Geometric phase fork-shaped grating based on femtosecond laser direct writing Type X structure, preparation method and application of geometric phase fork-shaped grating in vortex light aspect

Abstract

The invention discloses a femtosecond laser direct-writing Type X structure-based geometric phase fork-shaped grating, a preparation method and application of the femtosecond laser direct-writing Type X structure-based geometric phase fork-shaped grating in vortex light, and belongs to the technical field of laser processing, and the femtosecond laser direct-writing Type X structure-based geometric phase fork-shaped grating comprises design and parameter calculation of a geometric phase fork-shaped grating device, determination of a processing parameter window of a Type X structure and the femtosecond laser direct-writing fork-shaped grating. According to the invention, femtosecond laser is utilized to induce and generate an anisotropic nanopore structure with ultra-high transmittance higher than 97% in fused quartz and other transparent materials, namely a Type X structure, the structure has a birefringence characteristic, and the slow axis angle of the structure is always perpendicular to the laser polarization direction, so that the slow axis angle can be continuously adjusted by adjusting laser polarization. The Type X structure serves as a metasurface unit of the geometric phase fork-shaped grating, geometric phase regulation and control are achieved by controlling slow axis orientation of the Type X structure, and therefore generation and regulation and control of vortex light are achieved. The method is high in efficiency and simple in process.

Description

Technical Field

[0001] This invention belongs to the field of laser processing technology, specifically relating to a geometric phase fork grating based on a femtosecond laser direct-write Type X structure, its fabrication method, and its application in vortex light. Background Technology

[0002] Vortex light is a type of beam with a phase singularity, whose phase can be expressed as exp(ilᵀ), where l is the topological charge and ᵀ is the azimuth angle. Such beams carry quantized orbital angular momentum (OAM) and can provide an infinite set of eigenmodes (l = 1, 2, 3, ...). The orbital angular momentum carried by optical vortices, as another fundamental optical parameter besides amplitude, wavelength, and polarization, has become an important area of ​​research in optics. Optical vortices have therefore attracted widespread attention and are widely used in various fields such as optical tweezers, high-capacity optical communication, data storage, and quantum optics.

[0003] However, all these potential applications require the efficient generation and manipulation of vortex beams with different topological charges. To this end, researchers have proposed various vortex beam generation methods, including spiral phase plates, Q-plates, and liquid crystal-based spatial light modulators. However, these methods often require multiple optical components, resulting in complex equipment, or have limitations in efficiency and bandwidth.

[0004] In recent years, metasurfaces, as compact planar optical elements composed of subwavelength structures, have provided a new solution for the generation of vortex light. However, existing metasurface technologies still have significant drawbacks: plasmonic metasurfaces suffer from significant absorption losses in the visible and ultraviolet light ranges, limiting their practical applications; while dielectric metasurfaces exhibit high conversion efficiency in the generation of vortex light in the infrared band, their fabrication typically relies on techniques such as electron beam lithography, resulting in cumbersome processing steps, complex fabrication processes, and high costs.

[0005] Therefore, the low efficiency of vortex light generation and control and the complex fabrication process in the existing technology restrict the further development of orbital angular momentum optical devices. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a geometric phase fork grating based on a femtosecond laser-written Type X structure, its fabrication method, and its application in vortex light. This invention utilizes a femtosecond laser to induce anisotropic nanopore structures with ultra-high transmittance (above 97%), i.e., Type X structures, within transparent materials such as fused silica. These structures exhibit birefringence, and their slow axis angle is always perpendicular to the laser polarization direction. Therefore, the slow axis angle can be continuously adjusted by regulating the laser polarization. The Type X structure serves as the metasurface unit of the geometric phase fork grating in this invention. By controlling its slow axis orientation, geometric phase modulation is achieved, thereby realizing the generation and control of vortex light. This method is not only highly efficient but also simple in fabrication.

[0007] This invention is achieved through the following technical solution:

[0008] In a first aspect, the present invention provides a method for fabricating a geometric phase fork grating based on a femtosecond laser direct-write Type X structure, specifically including the following steps:

[0009] Step 1: Design and parameter calculation of the geometric phase fork grating device;

[0010] The specific steps are as follows: determine the size, phase gradient period P, and topological charge l of the fork-shaped grating according to the application requirements; calculate the two-dimensional phase distribution of the fork-shaped grating; and quantize the calculated continuous two-dimensional phase distribution into an Nth-order discrete phase φ. n Then, an Nth-order discrete phase φ is established. n The mapping relationship between the slow axis angle and the Type X structure's slow axis angle is used to obtain the slow axis angle of the Type X structure to be processed. A two-dimensional distribution;

[0011] Step 2: Determine the machining parameter window for the Type X structure;

[0012] The specific steps are as follows: Line-by-line scanning is performed using a femtosecond laser direct-write processing system. Lasers of different wavelengths, pulse widths, and repetition frequencies are selected and focused onto objectives with different numerical apertures. By controlling the movement of the displacement platform, multiple sets of exposure times and scanning speeds are achieved, resulting in multiple processing parameter windows. Based on morphological characteristics and birefringence properties, these processing parameter windows are divided into Type I, Type X, and Type II structures, thus determining the processing parameter window for the Type X structure. The phase retardation of the Type X structure is characterized using a birefringence microscope.

[0013] Step 3: Femtosecond laser direct writing of the fork-shaped grating;

[0014] The specific steps are as follows: First, based on the fork-shaped grating designed in step one, generate the corresponding laser processing data; then, calculate the total phase delay of the fork-shaped grating device. Divide by the phase delay of the Type X structure obtained in step two to calculate the number of processing layers required for the device; then, resolve the spatial coordinates of the fork grating using a calculation tool; then import the coordinates into the femtosecond laser direct writing control system, and simultaneously focus the laser focus on the interior of the sample, move the sample by controlling the displacement platform, and select the initial processing position; finally, using the processing parameter window of the Type X structure determined in step two, control the displacement platform to drive the sample to perform high-speed line-by-line scanning along the X-axis; after completing one row, control the displacement platform to step along the Y-axis to the next row, repeat this process to complete the scanning of a single-layer plane; after the single-layer scanning is completed, control the displacement platform to step along the Z-axis to the next layer, repeat this process to complete the high-precision processing of the geometric phase fork grating.

[0015] Furthermore, in step one, the slow axis angle of the Type X structure is controlled by the laser polarization direction and is always perpendicular to the laser polarization direction; the laser polarization angle takes N discrete values ​​in the range of 0-180°, where 1≤N≤180, corresponding to N slow axis angles of the Type X structure; different colors are obtained by measuring the Type X structure with different slow axis orientations under a birefringence microscope.

[0016] Further, in step one, the two-dimensional phase distribution of the fork-shaped grating is calculated according to the phase distribution formula of the fork-shaped grating, as follows:

[0017] ,

[0018] Where x and y represent the position coordinates in a Cartesian coordinate system on a two-dimensional plane, x0 and y0 represent the coordinate positions of the device center, P is the phase gradient period, l is the topological charge, and φ is the phase gradient period. GP The phase of the fork-shaped grating;

[0019] Based on the slow axis angle θ of the Type X structure and the phase φ of the fork grating GP Correspondence The discrete phase φ is calculated. n Its corresponding Type X structure slow axis angle θ n The mapping relationship.

[0020] Furthermore, in step two, if the refractive index of the structure changes positive and the transmittance is greater than 99%, it is a Type I structure; if the structure can be detected as having birefringence and the optical transmittance is greater than 97%, it is a Type X structure; if the structure can be detected as having birefringence but the optical transmittance is less than 80%, it is a Type II structure based on a nanograting.

[0021] In step two, the birefringent microscope is an Oosight imaging system equipped with an Olympus BX53 optical microscope.

[0022] Furthermore, in steps two and three, the wavelength of the femtosecond laser at the center of the femtosecond laser in the femtosecond laser direct writing processing system is 343-1030 nm, the pulse width is 100 fs-10 ps, ​​the repetition frequency is 1 kHz-40 MHz; the objective lens NA is 0.16-0.65, the magnification is 10×-60×; and the single-pulse ablation energy is 0.1-1.5 μJ.

[0023] The displacement platform is an Aerotech three-axis air-bearing displacement platform, wherein the X-axis has a movement range of 0-150 mm and a movement accuracy of 0-200 nm; the Y-axis has a movement range of 0-100 mm and a movement accuracy of 0-200 nm; and the Z-axis has a movement range of 0-60 mm and a movement accuracy of 0-200 nm.

[0024] The scanning speed is 0.1-300 mm / s; the point spacing of the processing data is 0.1-2 μm; the single-point exposure time is 10-700 μs; the laser polarization is modulated by a Glan prism, a Pockel cell, and a quarter-wave plate.

[0025] Furthermore, in step three, the sample is a fused silica glass sample with a thickness of 0.1-7 mm.

[0026] Furthermore, in step three, the total phase delay of the fork-shaped grating device is half of the designed operating wavelength, that is, a phase delay corresponding to π radians, as shown in the formula: .

[0027] Furthermore, in step three, the two-dimensional spatial coordinates and phase distribution of the fork-shaped grating are analyzed and stored as a .csv file using MATLAB calculation tools. The processing system controls the polarization direction and focusing position of the processing laser by reading the .csv file.

[0028] Secondly, the present invention provides a geometric phase fork grating based on a femtosecond laser direct-write Type X structure, which is prepared by the method described in the first aspect. The geometric phase fork grating is composed of multiple Type X structures with different slow axis orientations and can convert an incident Gaussian beam into a vortex beam carrying orbital angular momentum.

[0029] Thirdly, this invention also provides the application of a geometric phase fork grating based on a femtosecond laser direct-write Type X structure in the generation and manipulation of vortex light, specifically including:

[0030] When the incident light is left-handed circularly polarized light, the output light is right-handed circularly polarized vortex light with a topological charge of -l;

[0031] When the incident light is right-handed circularly polarized light, the output light is left-handed circularly polarized vortex light with a topological charge of +l;

[0032] When the incident light is linearly polarized, a pair of symmetrical vortexes with topological charges of -l and +l are simultaneously output at ±1 orders.

[0033] The device design and fabrication principle of the present invention based on the femtosecond laser direct-write Type X structure geometric phase fork grating is as follows:

[0034] The phase distribution of the geometric phase fork grating described in this invention is composed of two linearly superimposed parts: one is the linear phase of the geometric phase grating, and the other is the spiral phase of the S-wave plate; its expression is: In the formula, P is the grating phase gradient period, which determines the diffraction angle of the beam; l is the topological charge, which determines the magnitude of the orbital angular momentum of the generated optical vortex; x and y represent the position coordinates in a Cartesian coordinate system on a two-dimensional plane; x0 and y0 represent the coordinate positions of the device center; subsequently, the obtained continuous phase is quantized into N-order discrete phases according to design requirements, and corresponds one-to-one with N different orientations of Type X structures, so that the overall device achieves the geometric phase control of the target. Through this design, the fork-shaped grating of the present invention can convert the incident Gaussian beam into a vortex beam carrying a preset orbital angular momentum, and make it undergo directional diffraction, thereby achieving effective control over the orbital angular momentum and diffraction direction of the vortex beam.

[0035] This invention employs femtosecond laser direct writing technology to fabricate the geometric phase fork grating. A femtosecond laser pulse is precisely focused onto the interior of fused silica material using an objective lens, and a Type X structure with a predetermined slow axis angle is written into the material using a line-by-line scanning method. Simultaneously, by characterizing the phase delay of a single-layer Type X structure, multiple layers are precisely calculated and superimposed to achieve a total phase delay of half a wave at the target wavelength, thus realizing the theoretically highest geometric phase conversion efficiency.

[0036] The principle of the application of the geometric phase fork grating based on the femtosecond laser direct-write Type X structure in generating and controlling vortex light is as follows:

[0037] Control and verification of orbital angular momentum: by changing the topological charge design value of the fork-shaped grating This allows for direct control of the topological charge of the generated vortex beam. Under a fixed phase gradient period, vortex beams with different... The fork-shaped grating can obtain vortex beams with corresponding topological charges at ±1 diffraction orders. Specifically, when the beam is incident on the geometric phase fork-shaped grating prepared in this invention, based on its geometric phase distribution, the fork-shaped grating converts the incident Gaussian beam into a first-order diffracted vortex beam. Its output characteristics are closely related to the polarization state of the incident light: when the incident light is left-handed circularly polarized, it is diffracted to the -1st order and converted into a vortex beam with a topological charge of -1, and the output polarization state becomes right-handed circularly polarized; when the incident light is right-handed circularly polarized, it is diffracted to the +1st order and converted into a vortex beam with a topological charge of +1, and the output polarization state becomes left-handed circularly polarized; when the incident light is linearly polarized, it can be regarded as a superposition of left-handed and right-handed circularly polarized light, thus generating a pair of symmetrical vortex beams with opposite topological charges (-1 and +1) at both ±1st orders.

[0038] Improving vortex light generation efficiency: The Type X structure exhibits high transmittance in the visible light band, enabling it to utilize most of the incident light energy for geometric phase modulation rather than being absorbed or scattered by the medium. Therefore, the fork-shaped grating formed by this structure can almost completely transfer the incident light energy from zero-order diffraction to a first-order diffraction vortex beam carrying orbital angular momentum, thereby significantly improving the device's conversion efficiency.

[0039] Compared with the prior art, the advantages of the present invention are as follows:

[0040] (1) This invention utilizes a Type X birefringent structure with high transmittance and high uniformity to fabricate a fork-shaped grating device, achieving a high optical vortex rotation conversion efficiency of up to 98.4% at the designed center wavelength. In a spectral range of 450 nm to 690 nm, its conversion efficiency can still be maintained above 80%, demonstrating excellent broadband working capability.

[0041] (2) Based on the nanoscale Type X structure, the present invention enables the geometric phase change between adjacent structures to transition continuously within a smaller spatial scale, thereby supporting faster phase gradient changes and realizing high-order OAM beam generation and control with a topological charge of up to 102, providing a reliable hardware implementation basis for high-capacity OAM multiplexed optical communication systems and high-dimensional quantum coding.

[0042] (3) Compared with the traditional large optical system composed of multiple components such as spatial light modulator and spiral phase plate, the fork grating based on Type X structure provided by the present invention is a monolithically integrated planar optical element with an extremely compact structure, significantly reduced volume, no need for complex mechanical assembly and adjustment, and greatly improves the stability of the system. Attached Figure Description

[0043] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0044] Figure 1 This is a schematic diagram illustrating the design principle of the geometric phase fork grating of the present invention;

[0045] The geometric phase distribution of the fork grating is shown, which is the superposition of the one-dimensional grating phase and the S-wave plate phase.

[0046] Figure 2 This is a schematic diagram of the optical path of the femtosecond laser processing system used in this invention;

[0047] In this process, an electronically controlled attenuator modulates the single-pulse energy; a Glan prism, a Pockel cell, and a quarter-wave plate jointly modulate the angle of the linearly polarized light; after beam expansion, the diameter of the laser spot increases to fill the entrance pupil of the objective lens; finally, the laser is focused into the sample through the objective lens.

[0048] Figure 3 Optical elements with different topological charges are fabricated using the fork-shaped grating device fabrication method described in this invention;

[0049] ae shows the birefringence diagrams of the fork gratings with topological charges l=1, 2, 3, 5, 10 respectively;

[0050] Figure 4 This is a schematic diagram of the verification optical path for testing the performance of the fork-shaped grating device in this invention;

[0051] Where a is the optical path of the Gaussian light incident on the fork grating, and b is the test optical path of the vortex light incident on the fork grating;

[0052] Figure 5 To illustrate the effect of generating and controlling vortex light with different topological charges using the fork-shaped grating described in this invention, and to characterize the topological charge number;

[0053] Among them, the intensity map of the vortex light field generated by the device under different design topological charges (l = 1, 2, 3, 5, 10) (a) and its corresponding interference pattern (b) are shown to verify the accuracy of the generated topological charges.

[0054] Figure 6 Figure showing the characterization and testing results of the high-order vortex light generation device;

[0055] In this example, 'a' shows the l generated when a vortex beam with l = -2 (+2) is incident on a fork-shaped grating with l = 50. forkIntensity distributions of higher-order vortex beams at l=-52 and +52; b shows the intensity distribution of vortex beams at l=-2(+2) incident on a forked grating at l=100. fork The intensity distribution of higher-order vortex beams with l=-102 and +102 is shown in c; the pattern formed by the interference of the vortex beam with l=-52(+52) with a cylindrical lens is shown in d; the pattern formed by the interference of the vortex beam with l=-102(+102) with a cylindrical lens is shown in d.

[0056] Figure 7 The graph shows the broadband performance test results of the fork-shaped grating described in this invention.

[0057] Where, a is a schematic diagram of the incident structure of linearly polarized light of different wavelengths, and b is the corresponding horizontal light intensity profile.

[0058] The study demonstrates the intensity distribution of the vortex light generated by the fork-shaped grating and the corresponding horizontal light intensity profile over a wide wavelength range of 450 nm to 690 nm, proving its effective broadband operation capability.

[0059] Figure 8 This is a statistical analysis of the working efficiency of the fork-shaped grating described in this invention in different wavelength bands. Detailed Implementation

[0060] To clearly and completely describe the technical solution and its specific working process of the present invention, the specific embodiments of the present invention are as follows, in conjunction with the accompanying drawings:

[0061] Example 1

[0062] This embodiment provides a method for fabricating a geometric phase fork grating based on a femtosecond laser direct-write Type X structure, specifically including the following steps:

[0063] Step 1: Design and parameter calculation of the geometric phase fork grating device;

[0064] The specific steps are as follows: Based on the diameter of the light spot in the test optical path, the size of the fabricated fork-shaped grating device is selected as 1.2 mm; according to the required optical performance, the phase gradient period P of the fork-shaped grating is determined to be 50 μm, and the topological charge l is 1, 2, 3, 5, 10, respectively, where P determines the diffraction angle of the ±1st order vortex light, and l determines the topological charge of the vortex light; according to the phase distribution formula of the fork-shaped grating... The two-dimensional phase distribution of the fork-shaped grating was calculated; next, the calculated continuous phase was quantized into 180 equally spaced discrete phases. (2°, 4°, 6°…360°). Based on the slow axis angle θ of the Type X structure and the phase φ of the fork grating. GP The correspondence is Each discrete phase is calculated The corresponding slow axis angle θn (1°, 2°, 3°…180°) yields the slow axis angle of the Type X structure to be machined. The device has a two-dimensional distribution. The designed operating wavelength is 515 nm, therefore the total delay should be approximately 515 / 2 ≈ 257 nm.

[0065] Depend on Figure 1 It can be seen that the geometric phase of the fork grating is a linear superposition of the phase of the one-dimensional grating and the phase of the S-wave plate. Figure 1 a shows the theoretical geometric phase of three geometric phase elements ( The distribution diagram, from left to right, shows: a one-dimensional grating, an S-wave plate, and the forked grating generated therefrom. The phase values ​​of all elements vary between 0 and 2π, with a phase period of 50 μm and a topological charge of 1. Figure 1 Figure b shows the slow-axis orientation (θ) measurement distribution of three corresponding geometrical phase elements fabricated in fused silica using femtosecond laser direct writing technology. From left to right, these are a phase grating, an S-wave plate, and a fork grating. The slow-axis orientation at each point in the figure is determined by the relationship θ = / 2 The specific location is calculated and indicated by the false-color bar on the right side of the attached figure (illustrated).

[0066] Step 2: Determine the machining parameter window for the Type X structure;

[0067] A femtosecond laser direct-write processing system was used to scan Corning 7979 glass samples line by line. The selected wavelength was 1030 nm, with pulse widths ranging from 170-500 fs, repetition rates from 100-1000 kHz, objective numerical apertures from 0.16-0.5, pulse energy from 0.4-1.4 μJ, exposure times from 50-300 μs, scanning speeds from 1-10 mm / s, and spot spacing from 0.5-2 μm. The resulting structures were classified based on morphological characteristics and birefringence measurements. The processing parameter window for Type X structures was identified: structures with a positive refractive index change and transmittance greater than 99% were Type I structures; structures with detectable birefringence and optical transmittance greater than 97% were Type X structures; and structures with detectable birefringence but optical transmittance less than 80% were Type II structures based on nanogratings. Comparison of results showed that a laser pulse width of 400 fs and a repetition rate of 200 kHz were optimal. At kHz, objective numerical aperture of 0.16, scanning speed of 6 mm / s, spot pitch of 1 μm, single-point exposure time of 160 μs, and laser energy of 0.9 μJ, the Type X structure has a large parameter window and a high phase retardation, with a single-layer retardation of up to 64 nm.

[0068] Depend on Figure 2As can be seen, the femtosecond laser direct writing processing system used in this embodiment is as follows: the 1030nm femtosecond laser emitted from the laser passes through a reflector and an electronically controlled attenuator in sequence, then through a reflector, a Glan prism, a Pockels cell and a quarter-wave plate, then through a beam expander, and then through another reflector to reach the objective lens for focusing.

[0069] Step 3: Femtosecond laser direct writing of the fork-shaped grating;

[0070] In this embodiment, the target device is a fork-shaped grating with a period P = 50 μm and a diameter of 1.2 mm. Based on the phase distribution diagram of the corresponding fork-shaped grating designed in step one, the corresponding laser processing data is obtained: the number of processing layers required for the fork-shaped grating device is calculated. Layer; using computational tools such as MATLAB, the three-dimensional spatial coordinates and slow axis angles corresponding to each unit of the fork-shaped grating are analyzed. Then, the laser processing data is imported into the femtosecond laser direct writing control system, and the laser focus is simultaneously focused on the interior of the fused silica material to select the initial processing position; finally, line-by-line scanning is performed using the Type X structural parameters determined in step two: laser pulse width 400 fs, repetition rate 200 kHz, objective lens numerical aperture 0.16, scanning speed 6 mm / s, spot spacing 1 μm, single-point exposure time 160 μs, and laser energy 0.9 μJ.

[0071] Depend on Figure 3 It can be seen that a 1.2 mm diameter fork-shaped grating (with a period P = 50 μm) fabricated using femtosecond laser direct writing of a Type X structure is demonstrated to perform under different topological charges ( Distribution of slow axis orientation (θ) measurements under the range of θ = 1, 2, 3, 5, 10.

[0072] Example 2

[0073] This embodiment provides the application of a geometric phase fork grating based on a femtosecond laser direct-write Type X structure in the generation and manipulation of vortex light, specifically including:

[0074] like Figure 4 As shown, the optical path used to test the performance of the fork-shaped grating device is illustrated. Figure 4 'a' represents the optical path of Gaussian light incident on the forked grating: the laser is sequentially incident on the quarter-wave plate and the sample to be measured, and the light field is collected by a CMOS camera; Figure 4 Figure b illustrates the test optical path of a vortex light incident on a fork-shaped grating: a laser is sequentially incident on a quarter-wave plate, an S-wave plate, and the sample under test, and the light field is collected by a CMOS camera.

[0075] 1. Testing the generation and modulation effect of vortex light using fork-shaped gratings with different topological charges and geometric phases;

[0076] First, the effect of Gaussian light incident on a low-order topological fork-shaped grating on generating and modulating vortex light was tested. The test optical path was selected as follows: Figure 4 The optical path in section a uses a wavelength of 515 nm. The quarter-wave plate angle is adjusted to ensure the laser light incident on the device is linearly polarized. The test results are as follows: Figure 5 As shown in Figure a, all fork-shaped gratings generated vortex light at the ±1st order diffraction orders, with the 0th order spot being extremely weak, indicating that the fork-shaped gratings have a high efficiency in converting vortex light. The diameter of the vortex light also increases with the increase of the topological charge number, theoretically... The topological charge of the generated vortex beam can be verified using the astigmatic transformation method: by acquiring the interference pattern of the vortex beam on the focal plane of the cylindrical lens, the number of dark fringes produced directly corresponds to the topological charge of the beam. The test results are as follows: Figure 5 As shown in b, the number of dark fringes in the interference pattern is equal to the topological charge of the vortex light, which are 1, 2, 3, 5, and 10, respectively.

[0077] Next, we tested the results of generating and modulating vortex light by incident vortex light onto a higher-order topological fork-shaped grating. The test optical path was selected as follows: Figure 4 In the optical path of b, a wavelength of 515 nm is selected. The quarter-wave plate angle is adjusted to convert the laser into circularly polarized light, which is then incident on an S-wave plate with l=2 and exits as a vortex beam with l=2. The vortex beam is then incident on a geometric phase fork grating with l=50, and the test results are as follows. Figure 6 As shown in a, the diffracted light is produced at the -1st order. The vortex light is produced at the +1 level. The vortex light. Similarly, when testing a fork-shaped grating with l=100, the diffracted light produces vortex light at ±102 along ±1, as shown below. Figure 6 As shown in b. The topological charge effect of higher-order vortex beams is verified using interferometry, as shown in Figure b. Figure 6 As shown in c and d of 6, the number of dark stripes is 52 and 102, respectively.

[0078] II. Testing the broadband performance of the geometric phase fork grating;

[0079] Although the forked grating in this embodiment is designed to operate at a wavelength of 515 nm, the geometric phase itself is wavelength-independent, and the Type X structure has high transmittance and low scattering. Therefore, this device exhibits certain broadband performance, maintaining high efficiency across a wide spectral range of 450-690 nm. The test optical path is selected... Figure 4 In the optical path of component a, laser wavelengths of 450 nm, 515 nm, 580 nm, 600 nm, 632 nm, and 690 nm were selected. Linearly polarized light of different wavelengths was incident on a fork-shaped grating with P = 50 μm and l = 1. The test results are as follows: Figure 7As shown, the device stably generates two vortexes with opposite topological charges at ±1 order throughout the entire test spectrum range of 450-690 nm. Furthermore, different diffraction angles were observed at different wavelengths: the longer the wavelength, the larger the diffraction angle. Figure 7 b shows the corresponding horizontal light intensity profile, proving its effective broadband working capability.

[0080] Since the device is designed for a wavelength of 515 nm, when the wavelength deviates from the design wavelength, the phase delay of the device will no longer be the ideal half-wavelength, resulting in a decrease in efficiency. For example... Figure 7 As shown in b, the intensity proportion of the intermediate zero-order light gradually increases with wavelength shift. The theoretical operating efficiency of the device at different wavelengths is determined by the formula... Quantitative calculation, where S3 represents the circularly polarized component of the incident light. This represents the phase delay. According to the formula, when... hour The value is the largest, therefore the geometric phase conversion efficiency is highest when the total delay of the device is half of the design operating wavelength. The actual operating efficiency of the device at different wavelengths is calculated as the ratio of the measured ±1st order vortex intensity to the sum of the ±1st order and 0th order vortex intensities: Calculated. For example... Figure 8 As shown, the geometric phase fork grating based on the Type X structure achieves an efficiency of up to 98.4% when operating at 515 nm and 80.1% when operating at 690 nm, quantitatively confirming the broadband performance of this fork grating device.

[0081] In this example, the geometric phase fork grating based on the femtosecond laser direct-write Type X structure achieves an efficiency of 98.4% at the design wavelength of 515 nm, a significant improvement over existing technologies. Furthermore, the fork grating maintains high efficiency across a wide wavelength range of 450 nm to 690 nm, supports flexible control of topological charge between l=1 and 100, and can generate topological charges up to ±10², demonstrating the effectiveness of the method.

[0082] The preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the specific details of the above embodiments. Within the scope of the technical concept of the present invention, various simple modifications can be made to the technical solution of the present invention, and these simple modifications all fall within the protection scope of the present invention.

[0083] It should also be noted that the various specific technical features described in the above specific embodiments can be combined in any suitable manner without contradiction. In order to avoid unnecessary repetition, the present invention will not describe the various possible combinations separately.

[0084] Furthermore, various different embodiments of the present invention can be combined in any way, as long as they do not violate the spirit of the present invention, they should also be regarded as the content disclosed by the present invention.

Claims

1. A method for fabricating a geometric phase cross-grating based on femtosecond laser direct writing Type X structure, characterized in that, Specifically comprising the following steps: Step one: design and parameter calculation of geometric phase cross grating device; The specific steps are: determining the size, phase gradient period P and topological charge number l of the forked grating according to application requirements, calculating the two-dimensional phase distribution of the forked grating, and quantizing the calculated continuous two-dimensional phase distribution into N-order discrete phase n , and then establishing the mapping relationship between the N-order discrete phase n and the slow axis angle of the Type X structure to obtain the two-dimensional distribution of the slow axis angle of the Type X structure to be processed . Step two: determine the processing parameter window of Type X structure; The specific steps are: using femtosecond laser direct writing processing system to process line by line, selecting lasers with different wavelengths, pulse widths and repetition frequencies, focusing the laser on different numerical aperture objectives, controlling the movement of the displacement platform to realize the processing of multiple exposure times and scanning speeds, and obtaining multiple processing parameter windows; According to the topographic features and birefringence characteristics, the above processing parameter windows are divided into Type I structure, Type X structure and Type II structure, so as to determine the processing parameter window of Type X structure; Birefringence microscope is used to characterize the phase retardation of Type X structure; Step three: femtosecond laser direct writing cross grating; The specific steps are as follows: firstly, laser processing data is generated according to the designed fork-shaped grating in step one; then, the total phase delay of the fork-shaped grating device is divided by the phase delay of the Type X structure represented in step two to calculate the required processing layers of the device of the Type X structure represented in step two to calculate the required processing layers of the device Then, the spatial coordinates of the cross grating are analyzed by the calculation tool; Then the coordinates are imported into the femtosecond laser direct writing control system, and the laser focus is focused inside the sample, the sample is moved by controlling the displacement platform, and the initial processing position is selected; Finally, the processing parameter window of Type X structure determined in step two is used to control the displacement platform to drive the sample to scan along the X axis at high speed; After completing a row, control the displacement platform to step along the Y axis to the next row, repeat the process, and complete the scanning of a single layer plane; After the single layer scanning is completed, control the displacement platform to step along the Z axis direction to the next layer, repeat the process, and complete the high-precision processing of the geometric phase cross grating.

2. The method for fabricating geometric phase cross-gratings based on femtosecond laser direct writing Type X structures according to claim 1, wherein, In step one, the slow axis angle of the Type X structure is adjusted by the polarization direction of the laser, which is always perpendicular to the polarization direction of the laser; The polarization angle of the laser is taken as N discrete values in the range of 0-180°, wherein 1≤N≤180, corresponding to N slow axis angle Type X structures; Different slow axis orientation Type X structures are measured to be different colors under the birefringence microscope.

3. The method for fabricating geometric phase cross-gratings based on femtosecond laser direct writing Type X structures according to claim 1, wherein, In step one, the two-dimensional phase distribution of the cross grating is calculated according to the phase distribution formula of the cross grating, which is as follows: ， wherein x, y represent the position coordinates of the rectangular coordinate system in the two-dimensional plane, x0, y0 represent the coordinate position of the device center, P is the phase gradient period, l is the topological charge number, and GP is the fork grating phase; According to the corresponding relationship between the slow axis angle θ of the Type X structure and the cross grating phase GP The mapping relationship between each discrete phase 𝜙 n and the slow axis angle θ of the Type X structure corresponding thereto n is calculated.​ 4. The method for fabricating geometric phase cross-gratings based on femtosecond laser direct writing Type X structures according to claim 1, wherein, In step two, the structure refractive index changes positively and the transmittance is greater than 99%, which is Type I structure; The structure can be detected to have birefringence properties and the optical transmittance is greater than 97%, which is Type X structure; The structure can be detected to have birefringence properties but the optical transmittance is less than 80%, which is Type II structure based on nanometer grating; In step two, the birefringence microscope is Oosight imaging system with Olympus BX53 optical microscope.

5. The method for fabricating geometric phase cross-gratings based on femtosecond laser direct writing Type X structures according to claim 1, wherein, In steps two and three, the wavelength of the femtosecond laser center of the femtosecond laser direct writing processing system is 343-1030 nm, the pulse width is 100 fs-10 ps, and the repetition frequency is 1 kHz-40 MHz; The objective lens NA is 0.16-0.65, and the magnification is 10-60 times; The single pulse ablation energy is 0.1-1.5 μJ; The displacement platform is an Aerotech three-axis air float displacement platform, wherein the X-axis moving range is 0-150 mm, the moving precision is 0-200 nm; the Y-axis moving range is 0-100 mm, the moving precision is 0-200 nm; the Z-axis moving range is 0-60 mm, the moving precision is 0-200 nm; The scanning speed is 0.1-300 mm / s; the point distance of the processing data is 0.1-2 μm, the single-point exposure time is 10-700 μs; the laser polarization adopts the common modulation of the Glan prism, the Pockels cell and the quarter-wave plate.

6. The method for fabricating geometric phase cross-gratings based on femtosecond laser direct writing Type X structures according to claim 1, wherein, In step three, the sample is a fused quartz glass sample, and the thickness is 0.1-7 mm.

7. The method for fabricating geometric phase cross-gratings based on femtosecond laser direct writing Type X structures of claim 1, wherein, In step three, the total phase retardation of the cross grating device is half of the design working wavelength, i.e. the phase retardation corresponding to π radians, and the formula is .

8. The method for fabricating geometric phase cross-gratings based on femtosecond laser direct writing Type X structures of claim 1, wherein, In step three, the two-dimensional spatial coordinates and phase distribution of the forked grating are calculated by the MATLAB calculation tool and stored as a.csv format file, and the processing system controls the polarization direction and focusing position of the processing laser by reading the.csv file.

9. A geometric phase cross-grating based on femtosecond laser direct written Type X structure, prepared by the method according to any one of claims 1 to 8, characterized in that, The geometric phase forked grating is composed of multiple TypeX structures with different slow axis orientations, and can convert the incident Gaussian beam into a vortex beam carrying orbital angular momentum.

10. Use of the femtosecond laser direct written Type X structure based geometric phase cross grating according to claim 9 for generating and manipulating vortex light, characterized in that, Specifically comprising: When the incident light is left-handed circularly polarized light, the output is right-handed circularly polarized vortex light with a topological charge of-l; When the incident light is right-handed circularly polarized light, the output is left-handed circularly polarized vortex light with a topological charge of+l; When the incident light is linearly polarized light, a pair of symmetric vortex light with a topological charge of-l and+l is simultaneously output at the±1 level.

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