceleration is different from the characteristic that general light beam propagates along a straight line in free space, but has a parabolic trajectory.The self-repairing is that when a part of the airy light beam is blocked in the cross-section direction during propagation, the remaining part of the airy light beam restores to the light intensity distribution at the blocking position in the cross-section after a certain distance of transmission.The characteristics of airy light beam make it can carry a large amount of data and transmit quickly and accurately, and can bypass some obstacles that ordinary light beam cannot penetrate, to realize high-quality transmission in short distance.So far, the unique characteristics of airy light beam have been widely used in many fields, including optical particle removal, curved plasma channel, time-space photon bullet, laser micro-processing and super-resolution imaging, etc., and the research of non-diffraction and self-acceleration light has become a frontier subject.

[0003] The existing generation method of airy light beam is mainly based on spatial light modulator to generate airy light beam in full phase mode.Theory analysis, the numerical simulation lens phase distribution and cubic phase distribution are directly loaded to spatial light modulator, the system composed of transmission between two polarizers can create a transmission function with negative value, and the observation result can be used for other various wavefront modulation in the case of requiring negative value in transmission function, so as to generate airy light beam at the focal plane of lens.The control and measurement of airy light beam are mainly based on multi-coordinate transformation technology, which establishes an additional coordinate system for different component light beams of airy light beam, realizes the disassembly of composite light field.Then the transformation between polar coordinate system, rectangular coordinate system and elliptical coordinate system is carried out for one-dimensional airy light beam and two-dimensional airy light beam, to realize the control of airy light beam transverse and longitudinal sidelobes. SUMMARY

[0004] Therefore, the present application aims to provide a kind of generation and control device and method of digitalized airy-like light beam, to at least solve the deficiencies in the related art.

[0005] The present application provides a kind of generation and control device of digitalized airy-like light beam, including light source, first reflection system, thin lens system, phase modulation system, second reflection system and observation system;

[0006] The thin lens system comprises a first thin lens and a second thin lens, the phase modulation system comprises a first spatial light modulator and a second spatial light modulator, the light source is used for generating circularly polarized laser, and the circularly polarized laser sequentially passes through the first reflection system, the first spatial light modulator, the first thin lens, the second thin lens, the second spatial light modulator and the second reflection system to generate an Airy-like light beam;

[0007] The first reflection system and the second reflection system are used for calibrating incident light, the first thin lens is used for inverse Fourier transform of incident light, the second thin lens is used for Fourier transform of incident light, the first spatial light modulator and the second spatial light modulator are respectively used for cubic phase modulation of incident light waves, and the observation system is used for capturing the intensity distribution of the generated Airy-like light beam.

[0008] Further, a beam expander is arranged between the light source and the first reflection system, and the beam expander is used for expanding and collimating the circularly polarized laser generated by the light source.

[0009] Further, the phase modulation system further comprises a third spatial light modulator, a beam splitter is arranged between the second reflection system and the third spatial light modulator, the beam splitter is used for splitting the laser beam into a first light wave and a second light wave, the third spatial light modulator is used for spectrum analysis of the first light wave, and the analysis result is output to the observation system, and the observation system is used for capturing the second light wave.

[0010] Further, circular apertures are arranged between the first spatial light modulator and the beam expander, and between the first thin lens and the second thin lens, and the circular apertures are used for adjusting the energy distribution of incident light.

[0011] Further, the observation system comprises a CCD camera, the CCD camera is installed on a parallel moving platform, the parallel moving platform is parallel to the propagation Z axis of the light beam, and the CCD camera moves along the propagation optical axis of the light beam through the parallel moving platform.

[0012] The application further provides a digital Airy-like light beam generation and control method applied to the digital Airy-like light beam generation and control device.

[0013] Step 1: expanding the circularly polarized laser emitted by the light source to obtain expanded laser;

[0014] Step two: adjust the primary energy distribution of the expanded laser beam, and irradiate the beam after the primary energy distribution adjustment on the mirror of the first reflection system for calibration, and then irradiate the calibrated beam on the first spatial light modulator to make the first spatial light modulator perform cubic phase modulation on the calibrated beam;

[0015] Step three: reflect the beam after the cubic phase modulation to the first thin lens for inverse Fourier transform, and then irradiate the beam after the inverse Fourier transform on the second thin lens for Fourier transform, and then irradiate the beam after the Fourier transform on the second spatial light modulator to make the second spatial light modulator perform spiral phase modulation on the beam after the Fourier transform;

[0016] Step four: reflect the beam after the spiral phase modulation through the second mirror to the beam splitter to generate a first beam and a second beam, irradiate the first beam on the third phase spatial light modulator for spectrum analysis, and irradiate the second beam on the observation system for capture to obtain the intensity distribution of the corresponding Airy beam.

[0017] Further, the step of energy distribution adjustment comprises:

[0018] Adjust the energy distribution of the light field corresponding to the incident light by using a circular aperture.

[0019] Further, the phase mode function encoded by the first spatial light modulator is:

[0020] ;

[0021] wherein, and are wave vector components, and the wave vector , and are the control parameters of the first spatial light modulator in the transverse and longitudinal directions respectively, and are the actual displacements of the beam in space, m and n are the proportional coefficients of the transverse and longitudinal phase shift amounts respectively;

[0022] The phase mode function encoded by the second spatial light modulator is:

[0023] ;

[0024] wherein, , and the wave vector , represents the focal length of the first thin lens, l represents the topological charge number, Indicates the azimuth angle.

[0025] Furthermore, the phase mode function encoded by the first spatial light modulator is:

[0026] ;

[0027] in, This represents the phase mask function corresponding to the first spatial light modulator. Indicates the cubic phase term in x Control parameters in the direction of axial propagation Indicates the cubic phase term in y Control parameters in the direction of axial propagation This indicates the focal length of the first thin lens. This indicates the focal length of the second thin lens. x express x The value of the first variable corresponding to the direction of axial propagation. y express y The value of the second variable corresponding to the direction of axial propagation;

[0028] The phase mode function encoded by the second spatial light modulator is:

[0029] ;

[0030] in, This represents the phase mask function corresponding to the first spatial light modulator. Indicates the astigmatism measurement coefficient. , l Represents the topological charge number. Indicates the azimuth angle.

[0031] Furthermore, the expression for the trajectory of the light beam in space is:

[0032] ;

[0033] in, Indicates Fourier transform, Represents a spatial domain function. Represent its spectral function, and These represent the horizontal and vertical frequencies in space, respectively.

[0034] Compared with the prior art, the beneficial effects of the present invention are:

[0035] 1. The application utilizes a spatial light modulator-lens combination to generate an Airy-like beam, compensates for the quadratic spectral phase, and the focal length of the lens does not affect the output result, so that an Airy-like beam with sufficient energy can be obtained. In addition, the application has good adaptability, not only can be applied to Airy transformation of Gaussian beams or Gaussian-related beams, but also can be extended to hollow beams, vector vortex beams, pulsed beams, and coherent beams, etc., so that the cost is reduced, can be widely applied in the field of optoelectronics, and makes the Airy beam have more wavelengths.

[0036] 2. By loading a cubic phase film with a phase shift on the spatial light modulator, the target beam generates a corresponding displacement in the output plane. Based on the Fourier transform displacement theorem, by adjusting the proportional coefficient of the transverse and longitudinal relative phase shift, the transverse and longitudinal displacement of the target beam is measured, the linear relationship between the phase shift and the displacement is determined, so as to determine the motion trajectory of the target beam, and the regulation of the initial plane position of the target beam is realized. The starting point of the beam trajectory can be located on any plane after the Fourier lens, so that the regulation range of the target beam is increased, and the disadvantage that the Airy-like beam generated by using the continuous phase plate with cubic distribution cannot be dynamically regulated is made up. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 It is the overall structure diagram of the digital Airy-like beam generation and regulation device in the first embodiment of the application.

[0038] Figure 2 It is the generation schematic diagram of the first vortex phase in the first embodiment of the application.

[0039] Figure 3 It is the generation schematic diagram of the second cubic vortex phase in the first embodiment of the application.

[0040] Figure 4 It is the generation schematic diagram of the second cubic vortex phase in the first embodiment of the application.

[0041] Figure 5 It is the flow chart of the digital Airy-like beam generation and regulation method in the second embodiment of the application.

[0042] MAIN ELEMENT SYMBOL EXPLANATION:

[0043] Laser, light source; L 1, first thin lens; L 2, second thin lens; L 3, third thin lens; L 4, fourth thin lens; L 5, fifth thin lens; RM 1, first mirror; RM 2, second mirror; SLM 1, ; SLM2、; BS , beam splitter; CCD, f 1, focal length of the first thin lens; f2 , focal length of the second thin lens; f 3, focal length of the third thin lens; f 4, focal length of the fourth thin lens; f 5, focal length of the fifth thin lens;

[0044] The following detailed description will further describe the present application in conjunction with the above-mentioned drawings. DETAILED DESCRIPTION

[0045] In order to facilitate the understanding of the present application, the following will be a more comprehensive description of the present application with reference to the relevant drawings. The drawings show several embodiments of the present application. However, the present application can be realized in many different forms and is not limited to the embodiments described herein. On the contrary, the purpose of providing these embodiments is to make the disclosure of the present application more thorough and comprehensive.

[0046] It should be noted that when an element is referred to as "fixed to" another element, it can be directly on another element or there can be a middle element. When an element is considered to be "connected" to another element, it can be directly connected to another element or there can be a middle element. The terms "vertical", "horizontal", "left", "right" and similar expressions used herein are for illustrative purposes only.

[0047] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present application belongs. The terms used in the specification of the present application herein are only for the purpose of describing specific embodiments and are not intended to limit the present application. The term "and / or" used herein includes any and all combinations of one or more related listed items.

[0048] At present, the regulation and measurement of Airy beams usually need to move the phase film or incident light mechanically, change its trajectory shape, or use a specially designed phase film to make it move along a specific trajectory. Although the regulation of the trajectory can be achieved, there are problems such as complex device and large error, and the starting point of the beam trajectory is always fixed on the back focal plane of the Fourier lens, so the regulation range of the trajectory is small.

[0049] In order to meet the actual application requirements, it is necessary to seek a control method which can greatly control the trajectory of the Airy beam and does not need to mechanically move the experimental device. The application carries out optical Airy transformation (i.e. twice optical Fourier transform and once cubic phase modulation) on the incident Gaussian and Gaussian-like light beam to generate an Airy-like light beam, writes a phase shift on the phase part of the frequency spectrum by digitizing, thereby realizing accurate control of the Airy-like light beam.

[0050] The application utilizes the method of writing a phase shift in the frequency domain to control the position and transmission trajectory of the Airy beam. The defects of the previous control scheme, such as complex optical system, cumbersome operation and large error, are improved. By applying a phase shift to the cubic phase, the application can flexibly control the action area of the initial plane of the Airy beam, and the spot shape does not change. In addition, the experimental device does not need to be mechanically moved, which avoids unnecessary errors caused by mechanical movement of the experimental device, reduces the error and simplifies the operation. On this basis, the control range of the light beam can also be increased.

[0051] Embodiment one

[0052] Please refer to Figure 1 , which shows the generation and control device of the digital Airy-like light beam in the first embodiment of the application, the device comprises:

[0053] a light source, a first reflection system, a thin lens system, a phase modulation system, a second reflection system and an observation system;

[0054] The thin lens system comprises a first thin lens and a second thin lens, the phase modulation system comprises a first spatial light modulator and a second spatial light modulator, the light source is used to generate circularly polarized laser, and the circularly polarized laser generates an Airy-like light beam after sequentially passing through the first reflection system, the first spatial light modulator, the first thin lens, the second thin lens, the second spatial light modulator and the second reflection system;

[0055] It should be noted that, in this embodiment, the pixel size of the first spatial light modulator and the second spatial light modulator is 12 μm ×12 μm , and the resolution is 1920×1080 pixels ; there are two phase encoding modes in this embodiment, when other Airy-like vortex light beams are generated by the spatial light modulator, for example, an Airy vortex light beam, a vortex phase mask needs to be superimposed on the cubic phase. The vortex phase can be obtained by multiplying the spherical phase and the single-phase phase by a computer, and the generated phase is modulated, the phase factor with a transmission distance z is written into the phase film, two phases with different modes are superimposed, and the first vortex phase (such as Figure 2As shown in the figure, a represents the spherical phase, b represents the single-phase phase with topological charge m=3, and c represents the vortex phase. A corresponding cubic phase diaphragm is loaded onto the first spatial light modulator to modulate the incident light field, and its phase mode function is:

[0056] ;

[0057] in, and For wave vector components, wave vector , and These are the lateral and longitudinal control parameters for the first spatial light modulator, respectively. and This represents the actual displacement of the light beam in space. m and n These are the proportionality coefficients for the lateral and longitudinal phase shifts, respectively;

[0058] The surface of the second spatial light modulator is loaded with helical phase films with different topological charges and transmission distances. Its corresponding phase mode function is:

[0059] ;

[0060] in, , wave arrow , This indicates the focal length of the first thin lens. l Represents the topological charge number. Indicates the azimuth angle.

[0061] In other alternative embodiments, two different phase modes are superimposed to construct a second cubic vortex phase (according to the formula: To analyze the generated phase mask, such as Figure 3 As shown in the figure, a represents a cubic phase mask, b represents a spiral phase with topological charge m=3, and c represents a cubic vortex phase mask. A cubic vortex phase mask can be generated by superimposing vortex phase modes on a cubic phase mask. It can be modulated in the range of 0 to 2π. The phase mode function encoded by the first spatial light modulator is:

[0062] ;

[0063] in, This represents the phase mask function corresponding to the first spatial light modulator. Indicates the cubic phase term in x Control parameters in the direction of axial propagation Indicates the cubic phase term in y Control parameters in the direction of axial propagation denotes a focal length of the first thin lens, denotes a focal length of the second thin lens, x denotes x a corresponding first variable value in the axial propagation direction, y denotes y a corresponding second variable value in the axial propagation direction;

[0064] The phase pattern function encoded by the second spatial light modulator is:

[0065] ;

[0066] wherein, denotes a corresponding phase mask function of the first spatial light modulator, denotes an astigmatism measurement coefficient, , l denotes a topological charge number, denotes an azimuthal angle.

[0067] The first reflection system and the second reflection system are configured to collimate incident light, the first thin lens is configured to perform inverse Fourier transform on incident light, the second thin lens is configured to perform Fourier transform on incident light, the first spatial light modulator and the second spatial light modulator are configured to perform cubic phase modulation on incident light waves, respectively, and the observation system is configured to capture the intensity distribution of the generated Airy-like beam.

[0068] It should be noted that the light source is selected as a laser, the first reflection system and the second reflection system are selected as mirrors, and the spatial light modulator-lens combination is used to completely compensate the quadratic spectral phase and leave an adjustable cubic phase on the incident Gaussian pulse. A multi-parameter regulation platform is built by using the observation system (in which a computer holographic technology is arranged) to combine the transmission matrix with a propagation distance z and the phase modulation function of the lens to write into the cubic phase film, and then to digitize the Fourier lens and the transmission distance. A Fresnel transmission and far-field diffraction theoretical model is further constructed to convert many complex and variable information into measurable numbers and data, and then to establish a proper digital model by using the numbers and data. The incident and outgoing light fields are sampled by using a discrete summation algorithm of fast Fourier transform, and the joint regulation of the incident light field is realized by changing the related parameters.

[0069] The Gaussian beam generated by the laser is subjected to cubic phase modulation, and then subjected to Fourier lens transform to generate an Airy accelerating beam. The generation principle of the Airy beam is as shown in Figure 4As shown, the incident Gaussian and Gaussian-like beams are Fourier transformed by optical lenses, and a film piece satisfying a cubic phase distribution is loaded on a spatial light modulator, the incident light passes through the spatial light modulator and is then reflected out to complete phase modulation, and the light beam then passes through the Fourier lens to obtain the intensity distribution of the Airy-like beam at the back focal plane of the lens. The focal plane of the lens is the initial plane of the Airy-like beam, and changing the position of the CCD can record the light field distribution, light lobe size and coordinate information of the light beam at different diffraction distances.

[0070] Further, a beam expander is arranged between the light source and the first reflection system, the beam expander is used for expanding and collimating the circularly polarized laser generated by the light source, a conical lens system is arranged between the beam expander and the first reflection system, the conical lens system comprises a first conical lens and a second conical lens, and the conical lens system is used for rotating and symmetrically distributing the light wave vectors incident on the first conical lens exit surface and the second conical lens exit surface on the first conical lens exit surface and the second conical lens exit surface.

[0071] It should be noted that in the embodiment, the beam expander is composed of a third thin lens and a fourth thin lens arranged from left to right, and the Gaussian beam emitted by the laser passes through the third thin lens and the fourth thin lens for expansion, wherein the focal length of the third thin lens is f 3=15mm. The focal length of the fourth thin lens is f 4=180mm.

[0072] Specifically, a circular aperture is arranged between the first conical lens and the beam expander, and between the first thin lens and the second thin lens, and the circular aperture is used for adjusting the energy distribution of the incident light.

[0073] It should be noted that in the embodiment, the diameter of the circular aperture arranged between the first conical lens and the beam expander is CA 1mm, and the diameter of the circular aperture arranged between the first thin lens and the second thin lens is d 2mm. CA d

[0074] In the embodiment, the phase modulation system further comprises a third spatial light modulator, a beam splitter is arranged between the second reflection system and the third spatial light modulator, the beam splitter is used for splitting the laser beam into a first light wave and a second light wave, the third spatial light modulator is used for performing spectrum analysis on the first light wave and outputting the analysis result to the observation system, and the observation system is used for capturing the second light wave.

[0075] ​​Further, the observation system comprises a CCD camera, which is installed on a parallel moving platform parallel to the Z-axis of the light beam, and the CCD camera moves along the Z-axis of the light beam through the parallel moving platform.

[0076] In the specific implementation, a He-Ne laser with a central wavelength of 632 nm is selected as the light source. The Gaussian light beam emitted by the laser first passes through a beam expander for beam expansion; then passes through a circular aperture between the first conical lens and the beam expander CA 1Adjust the energy distribution of the light field, and the light field passes through a mirror in the first reflection system RM 1After calibration, the light field is incident on the first spatial light modulator SLM 1Surface, SLM 1The surface is phase-modulated by loading a corresponding cubic phase film on the surface, and the phase-modulated light field passes through a first thin lens L 1After inverse Fourier transform, the light field passes through a circular aperture between the first thin lens and a second thin lens CA 2Adjust the energy distribution of the light field, and the light field is incident on the second spatial light modulator SLM 2Surface, on which a spiral phase film with different topological charges and transmission distances is loaded. A certain displacement is applied to the phase film, and the light field is Fourier-transformed by the second thin lens L 2After Fourier transform, a corresponding displacement transform is also generated, satisfying:

[0077]

[0078] Again, the light field passes through the mirrors of the second reflection system RM 2After calibration, the light field passes through a beam splitter BS The obtained result is captured on the screen of a third spatial light modulator SLM 3and a charge-coupled device camera (CCD camera). In the experiment, the phase pattern after a series of transformations is input into the spatial light modulator, and the corresponding experimental result can be obtained in the CCD camera.

[0079] In summary, the digital Airy-like beam generation and control device in the above embodiments uses a spatial light modulator-lens combination to generate an Airy-like beam, compensates for the quadratic spectral phase, and the focal length of the lens does not affect the output result, so that an Airy-like beam with sufficient energy can be obtained. In addition, the device has good adaptability, and can not only be applied to Airy transformation of Gaussian beams or Gaussian-related beams, but also can be extended to hollow beams, vector vortex beams, pulsed beams, and coherent beams. This makes the cost lower, can be widely applied in the field of optoelectronics, and makes the Airy beam have more wavelengths. By loading a cubic phase film with a phase shift on the spatial light modulator, the target beam generates a corresponding displacement in the output plane. Then based on the Fourier transform displacement theorem (i.e. the displacement amount and the phase shift are linearly related), by adjusting the proportional coefficient of the transverse and longitudinal relative phase shifts, the transverse and longitudinal displacements of the target beam are measured, the linear relationship between the phase shift and the displacement is determined, and the motion trajectory of the target beam is determined, so that the control of the initial plane position of the target beam is realized. The starting point of the beam trajectory can be located on any plane after the Fourier lens, so that the control range of the target beam is increased, and the disadvantage that the Airy-like beam generated by using the continuous phase plate with a cubic distribution cannot be dynamically controlled is compensated. A multi-parameter control platform is built by using computer holography technology, and a Fresnel transmission and far-field diffraction model is constructed. By changing the characteristics of the incident light field and the control parameters of the phase film, the joint control of the beam size, the transverse acceleration, the phase mode and other parameters in the fixed output plane is realized, which can greatly reduce the interference of external conditions and the loss in the transmission evolution process, and provides a basic condition for reversible beam shaping technology.

[0080] Embodiment two

[0081] Another aspect of the present application also provides a method for generating and controlling a digital Airy-like beam, please refer to Figure 5 , which is a method for generating and controlling a digital Airy-like beam in the second embodiment of the present application, applied to the above-mentioned digital Airy-like beam generation and control device, the method for generating and controlling a digital Airy-like beam comprises steps S101-S104:

[0082] S101, expanding the circularly polarized laser emitted by the light source to obtain expanded laser;

[0083] In specific implementation, a He-Ne laser with a central wavelength of 632nm is selected as the light source. The Gaussian beam emitted by the laser passes through a beam expander for expansion to obtain expanded laser.

[0084] S102, adjust the primary energy distribution of the expanded laser beam, and irradiate the laser beam with adjusted primary energy distribution on a mirror of the first reflection system for calibration, and then irradiate the calibrated laser beam on the first spatial light modulator, so that the first spatial light modulator performs cubic phase modulation on the calibrated laser beam;

[0085] In specific implementation, a circular aperture is arranged between the first spatial light modulator and the beam expander CA 1adjust the energy distribution of the laser beam, and irradiate the laser beam with adjusted energy distribution on a first mirror of the first reflection system for calibration RM 1, and then irradiate the calibrated laser beam on the first spatial light modulator SLM 1, so that the first spatial light modulator SLM 1performs cubic phase modulation on the calibrated laser beam;

[0086] S103, reflect the laser beam with cubic phase modulation to the first thin lens for inverse Fourier transform, and then adjust the secondary energy distribution of the laser beam with inverse Fourier transform, and irradiate the laser beam with adjusted secondary energy distribution on the second thin lens for Fourier transform, and then irradiate the laser beam with Fourier transform on the second spatial light modulator, so that the second spatial light modulator performs spiral phase modulation on the laser beam with Fourier transform;

[0087] In specific implementation, after the laser beam with cubic phase modulation is reflected to L 1for inverse Fourier transform, and a circular aperture is arranged between the first thin lens and the second thin lens CA 2to adjust the energy distribution of the light field, and then irradiate the laser beam with adjusted energy distribution on the second thin lens L 2for Fourier transform, a corresponding displacement transform is also generated, and the following equation is satisfied:

[0088]

[0089] Irradiate the laser beam with Fourier transform on the second spatial light modulator SLM 2surface, and apply a certain displacement to the phase film on the surface by loading a spiral phase film with different topological charges and transmission distances on the surface.

[0090] It should be noted that in the embodiment, the pixel size of the first spatial light modulator and the second spatial light modulator is 12 μm ×12 μm , and the resolution is 1920×1080 pixelsIn this embodiment, there are two phase encoding methods. When using a spatial light modulator to generate other Airy-type vortex beams, such as Airy vortex beams, a vortex phase mask needs to be superimposed on the cubic phase. The vortex phase can be obtained by multiplying the spherical phase and the single-phase phase transmission using a computer. Simultaneously, the generated phase is modulated, and a phase factor with a transmission distance z is written into the phase diaphragm. Two different phase modes are superimposed to construct the first type of vortex phase (e.g., ...). Figure 2 As shown in the figure, a represents the spherical phase, b represents the single-phase phase with topological charge m=3, and c represents the vortex phase. A corresponding cubic phase diaphragm is loaded onto the first spatial light modulator to modulate the incident light field, and its phase mode function is:

[0091] ;

[0092] in, and For wave vector components, wave vector , and These are the lateral and longitudinal control parameters for the first spatial light modulator, respectively. and This represents the actual displacement of the light beam in space. m and n These are the proportionality coefficients for the lateral and longitudinal phase shifts, respectively;

[0093] The surface of the second spatial light modulator is loaded with helical phase films with different topological charges and transmission distances. Its corresponding phase mode function is:

[0094] ;

[0095] in, , wave arrow , This indicates the focal length of the first thin lens. l Represents the topological charge number. Indicates the azimuth angle.

[0096] In other embodiments, two different phase modes are superimposed to construct a second cubic vortex phase (according to the formula: To analyze the generated phase mask, such as Figure 3 As shown in the figure, a represents a cubic phase mask, b represents a spiral phase with topological charge m=3, and c represents a cubic vortex phase mask. A cubic vortex phase mask can be generated by superimposing vortex phase modes on a cubic phase mask. It can be modulated in the range of 0 to 2π. The phase mode function encoded by the first spatial light modulator is:

[0097] ;

[0098] in, This represents the phase mask function corresponding to the first spatial light modulator. Indicates the cubic phase term in x Control parameters in the direction of axial propagation Indicates the cubic phase term in y Control parameters in the direction of axial propagation This indicates the focal length of the first thin lens. This indicates the focal length of the second thin lens. x express x The value of the first variable corresponding to the direction of axial propagation. y express y The second variable value corresponding to the direction of axial propagation.

[0099] The phase mode function encoded by the second spatial light modulator is:

[0100] ;

[0101] in, This represents the phase mask function corresponding to the first spatial light modulator. Indicates the astigmatism measurement coefficient. , l Represents the topological charge number. Indicates the azimuth angle.

[0102] S104, the spiral phase-modulated beam is reflected by the second mirror into the beam splitter to generate a first beam and a second beam. The first beam is injected into the third phase spatial light modulator for spectral analysis, and the second beam is injected into the observation system for capture to obtain the intensity distribution of the corresponding Airy-type beam.

[0103] In practical implementation, the spiral phase-modulated beam passes through the second reflecting mirror of the second reflection system. RM 2. After calibration, the beam is reflected back to the beam splitter. BS In the middle, beam splitter BS The obtained results are used in a third-space light modulator. SLM 3. The results were captured on the screen of a charge-coupled device (CCD) camera. In the experiment, the phase mode, after a series of transformations, was input into a spatial light modulator, and the corresponding experimental results could be obtained from the CCD camera.

[0104] In this embodiment, the specific theoretical analysis is as follows:

[0105] Control and Measurement of Displacement and Transmission Trajectory: Under the condition of paraxial approximation, we can use the generalized Huygens-Fresnel diffraction integral formula to study the spatial domain transmission problem of optical systems, starting from the input plane of the optical Airy transform system. The light field evolution onto the output plane may be described by the following equation:

[0106] ;

[0107] ;

[0108] Loading phase mask with phase shift on spatial light modulator can make the light beam produce corresponding displacement on the back focal plane of Fourier lens. In order to introduce different size of phase shift, the phase modulation function corresponding to the phase shift mask loaded on the spatial light modulator is:

[0109] ;

[0110] wherein, and are wave vector components, and respectively determine the control parameters of the spatial light modulator in the lateral and longitudinal directions. and are the actual displacements of the light beam in space. m and n are the proportional coefficients of the lateral and longitudinal phase shift amounts respectively.

[0111] The generation of Airy beam needs to use lens for Fourier transform, and according to the shift theorem of Fourier transform:

[0112] ;

[0113] wherein, denotes Fourier transform, denotes the function in spatial domain, denotes the spectral function thereof, and denote the horizontal and vertical frequencies in space respectively.

[0114] If the incident wave field function is displaced in the spatial domain, the spectral function will have a corresponding phase shift in the frequency domain. Conversely, if a phase shift is applied to the spectral plane of the light beam, a corresponding displacement can be obtained on the back focal plane of the lens, which is the initial plane of the Airy beam. The lateral and longitudinal phase shifts can respectively make the light beam produce lateral and longitudinal displacement, and when the lateral and longitudinal phase shifts exist at the same time, the target light beam (i.e. the generated Airy beam) can also produce a slant displacement on the focal plane of the output plane. Through two-dimensional optical Fourier transform, the moving track of the corresponding light beam in space can be obtained.

[0115] The digital Airy-like beam generation and control method in the above embodiments of the application is applied to the digital Airy-like beam generation and control device, an Airy-like beam is generated by using a spatial light modulator-lens combination, the quadratic spectral phase is compensated, and the focal length of the lens does not affect the output result, so that an Airy-like beam with sufficient energy can be obtained. In addition, the device has good adaptability, and can not only be applied to Airy transformation of Gaussian beams or Gaussian-related beams, but also can be extended to hollow beams, vector vortex beams, pulsed beams, and coherent beams. This makes the cost reduced, can be widely applied in the field of optoelectronics, and makes the Airy beam have more wavelengths. By loading a cubic phase film with a phase shift on the spatial light modulator, the target beam generates a corresponding displacement on the output plane. Then, based on the Fourier transform displacement theorem (i.e., the displacement amount and the phase shift are linearly related), by adjusting the proportional coefficient of the transverse and longitudinal relative phase shifts, the transverse and longitudinal displacements of the target beam are measured, the linear relationship between the phase shift and the displacement is determined, and thus the motion trajectory of the target beam is determined, so that the control of the initial plane position of the target beam is realized. The starting point of the beam trajectory can be located on any plane after the Fourier lens, so that the control range of the target beam is increased, and the disadvantage that the Airy-like beam generated by using the cubic distribution continuous phase plate cannot be dynamically controlled is compensated. A multi-parameter control platform is built by using computer holographic technology, and a Fresnel transmission and far-field diffraction model is constructed. By changing the characteristics of the incident light field and the control parameters of the phase film, the joint control of the beam size, the transverse acceleration, the phase mode and other parameters on the fixed output plane is realized, which can greatly reduce the interference of external conditions and the loss in the transmission evolution process, and provides a basic condition for reversible beam shaping technology.

[0116] The technical features of the above-described embodiments can be combined in any manner. To make the description concise, all possible combinations of the technical features in the above-described embodiments are not described, but as long as the combinations of the technical features do not contradict, they should be considered within the scope of the present disclosure.

[0117] The above-described embodiments only express several implementation manners of the present application, and the description is relatively specific and detailed, but it should not be understood as a limitation on the scope of the patent. It should be noted that for ordinary skilled persons in the art, some modifications and improvements can be made without departing from the concept of the present application, and these are within the protection scope of the present application. Therefore, the protection scope of the patent of the present application should be subject to the appended claims.

Claims

1. A device for generating and controlling a digital Airy-type beam, characterized in that, It includes a light source, a first reflection system, a thin lens system, a phase modulation system, a second reflection system, and an observation system; The thin lens system includes a first thin lens and a second thin lens, the phase modulation system includes a first spatial light modulator and a second spatial light modulator, the light source is used to generate circularly polarized laser, and the circularly polarized laser sequentially passes through the first reflection system, the first spatial light modulator, the first thin lens, the second thin lens, the second spatial light modulator and the second reflection system to generate an Airy-type beam; The first and second reflection systems are used to calibrate the incident light, the first thin lens is used to perform an inverse Fourier transform on the incident light, the second thin lens is used to perform a Fourier transform on the incident light, the first spatial light modulator and the second spatial light modulator are respectively used to perform cubic phase modulation on the incident light wave, and the observation system is used to capture the intensity distribution of the generated Airy-type beam.

2. The digital Airy-type beam generation and control device according to claim 1, characterized in that, A beam expander is provided between the light source and the first reflection system. The beam expander is used to expand and collimate the circularly polarized laser generated by the light source.

3. The digital Airy-type beam generation and control device according to claim 2, characterized in that, The phase modulation system further includes a third spatial light modulator. A beam splitter is provided between the second reflection system and the third spatial light modulator. The beam splitter is used to split the laser beam into a first light wave and a second light wave. The third spatial light modulator is used to perform spectral analysis on the first light wave and output the analysis results to the observation system. The observation system is used to capture the second light wave.

4. The digital Airy-type beam generation and control device according to claim 3, characterized in that, A circular aperture is provided between the first spatial light modulator, the beam expander, the first thin lens, and the second thin lens. The circular aperture is used to adjust the energy distribution of the incident light.

5. The digital Airy-type beam generation and control device according to claim 4, characterized in that, The observation system includes a CCD camera mounted on a parallel moving platform. The parallel moving platform is parallel to the Z-axis of the beam propagation, and the CCD camera moves along the optical axis of the beam propagation via the parallel moving platform.

6. A method for generating and controlling a digital Airy-like beam, applied to the digital Airy-like beam generation and control device of claim 5, wherein the method for generating and controlling the digital Airy-like beam comprises the following steps: Step 1: Expand the circularly polarized laser emitted by the light source to obtain expanded laser beam; Step 2: Perform energy distribution adjustment on the expanded laser beam, and calibrate the beam after energy distribution adjustment by illuminating the reflector of the first reflection system. Then, incident the calibrated beam onto the first spatial light modulator so that the first spatial light modulator performs cubic phase modulation on the calibrated beam. Step 3: The cubic phase modulated beam is reflected to the first thin lens for inverse Fourier transform, and the energy distribution of the beam after inverse Fourier transform is adjusted twice before being injected into the second thin lens for Fourier transform. The beam after Fourier transform is then injected into the second spatial light modulator so that the second spatial light modulator performs helical phase modulation on the beam after Fourier transform. Step 4: The spiral phase-modulated beam is reflected by the mirror of the second reflection system into the beam splitter to generate a first beam and a second beam. The first beam is injected into the third phase spatial light modulator for spectral analysis, and the second beam is injected into the observation system for capture to obtain the intensity distribution of the corresponding Airy-type beam.

7. The method for generating and controlling digital Airy-type beams according to claim 6, characterized in that, The steps for regulating energy distribution include: The energy distribution of the light field corresponding to the incident light is adjusted by using a circular aperture.

8. The method for generating and controlling a digital Airy-type beam according to claim 6, characterized in that, The phase mode function encoded by the first spatial light modulator is: ； in, and For wave vector components, wave vector , and These are the lateral and longitudinal control parameters for the first spatial light modulator, respectively. and This represents the actual displacement of the light beam in space. m and n These are the proportionality coefficients for the lateral and longitudinal phase shifts, respectively; The phase mode function encoded by the second spatial light modulator is: ； in, , wave arrow , This indicates the focal length of the first thin lens. l Represents the topological charge number. Indicates the azimuth angle.

9. The method for generating and controlling a digital Airy-type beam according to claim 6, characterized in that, The phase mode function encoded by the first spatial light modulator is: ； in, This represents the phase mask function corresponding to the first spatial light modulator. Indicates the cubic phase term in x Control parameters in the direction of axial propagation Indicates the cubic phase term in y Control parameters in the direction of axial propagation This indicates the focal length of the first thin lens. This indicates the focal length of the second thin lens. x express x The value of the first variable corresponding to the direction of axial propagation. y express y The value of the second variable corresponding to the direction of axial propagation; The phase mode function encoded by the second spatial light modulator is: ； in, This represents the phase mask function corresponding to the first spatial light modulator. Indicates the astigmatism measurement coefficient. , l Represents the topological charge number. Indicates the azimuth angle.

10. The method for generating and controlling a digital Airy-type beam according to any one of claims 8-9, characterized in that, The expression for the trajectory of the light beam in space is: ； in, Indicates Fourier transform, Represents a spatial domain function. Represent its spectral function, and These represent the horizontal and vertical frequencies in space, respectively.

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