A high-order frequency-doubled orbital angular momentum mode generation device

Abstract

The present invention discloses a high-order frequency-doubled orbital angular momentum mode generating device. The device uses laser direct writing technology to erase the second-order nonlinear coefficient in a lithium niobate crystal to form a three-dimensional fork-shaped grating array. The fork-shaped grating of each layer is a pattern obtained by non-collinear interference of an OAM mode with a topological charge of l0 and a Gaussian mode according to holographic theory and then performing binarization processing. When processing each fork-shaped grating, its central region is avoided. The fundamental frequency beam passes through the processed lithium niobate crystal to satisfy the quasi-phase matching condition, and while performing frequency doubling conversion, the optical field is regulated to achieve the generation of a high-quality high-order nonlinear OAM mode.

Description

Technical Field

[0001] The present invention relates to the technical field of nonlinear optical field control, and particularly to a technology for generating high-quality high-order frequency-doubled orbital angular momentum modes in a three-dimensional nonlinear photonic crystal, and specifically to a device for generating high-order frequency-doubled orbital angular momentum modes. Background Art

[0002] Photon orbital angular momentum (Orbital angular momentum, abbreviated as OAM) has characteristics such as a helically distributed phase, infinite dimensions, and orthogonality. The light spot is like a doughnut with a circular dark spot in the middle. Since it was verified by Allen et al. in 1992, it has been widely used in fields such as optical manipulation, optical communication, quantum, imaging, detection, and optical encryption. High-order OAM modes can significantly improve application performance. The important applications of OAM modes in the optical field have promoted the research on their generation methods. In addition to the commonly used spiral phase plates, q-plates, computer-generated holograms, π / 2 mode converters, etc., there are also various micro-integrated OAM generation devices. If one wants to generate an OAM mode at a new frequency, traditional methods require two devices: first, frequency conversion is performed through a nonlinear medium, and then OAM is loaded through a linear device. To save cost and space, a direct method has emerged, which realizes beam shaping in one step while performing nonlinear conversion. The three-dimensional nonlinear photonic crystal not only designs the second-order nonlinear coefficient χ in the vertical propagation direction (2) to regulate the optical field, but also can consider the periodic structure in the propagation direction for quasi-phase matching of the fundamental wave. Compared with metal metasurfaces and two-dimensional nonlinear photonic crystals, the nonlinear efficiency of three-dimensional nonlinear photonic crystals has been greatly improved.

[0003] The femtosecond laser direct writing technology provides a flexible way for the preparation of three-dimensional nonlinear photonic crystals. It can not only erase the second-order nonlinear coefficient at any position inside the crystal, but also change the refractive index, with the advantages of low thermal effect and high resolution. Using femtosecond laser to erase the nonlinear coefficient in a lithium niobate crystal to form a three-dimensional fork-shaped grating array can be used to generate high-efficiency frequency-doubled OAM modes. However, processing the center position of the fork-shaped grating is a challenge. Limited by the laser processing resolution and thermal effect, the center position often deforms, reducing the spot quality, especially for the fork-shaped grating structure used to generate high-order OAM modes. Summary of the Invention

[0004] In view of this, in order to solve the above problems in the prior art, the present invention proposes a device for generating high-order frequency-doubled orbital angular momentum modes, which performs optical field control while performing frequency-doubled conversion to realize the generation of high-quality high-order nonlinear OAM modes.

[0005] The present invention solves the above problems through the following technical means:

[0006] In a first aspect, the present invention provides a high-order frequency-doubled orbital angular momentum mode generation device, which uses laser direct writing technology to erase the second-order nonlinear coefficient in a lithium niobate crystal to form a three-dimensional fork-shaped grating array;

[0007] The fork-shaped grating of each layer is a pattern obtained by non-collinear interference of an OAM mode with a topological charge of l0 and a Gaussian mode according to holographic theory and then performing binarization processing;

[0008] When processing each fork-shaped grating, its central region is avoided;

[0009] The fundamental frequency beam satisfies the quasi-phase matching condition through the processed lithium niobate crystal, and while performing frequency doubling conversion, it performs optical field regulation to achieve the generation of a high-quality high-order nonlinear OAM mode.

[0010] Preferably, the processed lithium niobate crystal is expressed by the formula:

[0011]

[0012] where x, y, and z are the three azimuth values of the rectangular coordinate system, is the azimuth angle in the x-z plane, l0 is the topological charge number of the OAM mode, and a is the radius of the central region avoided during processing; in the y-z plane, the spatial frequency G y = G z = 2π / Λ, where Λ is the grating period; T is the binarization function, and for any value Z, it is expressed as:

[0013]

[0014] The change Δχ (2) in the second-order nonlinear coefficient of the crystal caused by laser processing, and the nonlinear fork-shaped grating array is expressed as:

[0015]

[0016] where represents the original nonlinear coefficient of the lithium niobate crystal.

[0017] Preferably, when the fundamental wave is incident on the crystal along the y direction and polarized along the x direction, the change in the second-order nonlinear coefficient directly performs frequency doubling conversion on the fundamental wave, satisfying the quasi-phase matching condition:

[0018]

[0019] where are the wave vectors of the fundamental frequency and the second harmonic light respectively, is the reciprocal lattice vector required for the quasi-phase matching condition, and is expressed as:

[0020]

[0021] where m and n are arbitrary integers, are unit vectors in the y and z directions respectively; the quasi-phase matching of the positive and negative first-order harmonic OAM modes requires the reciprocal lattice vectors and the quasi-phase matching of the positive and negative second-order harmonic OAM modes requires the reciprocal lattice vectors and

[0022] Preferably, the laser direct writing technology is femtosecond laser direct writing technology.

[0023] In a second aspect, the present invention provides a preparation system for a high-order harmonic orbital angular momentum mode generation device for preparing the high-order harmonic orbital angular momentum mode generation device, including a first laser, a first half-wave plate, a first polarization beam splitter, a second half-wave plate, a first lens, a second lens, a small hole, a gradient attenuator, an objective lens, a CCD, a computer, a three-dimensional nano translation stage, and a magnesium-doped lithium niobate crystal;

[0024] The first laser emits laser light along the y direction, controls the power of the laser through the first half-wave plate and the first polarization beam splitter, makes the polarization of the laser become along the z direction through the second half-wave plate, shapes the light beam through the first lens, the small hole, and the second lens, controls the energy of the laser through the gradient attenuator, makes an energy compensation for the laser processing in depth. After the laser passes through the objective lens, it is focused on the magnesium-doped lithium niobate crystal, and the reflected light beam is collected by the CCD to observe the processing state in real time; the lithium niobate crystal is placed on the three-dimensional nano translation stage, and the computer is used to control the travel of the three-dimensional nano translation stage to make the laser scribble along the x direction to form a fork-shaped grating, and the same gratings are processed in multiple layers along the y direction to form a fork-shaped grating array while avoiding the central area.

[0025] Preferably, the preparation system for the high-order harmonic orbital angular momentum mode generation device further includes a shutter, and the shutter is arranged between the first laser and the first half-wave plate for controlling the opening and closing of the laser.

[0026] Preferably, the preparation system for the high-order harmonic orbital angular momentum mode generation device further includes a dichroic mirror, and the dichroic mirror is arranged between the gradient attenuator and the objective lens for reflecting the laser light emitted from the gradient attenuator to the objective lens, and at the same time transmitting the light beam reflected by the lithium niobate crystal to the CCD for collection.

[0027] Preferably, the first laser emits laser light with a wavelength of 800 nm, a pulse width of 34 fs, and a repetition frequency of 1 kHz along the y direction.

[0028] Preferably, the focal lengths of the first lens and the second lens are 75 mm.

[0029] In a third aspect, the present invention provides a high-order frequency-doubled orbital angular momentum mode generation system, which includes the high-order frequency-doubled orbital angular momentum mode generation device, and also includes a second laser, a third half-wave plate, a second polarization beam splitter, a fourth half-wave plate, a third lens, a filter, and a receiving screen;

[0030] The second laser emits laser light along the y direction, regulates the energy of the laser light through the third half-wave plate and the second polarization beam splitter, changes the polarization direction of the fundamental wave through the fourth half-wave plate to make the polarization of the fundamental wave along the x direction, then focuses it onto the high-order frequency-doubled orbital angular momentum mode generation device through the third lens, filters out the fundamental wave through the filter, and observes the frequency-doubled signal on the receiving screen.

[0031] Compared with the prior art, the beneficial effects of the present invention at least include:

[0032] The present invention is a high-quality high-order frequency-doubled orbital angular momentum mode generation technology, which uses femtosecond laser direct writing technology to erase the second-order nonlinear coefficient in the lithium niobate crystal to form a three-dimensional fork grating array. When processing each fork grating, the central area is avoided. The fundamental frequency light beam satisfies the quasi-phase matching condition through this structure, and the optical field is regulated while the frequency doubling conversion is carried out. Compared with the fork grating array processed without avoiding the central area, the spot quality of the high-order frequency-doubled OAM mode generated by this invention is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0034] Figure 1 It is the design principle of the high-order frequency-doubled orbital angular momentum mode generation device (three-dimensional nonlinear photonic crystal) of the present invention, where (a) the fork grating array in the lithium niobate crystal; (b) the fork grating; (c) the quasi-phase matching principle in the reciprocal space;

[0035] Figure 2 It is a schematic diagram of the preparation system (three-dimensional nonlinear photonic crystal processing) of the high-order frequency-doubled orbital angular momentum mode generation device of the present invention, where (a) the processing optical path; (b-d) the fork grating processing structure, the upper figure is the processing structure with a center, and the lower figure is the processing structure without a center;

[0036] Figure 3It is a structural diagram of the high-order frequency-doubled orbital angular momentum mode generation system of the present invention. Among them, (a) is the optical path for generating the frequency-doubled high-order OAM mode, and (b-d) are the spot diagrams of the three-dimensional nonlinear photonic crystal with and without a center. (b) is the frequency-doubled spot diagram with l0 = 2; (c) is the frequency-doubled spot diagram with l0 = 3; (d) is the frequency-doubled spot diagram with l0 = 4. Detailed implementation manners

[0037] To make the above objects, features, and advantages of the present invention more obvious and understandable, the technical solutions of the present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

[0038] The present invention can also be implemented or applied through other different specific examples, and various details in this specification can also be modified and changed based on different viewpoints and applications without departing from the spirit of the present invention.

[0039] It should be noted that if there are directional indications (such as up, down, left, right, front, back...) involved in the embodiments of the present invention, then such directional indications are only used to explain the relative positional relationship and movement conditions between components in a specific posture (as shown in the accompanying drawings). If this specific posture changes, then such directional indications will also change accordingly.

[0040] In addition, if there are descriptions involving "first", "second", etc. in the embodiments of the present invention, then such descriptions of "first", "second", etc. are only for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include at least one such feature. Secondly, the technical solutions between various embodiments can be combined with each other, but it must be based on the fact that those of ordinary skill in the art can implement it. When the combination of technical solutions results in contradictions or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the protection scope required by the present invention.

[0041] Embodiment 1

[0042] The present invention provides a high-order frequency-doubled orbital angular momentum mode generation device, which uses femtosecond laser direct writing technology to erase the second-order nonlinear coefficient in a lithium niobate crystal to form a three-dimensional fork-shaped grating array;

[0043] Each layer of fork-shaped grating is a pattern obtained by non-collinear interference of an OAM mode with a topological charge of l0 and a Gaussian mode according to holographic theory and then performing binarization processing;

[0044] When processing each fork-shaped grating, its central region needs to be avoided;

[0045] The fundamental-frequency beam passes through this structure to satisfy the quasi-phase matching condition, and while performing second-harmonic conversion, it regulates the optical field to achieve the generation of high-quality higher-order nonlinear OAM modes.

[0046] A device for generating higher-order second-harmonic orbital angular momentum modes provided in this embodiment, the fork-shaped grating array processed by femtosecond laser in a lithium niobate crystal is as Figure 1 (a) shown. The fork-shaped grating of each layer is a pattern obtained by non-collinear interference of the OAM mode with topological charge l0 and the Gaussian mode according to holographic theory and then performing binarization processing. Figure 1 (b) The upper figure above is the theoretical figure including the central region calculated according to the holographic principle. It can be seen that the central region of the hologram becomes denser and denser as l0 increases, and the processing difficulty becomes greater. The present invention proposes a processing scheme to avoid the central region of the fork-shaped grating. By sacrificing a very small second-harmonic conversion efficiency, the spot quality of the higher-order second-harmonic OAM mode is improved. Such a processing scheme is as Figure 1 (b) shown in the lower figure, and can be expressed by the formula:

[0047]

[0048] where x, y, and z are the three azimuth values of the rectangular coordinate system, is the azimuth angle in the x-z plane, l0 is the topological charge number of the OAM mode, is the azimuth angle in the x-z plane, l0 is the topological charge number of the OAM mode, and a is the radius of the central region avoided in processing. In the y-z plane, the spatial frequency G y = G z = 2π / Λ, where Λ is the grating period. T is the binarization function and for any value Z, it can be expressed as:

[0049]

[0050] Femtosecond laser processing can cause a change Δχ (2) in the second-order nonlinear coefficient of the crystal. The nonlinear fork-shaped grating array can be expressed as:

[0051]

[0052] where represents the original nonlinear coefficient of the lithium niobate crystal.

[0053] When the fundamental wave is incident on the crystal along the y direction and polarized along the x direction, the change in the second-order nonlinear coefficient directly performs second-harmonic conversion on the fundamental wave, satisfying the quasi-phase matching condition:

[0054]

[0055] wherein are the wave vectors of the fundamental frequency and second harmonic light respectively, is the reciprocal lattice vector required for the quasi-phase matching condition, expressed as:

[0056]

[0057] where m and n are arbitrary integers, are the unit vectors in the y and z directions respectively. Figure 1 (c) is the schematic diagram of quasi-phase matching in the reciprocal space of the structure on the yoz plane. The quasi-phase matching of the positive and negative first-order second harmonic OAM modes requires the reciprocal lattice vectors and The quasi-phase matching of the positive and negative second-order second harmonic OAM modes requires the reciprocal lattice vectors and

[0058] Embodiment 2

[0059] As Figure 2 shown, the present invention provides a preparation system for a high-order second harmonic orbital angular momentum mode generating device for preparing the high-order second harmonic orbital angular momentum mode generating device, including a first laser, a shutter, a first half-wave plate, a first polarization beam splitter, a second half-wave plate, a first lens, a second lens, a small hole, a gradient attenuator, an objective lens, a CCD, a computer, a three-dimensional nano translation stage, and a magnesium-doped lithium niobate crystal;

[0060] Fabricate a fork-shaped grating array in a 1.5 mm (x) × 2.5 mm (y) × 1 mm (z) lithium niobate crystal, as Figure 2(As shown in (a)), the first laser emits a laser beam with a wavelength of 800 nm, a pulse width of 34 fs, and a repetition frequency of 1 kHz along the y direction. The on / off of the laser is controlled by a shutter, the power of the laser is controlled by a first half-wave plate and a first polarization beam splitter, the polarization of the laser is changed to along the z direction by a second half-wave plate, the beam is shaped by a first lens with a focal length of 75 mm, a small hole, and a second lens with a focal length of 75 mm, the energy of the laser is controlled by a gradient attenuator to perform energy compensation in depth for laser processing, making the lines of the structure more uniform. After passing through an objective lens with a numerical aperture of 0.75, the laser is focused on a 5% magnesium-doped lithium niobate crystal, and the reflected beam is collected by a CCD to observe the processing state in real time. The lithium niobate crystal is placed on a three-dimensional nano translation stage, and the travel of the three-dimensional nano translation stage is controlled by a computer (Labview software) to etch lines along the x direction. The energy continuously decreases from 240 nJ to 200 nJ at a position 20 μm below 120 μm under the crystal surface, the length of the line is 100 μm, forming a fork-shaped grating. 15 layers of the same grating are processed along the y direction to form a fork-shaped grating array. The periods Λ of the y-axis and z-axis are 3.15 μm, and the radius a of the avoided central region is 1 μm. Figure 2 (b)-(d) are fork-shaped gratings with l0 = 2, 3, and 4 respectively. The upper figures are the processing structure diagrams without removing the central position, and the lower figures are the processing structure diagrams after removing the central position.

[0061] Example 3

[0062] As Figure 3 shown, the present invention provides a high-order frequency-doubled orbital angular momentum mode generation system, which includes the high-order frequency-doubled orbital angular momentum mode generation device, and also includes a second laser, a third half-wave plate, a second polarization beam splitter, a fourth half-wave plate, a third lens, a filter, and a receiving screen;

[0063] Figure 3 (a) is the optical path for generating the frequency-doubled OAM mode. The second laser emits a laser beam with a wavelength of 800 nm, a pulse width of 140 fs, and a repetition frequency of 80 MHz along the y direction. The energy of the laser is regulated by a third half-wave plate and a second polarization beam splitter, and the polarization direction of the fundamental wave is changed by a fourth half-wave plate to make the fundamental wave polarization along the x direction. Then, it is focused on the high-order frequency-doubled orbital angular momentum mode generation device through a third lens with a focal length of 75 mm. After filtering out the fundamental wave through a filter, the frequency-doubled signal is observed on the receiving screen. Figure 3(b)-(d) are the second harmonic generation spot diagrams of the l0 = 2, 3, 4 fork grating arrays in the lithium niobate crystal respectively. The upper figures are the second harmonic generation spots without removing the central position, and the lower figures are the second harmonic generation spots with the central position removed. It can be clearly seen that after removing the central position of the fork grating, the central dark spot of the generated second harmonic generation OAM mode is rounder and of higher quality. For the decentered l0 = 2, 3, 4 fork grating arrays, the normalized second harmonic generation efficiencies of the first-order OAM mode are 2×10 -5 W -1 , 1.6×10 -5 W -1 , 1.3×10 -5 W -1 respectively.

[0064] The present invention is a high-quality high-order second harmonic generation orbital angular momentum mode generation technology, which uses femtosecond laser direct writing technology to erase the second-order nonlinear coefficient in the lithium niobate crystal to form a three-dimensional fork grating array. When processing each fork grating, its central area is avoided. The fundamental beam passes through this structure to meet the quasi-phase matching condition, and the optical field is regulated during the second harmonic generation conversion. Compared with the fork grating array processed without avoiding the central area, the spot quality of the high-order second harmonic generation OAM mode generated by the present invention is improved.

[0065] The above embodiments only represent several implementation manners of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the patent of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several deformations and improvements can still be made, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the appended claims.

Claims

1. A high-order frequency-doubled orbital angular momentum mode generation device, characterized in that The device uses laser direct writing technology to erase the second - order nonlinear coefficient in the lithium niobate crystal, forming a three - dimensional fork - shaped grating array; The fork - shaped grating of each layer is a pattern obtained by non - collinear interference of the OAM mode with topological charge l0 and the Gaussian mode according to holographic theory, and then binarization processing; When processing each fork - shaped grating, its central area is avoided; When the fundamental wave is incident on the crystal along the y - direction and polarized along the x - direction, the change in the second - order nonlinear coefficient directly performs frequency doubling conversion on the fundamental wave. The fundamental frequency beam passes through the processed lithium niobate crystal to meet the quasi - phase - matching condition, and while performing frequency doubling conversion, it conducts optical field regulation to achieve the generation of high - quality high - order nonlinear OAM modes.

2. The high-order frequency-doubled orbital angular momentum mode generation device according to claim 1, wherein The processed lithium niobate crystal is expressed by the formula: where x, y, and z are the three azimuth values of the rectangular coordinate system, is the azimuth angle of the x-z plane, l0 is the topological charge number of the OAM mode, and a is the radius of the central area to be avoided during processing; in the y-z plane, the spatial frequency G y = G z = 2π / Λ, where Λ is the grating period; T is the binarization function, and for any value Z, it is expressed as: Change Δχ of the second-order nonlinear coefficient of the crystal caused by laser processing (2) , the nonlinear fork grating array is expressed as: Among them represents the original nonlinear coefficient of the lithium niobate crystal.

3. The high-order frequency-doubled orbital angular momentum mode generating device according to claim 2, wherein, When the fundamental wave is incident on the crystal along the y - direction and polarized along the x - direction, the change in the second - order nonlinear coefficient directly performs frequency doubling conversion on the fundamental wave, meeting the quasi - phase - matching condition: wherein are the wave vectors of the fundamental frequency and second harmonic waves respectively, is the reciprocal lattice vector required for the quasi-phase matching condition, expressed as: where m and n are arbitrary integers, are unit vectors in the y and z directions respectively; the quasi-phase matching of the positive and negative first-order harmonic OAM modes requires the reciprocal lattice vectors and The quasi-phase matching of the positive and negative second-order harmonic OAM modes requires the reciprocal lattice vectors and 4. The high-order frequency-doubled orbital angular momentum mode generation device according to claim 1, wherein The laser direct writing technology is femtosecond laser direct writing technology.

5. A preparation system for a high-order frequency-doubled orbital angular momentum mode generation device, which is used to prepare the high-order frequency-doubled orbital angular momentum mode generation device as described in any one of claims 1-4, and is characterized in that, It includes a first laser, a first half - wave plate, a first polarization beam splitter, a second half - wave plate, a first lens, a second lens, a small hole, a gradient attenuator, an objective lens, a CCD, a computer, a three - dimensional nano - translation stage, and a magnesium - doped lithium niobate crystal; The first laser emits laser light along the y - direction, controls the laser power through the first half - wave plate and the first polarization beam splitter, makes the polarization of the laser become along the z - direction through the second half - wave plate, shapes the light beam through the first lens, the small hole, and the second lens, controls the laser energy through the gradient attenuator to perform energy compensation in depth for laser processing. After the laser passes through the objective lens, it is focused on the magnesium - doped lithium niobate crystal, and the reflected light beam is collected by the CCD to observe the processing state in real time; The lithium niobate crystal is placed on the three - dimensional nano - translation stage, and the computer is used to control the travel of the three - dimensional nano - translation stage to make the laser scribble along the x - direction to form fork - shaped gratings. Multiple layers of the same gratings are processed along the y - direction to form a fork - shaped grating array, while avoiding the central area.

6. The preparation system of the high-order frequency-doubled orbital angular momentum mode generation device according to claim 5, characterized in that, The preparation system of the high - order frequency - doubled orbital angular momentum mode generating device further includes a shutter, and the shutter is arranged between the first laser and the first half - wave plate for controlling the opening and closing of the laser.

7. The preparation system of the high-order frequency doubling orbital angular momentum mode generating device according to claim 5, characterized in that The preparation system of the high - order frequency - doubled orbital angular momentum mode generating device further includes a dichroic mirror, and the dichroic mirror is arranged between the gradient attenuator and the objective lens for reflecting the laser light emitted from the gradient attenuator to the objective lens, and at the same time transmitting the light beam reflected by the lithium niobate crystal to the CCD for collection.

8. The preparation system of the high-order frequency-doubled orbital angular momentum mode generating device according to claim 5, wherein The first laser emits laser light with a wavelength of 800 nm, a pulse width of 34 fs, and a repetition frequency of 1 kHz along the y - direction.

9. The preparation system of the high-order frequency doubling orbital angular momentum mode generating device according to claim 5, wherein The focal lengths of the first lens and the second lens are 75 mm.

10. A high-order frequency-doubled orbital angular momentum mode generation system, comprising the high-order frequency-doubled orbital angular momentum mode generation device according to any one of claims 1-4, characterized in that, It further includes a second laser, a third half - wave plate, a second polarization beam splitter, a fourth half - wave plate, a third lens, a filter, and a receiving screen; The second laser emits laser light along the y direction. The energy of the laser is regulated by a third half-wave plate and a second polarization beam splitter. The polarization direction of the fundamental wave is changed by a fourth half-wave plate so that the fundamental wave polarization is along the x direction. Then, it is focused onto the high-order frequency-doubled orbital angular momentum mode generating device through a third lens. After filtering out the fundamental wave through a filter, the frequency-doubled signal is observed on the receiving screen.

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