A method for generating an ultra-long focal depth array beam

Abstract

The application discloses a method for generating an ultralong focal depth array beam, and belongs to the technical field of grating manufacturing. The method comprises the following steps: constructing a Bessel beam excitation phase and a circular Airy beam excitation phase, constructing a composite phase distribution according to the array Bessel beam excitation phase and the array circular Airy beam excitation phase, and encoding the composite phase distribution to a metasurface; irradiating the metasurface with a linear polarization state plane wave, so that a left-handed circular polarization component excites an array Bessel beam, and a right-handed circular polarization component excites an array circular Airy beam; the array circular Airy beam is converted into a Bessel propagation mode after self-focusing, is spliced with the array Bessel beam in an axial direction to form a continuous light field distribution, and an ultralong focal depth array beam is obtained. The method can be applied to the fields of parallel laser processing, three-dimensional microscopic imaging and microparticle manipulation, and can extend the focal depth of the array Bessel beam while keeping the transverse resolution close to the diffraction limit.

Description

Technical Field

[0001] This application relates to the field of grating manufacturing technology, and more specifically to a method for generating an ultra-long depth-of-focus array beam. Background Technology

[0002] The Dammann grating is a binary phase grating that, by setting several phase inflection points within its period, can generate an array of beams of equal intensity on the Fourier transform focal plane. It features high diffraction efficiency, the ability to flexibly generate arrays of beams with specific distributions, and precise phase control. Dammann gratings have shown significant application potential in parallel laser processing, multi-channel optical communication, optical trapping and manipulation, and microscopic imaging.

[0003] Bessel beams possess diffraction-free and self-healing properties, and with the same transverse beam dimension, the focal depth of a Bessel beam is greater than that of a Gaussian beam. Combining Bessel beams with Dammann gratings can generate array beams with diffraction-free characteristics, further expanding the application range of Dammann gratings. Researchers have already achieved the generation of Bessel beam arrays by combining the principles of Dammann gratings with metasurfaces. For example, some scholars have demonstrated the generation of Bessel beam arrays using Huygens metasurfaces by integrating the functions of Dammann gratings and axial cone mirrors; others have experimentally verified the generation of highly uniform and high-resolution Bessel beam arrays using all-dielectric metasurfaces by optimizing the design of Dammann grating supercells. Furthermore, methods for generating Bessel beam arrays based on Huygens metasurfaces have also been reported. This method optimizes the phase of Dammann grating unit cells using a genetic algorithm to achieve uniform power beam splitting, then superimposes the Bessel beam phases to obtain the total phase, and finally encodes the metasurface based on the optimized total phase.

[0004] In recent years, metasurfaces, as two-dimensional materials composed of subwavelength-scale unit cell arrays, have been found to flexibly control the phase, amplitude, and polarization of light fields at the subwavelength scale. Generating Bessel beams using metasurfaces has become a research hotspot. Some researchers have demonstrated the generation of Bessel beam arrays using Huygens metasurfaces by integrating the functions of Damien gratings and axial conical mirrors. Other researchers have proposed a method for generating Bessel beams using all-dielectric metasurfaces with full-phase modulation. This method achieves co-polarization and cross-polarization phase modulation by simultaneously and independently controlling the transmission phase and geometric phase, generating Bessel beams of different orders with orthogonal circular or linear polarization. These studies provide new technical approaches for the generation of Bessel beam arrays.

[0005] However, the aforementioned methods for generating Bessel beam arrays based on Dammann gratings and metasurfaces all share a common limitation: the focal depth of a Bessel beam is limited by the numerical aperture and diameter of the optical elements, resulting in a finite depth of focus. Although Bessel beams have a longer depth of focus compared to Gaussian beams, there is an inherent contradiction when achieving both high lateral resolution and long depth of focus simultaneously—increasing lateral resolution requires increasing the numerical aperture, but increasing the numerical aperture leads to a shorter depth of focus. To address this issue, novel structured beams such as circular Airy beams have attracted researchers' attention. Circular Airy beams possess unique self-focusing properties; their axial intensity is approximately zero before the focal point, and they automatically convert to Bessel propagation mode after the focal point. However, currently, there is a lack of effective technical solutions to utilize this characteristic of circular Airy beams to extend the depth of focus of arrayed Bessel beams.

[0006] Therefore, how to effectively extend the focal depth of the array Bessel beam generated by the Dammann grating while maintaining a lateral resolution close to the diffraction limit is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0007] The purpose of this application is to provide a method for generating ultra-long depth-of-focus array beams, which can solve at least one of the technical problems mentioned above. The specific solution is as follows: According to a specific embodiment of this application, this application provides a method for generating an ultra-long depth-of-focus array beam, comprising the following steps: Construct the excitation phases of the Bessel beam and the circular Airy beam; The Bessel beam excitation phase is superimposed with the Dammann grating phase to obtain the array Bessel beam excitation phase; The excitation phase of the circular Airy beam is superimposed with the phase of the Damman grating to obtain the excitation phase of the arrayed circular Airy beam; A composite phase distribution is constructed based on the excitation phase of the array Bessel beam and the excitation phase of the array circular Airy beam, and the composite phase distribution is encoded into the metasurface. The metasurface is illuminated by incident light, causing it to simultaneously excite an array of Bessel beams and an array of circular Airy beams. The spatial axial splicing position is determined based on the axial propagation characteristics of the array Bessel beam and the array circular Airy beam, and the spatial axial splicing of the array Bessel beam and the array circular Airy beam is completed at the spatial axial splicing position to obtain the target array beam.

[0008] Furthermore, the methods for constructing the Bessel beam excitation phase and the circular Airy beam excitation phase are as follows: The excitation phase of the Bessel beam is determined based on the numerical aperture, metasurface diameter, and incident wavelength. The excitation phase of the circular Airy beam is determined based on the inner diameter parameters and trajectory parameters of the Airy ring.

[0009] Furthermore, before determining the excitation phase of the circular Airy beam based on the Airy ring inner diameter parameter and trajectory parameter, the phase parameters of the circular Airy beam are optimized, including the following steps: Construct the axial optical field distribution corresponding to the Bessel beam; Construct the axial optical field distribution of a circular Airy beam corresponding to different Airy ring inner diameter parameters and trajectory parameters; The axial optical field distribution of the Bessel beam is combined with the axial optical field distribution of each of the circular Airy beams for calculation. Based on the combined calculation results, the inner diameter parameters and trajectory parameters of the Airy ring used for spatial axial splicing are determined.

[0010] Further, the step of superimposing the Bessel beam excitation phase with the Dammann grating phase to obtain the array Bessel beam excitation phase includes the following steps: The phase of the Bessel beam excitation is superimposed with the phase of the Damman grating; The phase distribution after superposition is normalized; The normalized phase distribution is used as the excitation phase of the array Bessel beam.

[0011] Further, the step of superimposing the excitation phase of the circular Airy beam with the phase of the Dammann grating to obtain the excitation phase of the arrayed circular Airy beam includes the following steps: The phase of the circular Airy beam excitation is superimposed with the phase of the Damman grating; The phase distribution after superposition is normalized; The normalized phase distribution is used as the excitation phase of the array circular Airy beam.

[0012] Further, the construction of the composite phase distribution based on the excitation phase of the array Bessel beam and the excitation phase of the array circular Airy beam includes the following steps: Establish the first phase channel corresponding to the left-handed circular polarization state; Establish the second phase channel corresponding to the right-hand circular polarization state; The excitation phase of the array Bessel beam is configured to the first phase channel; The excitation phase of the arrayed circular Airy beam is configured to the second phase channel; The composite phase distribution is constructed based on the first phase channel and the second phase channel.

[0013] Further, encoding the composite phase distribution onto the metasurface includes the following steps: The transmission phase and geometric phase are determined based on the excitation phase of the array Bessel beam and the excitation phase of the array circular Airy beam. The metasurface unit structure parameters are determined based on the transmission phase and the geometric phase; The metasurface is constructed based on the structural parameters of the metasurface unit.

[0014] Furthermore, the step of irradiating the metasurface with incident light to simultaneously excite an array of Bessel beams and an array of circular Airy beams includes the following steps: The metasurface was irradiated with a linearly polarized plane wave. The linearly polarized plane wave is decomposed into a left-hand circularly polarized component and a right-hand circularly polarized component. The left-hand circularly polarized component is used to excite the array Bessel beam; The right-hand circularly polarized component is used to excite the array of circular Airy beams.

[0015] Furthermore, the method for determining the spatial axial splicing position includes the following steps: Calculate the axial optical field distribution of the array Bessel beam along the propagation direction; Calculate the axial optical field distribution of the arrayed circular Airy beam along the propagation direction; The spatial axial splicing position is determined based on the axial optical field distribution of the array Bessel beam and the axial optical field distribution of the array circular Airy beam.

[0016] Furthermore, the method for spatial axial splicing includes the following steps: Determine the first propagation interval corresponding to the array Bessel beam; Determine the second propagation interval corresponding to the arrayed circular Airy beam; Adjust the excitation phase parameters of the circular Airy beam so that the second propagation interval is connected to the first propagation interval in the propagation direction; Based on the first and second propagation intervals after connection, the spatial axial splicing of the array Bessel beam and the array circular Airy beam is completed.

[0017] Compared with the prior art, the above-described solutions of this application have at least the following beneficial effects: 1. The present application discloses a method for generating an array beam with an ultra-long focal depth. The method obtains the array Bessel beam excitation phase by superimposing the Bessel beam excitation phase with the Damman grating phase, and obtains the array circular Airy beam excitation phase by superimposing the circular Airy beam excitation phase with the Damman grating phase. By utilizing the characteristic that the circular Airy beam converts into a Bessel propagation mode after self-focusing along the propagation direction, the array circular Airy beam and the array Bessel beam form a continuous optical field distribution in the axial direction, thus solving the technical problem of the focal depth of a single Bessel beam being limited by the numerical aperture and diameter of optical elements.

[0018] 2. This application discloses a method for generating an ultra-long depth-of-focus array beam. By configuring the excitation phase of the array Bessel beam in the first phase channel corresponding to a left-handed circularly polarized state, and configuring the excitation phase of the array circular Airy beam in the second phase channel corresponding to a right-handed circularly polarized state, both polarization channels are simultaneously excited by a linearly polarized plane wave. This allows the full width at half maximum (FWHM) of each sub-beam in the spliced ​​ultra-long depth-of-focus array beam to approach the diffraction limit within the extended depth-of-focus range. The depth-of-focus extension is achieved without sacrificing lateral resolution, thus achieving a balance between high lateral resolution and ultra-long depth of focus.

[0019] 3. This application discloses a method for generating ultra-long depth-of-focus array beams. By determining the required transmission phase and geometric phase rotation angle for each metasurface unit, and based on the transmission phase and geometric phase, the structural parameters of the metasurface unit are determined. A single-layer metasurface is used to simultaneously encode the excitation phase of both the array Bessel beam and the array circular Airy beam. Compared to traditional methods requiring multiple discrete optical elements for beam combining or splicing, this application only requires a single-layer metasurface to achieve simultaneous excitation and axial splicing of two array beams, avoiding alignment errors between multiple layers of elements. It offers advantages such as small size, light weight, and ease of integration. Attached Figure Description

[0020] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application. It is obvious that the drawings described below are merely some embodiments of this application, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. In the drawings: Figure 1 This is a flowchart illustrating a method for generating an ultra-long depth-of-focus array beam according to an embodiment of this application.

[0021] Figure 2 This is a schematic diagram of the excitation phase distribution of an array Bessel beam provided in an embodiment of this application.

[0022] Figure 3 This is a schematic diagram of the excitation phase distribution of an arrayed circular Airy beam provided in an embodiment of this application.

[0023] Figure 4 This is a schematic diagram of the simulation results of the axial section of the array Bessel beam provided in the embodiments of this application.

[0024] Figure 5 This is a schematic diagram of the simulation results of the axial section of the arrayed circular Airy beam provided in the embodiments of this application.

[0025] Figure 6 A schematic diagram of the simulation results of the axial section of the ultra-long depth-of-focus array beam provided in the embodiments of this application.

[0026] Figure 7 This is a schematic diagram simulating the transverse cross-sectional light intensity distribution of the array Bessel beam at different propagation positions, as provided in the embodiments of this application.

[0027] Figure 8 This is a schematic diagram simulating the transverse cross-sectional light intensity distribution of an arrayed circular Airy beam at different propagation positions, as provided in an embodiment of this application.

[0028] Figure 9 A schematic diagram simulating the transverse cross-sectional light intensity distribution of the spliced ​​ultra-long focal depth array beam at different propagation positions, as provided in the embodiments of this application.

[0029] Figure 10 This is a schematic diagram simulating the light intensity distribution at y=0 on the transverse cross section at different propagation positions of the spliced ​​ultra-long focal depth array beam provided in the embodiments of this application. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0031] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a product or device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a product or device. Without further limitation, an element defined by the phrase "comprising one" does not exclude the presence of other identical elements in the product or device that includes that element.

[0032] The embodiments of this application are described in detail below with reference to the accompanying drawings. This application provides a method for generating an ultra-long depth-of-focus array beam, taking a linearly polarized plane wave with a wavelength of 1550 nm as an example. The technical solution of this application is based on metasurface polarization optics theory. It utilizes the physical characteristic that a circular Airy beam has extremely low axial intensity before the focal point and automatically converts to a Bessel beam after the focal point. By polarization multiplexing, a Bessel beam Dammann grating and a circular Airy beam Dammann grating are integrated onto the same metasurface element, greatly extending the depth of focus of the array beam without reducing the lateral resolution.

[0033] like Figure 1 As shown in the figure, this application provides a method for generating an ultra-long depth-of-focus array beam, including the following steps: S1. Construct the Bessel beam excitation phase and the circular Airy beam excitation phase.

[0034] S101. The method for constructing the excitation phase of a Bessel beam consists of the following steps: The excitation phase of the Bessel beam is determined based on the numerical aperture, metasurface diameter, and incident wavelength of the metasurface. The expression for the excitation phase of the Bessel beam is:

[0035] in, λ represents the excitation phase of the Bessel beam; λ represents the wavelength of the incident plane wave, which is 1550 nm in this embodiment; NA represents the numerical aperture. Represents the radial coordinates on the metasurface. , x and y represent the horizontal and vertical coordinates in the Cartesian coordinate system, respectively, and D represents the diameter of the metasurface.

[0036] From the expression for the excitation phase of a Bessel beam, it can be seen that... It is only related to the radial coordinates on the hypersurface The relevant rotationally symmetric phase distribution is the basic data for phase superposition in subsequent steps. In the technical solution of this application embodiment, the numerical aperture NA is 0.12 and the metasurface diameter D is 300 μm.

[0037] For a Bessel beam, the maximum diffraction-free propagation distance, or depth of focus, is determined by the metasurface diameter D and the cone angle of the Bessel beam. θ The decision is made jointly, and the expression is:

[0038] in, This represents the maximum non-diffraction propagation distance, also known as the depth of focus. θThis represents the cone angle of the Bessel beam. In this embodiment, the focal depth of the Bessel beam is simulated to be 0.23 mm using the angular spectrum propagation method.

[0039] In the technical solution of this application embodiment, the phase distribution for generating Bessel beams can be accurately generated through analytical expressions, which has high computational efficiency and facilitates subsequent superposition operations with the phase of the Damman grating.

[0040] S102. Optimize the phase parameters of the circular Airy beam using the following steps: The technical solution of this application embodiment provides a preferred technical solution, in which the inner diameter parameter of the Airy ring is first determined before constructing the excitation phase of the circular Airy beam. and trajectory parameters Optimization is performed to obtain the optimal parameter combination corresponding to the circular Airy beam that can be smoothly spliced ​​axially with the Bessel beam in step S101. The optimization process is completed by scanning the axial optical field distribution of the circular Airy beam under different parameter combinations and evaluating it in combination with the axial optical field distribution of the Bessel beam.

[0041] S1021. Construct the axial optical field distribution corresponding to the Bessel beam.

[0042] In this embodiment, the axial optical field distribution corresponding to the Bessel beam in step S101 is constructed using the angular spectrum propagation method. In this embodiment, the focal depth of the Bessel beam is 0.23 mm, and the Bessel beam maintains non-diffraction characteristics in the range of 0.88 mm to 1.11 mm.

[0043] S1022. Constructing parameters for different Airy ring inner diameters. and trajectory parameters The corresponding axial optical field distribution of the circular Airy beam.

[0044] In parameter range and The scan is performed inside, targeting each set of parameters ( , The axial optical field distribution of the corresponding circular Airy beam is constructed using the angular spectrum propagation method. The range of parameters for scanning can be arbitrary, but a larger parameter range will increase the computational load and time, meaning it will take longer to find the optimal result. Therefore, the appropriate range should be selected based on the actual situation.

[0045] S1023. Combine the axial optical field distribution of the Bessel beam with the axial optical field distribution of each of the circular Airy beams for calculation.

[0046] The axial light field distribution of the Bessel beam obtained in step S1021 and the axial light field distribution of each circular Airy beam obtained in step S1022 are combined and calculated along the propagation direction. That is, the axial light intensity distribution of the Bessel beam and the axial light intensity distribution of each group of circular Airy beams are superimposed at the corresponding axial positions to obtain multiple sets of composite axial light fields.

[0047] S1024. Determine the inner diameter parameters and trajectory parameters of the Airy ring used for spatial axial splicing based on the combined calculation results.

[0048] For each set of composite axial light fields, the intensity uniformity index of the composite axial light field in the stitching region, i.e., near the end of the Bessel depth of focus, is calculated. The parameter combination with the optimal uniformity is selected as the Airy ring inner diameter parameter and trajectory parameter for spatial axial stitching. The intensity uniformity index is defined as the ratio of the standard deviation to the mean of the light intensity in the stitching region; a smaller index indicates better uniformity. In the embodiments of this application, the optimized Airy ring inner diameter parameter and trajectory parameter are as follows: , At this point, the focal depth end of the Bessel beam and the Bessel mode interval formed by the self-focusing of the circular Airy beam are perfectly connected, and the light intensity uniformity index of the splicing area is better than 95%.

[0049] The technical solution of this application optimizes the phase parameters of the circular Airy beam. By using a quantitative uniformity evaluation index, the optimal splicing parameters can be objectively determined. The light intensity of the two beam segments is continuous and smooth at the splicing interface, that is, the light intensity of the second segment (the Bessel mode after the circular Airy beam is converted) and the first segment (the original Bessel beam) is continuously and smoothly connected at the splicing interface (at 1.11mm).

[0050] S103. The method for constructing the excitation phase of a circular Airy beam is as follows: Based on the Airy ring inner diameter parameters obtained in step S1024 and trajectory parameters Determine the excitation phase of the circular Airy beam. The expression for the excitation phase of the circular Airy beam is:

[0051] in, This represents the excitation phase of the circular Airy beam; k = 2π / λ.

[0052] From the expression for the excitation phase of a circular Airy beam, we can see that the excitation phase of a circular Airy beam... Similarly, only with radial coordinates The circular Airy beam excitation phase, optimized through the embodiments of this application, exhibits the following propagation characteristics: the intensity of the circular Airy beam is approximately zero in the axial region from 0 to 1.11 mm before reaching the focal point; it automatically converts to a Bessel propagation mode after reaching the focal point at 1.11 mm, and maintains diffraction-free propagation within the range of 1.11 mm to 1.43 mm. The optimized parameters construct the circular Airy beam excitation phase, ensuring precise axial matching between the axial propagation characteristics of the circular Airy beam and the focal depth range of the Bessel beam. Furthermore, the axial focusing position and mode conversion range of the circular Airy beam can be flexibly adjusted using two adjustable parameters: the trajectory parameter and the inner diameter of the Airy ring, providing adjustable degrees of freedom for subsequent axial splicing with the Bessel beam.

[0053] S2, Excite the phase of the Bessel beam. The phase of the array Bessel beam is obtained by superimposing it with the phase of the Dammann grating.

[0054] A Damman grating is a binary phase grating that can generate an array of beams of equal intensity in the far field by setting several phase inflection points within the grating period. In this embodiment, the normalized phase inflection point coordinates of a 5×5 two-dimensional Damman grating are obtained using an optimization algorithm. The phase distribution of the Dammann grating is denoted as Phase distribution of the Dammann grating It is a two-dimensional periodic phase distribution, containing two phase values, 0 and π, within one period. The phase transition position is determined by the coordinates of the aforementioned inflection points. A higher two-dimensional array can also be selected depending on the actual situation, but a higher two-dimensional array requires hardware with higher computational performance; this application does not limit this. The technical solution of the embodiments of this application can choose any optimization algorithm from the prior art, such as genetic algorithms, particle swarm optimization algorithms, simulated annealing algorithms, and tree optimization algorithms, etc.; the technical solution of this application does not limit this.

[0055] S201, Excite the phase of the Bessel beam. Phase with the Daman grating The phases are added point by point.

[0056] S202. Normalize the superimposed phase distribution, i.e., through modulo operation. Map all phase values ​​to the range of 0 to 2π.

[0057] S203. The normalized phase distribution is used as the excitation phase of the array Bessel beam, denoted as... .

[0058] Array Bessel beam excitation phase It is one of the two sets of phases ultimately inscribed on the metasurface. The technical solution of this application embodiment can expand the phase distribution of a single Bessel beam into an array form by linear phase superposition. Each sub-beam in the 5×5 array maintains the non-diffraction propagation characteristics of the Bessel beam, providing a uniform array light source for subsequent splicing.

[0059] S3. The excitation phase of the circular Airy beam is added point by point to the phase of the Damman grating to obtain the excitation phase of the arrayed circular Airy beam.

[0060] S301, Excite the phase of the circular Airy beam. Phase with the Daman grating Phase superposition is performed.

[0061] S302. Normalize the superimposed phase distribution, i.e., through modulo operation. Map all phase values ​​to the range of 0 to 2π.

[0062] S303. The normalized phase distribution is used as the excitation phase of the arrayed circular Airy beam, denoted as... .

[0063] Arrayed circular Airy beam excitation phase This is the other of the two sets of phases that are ultimately inscribed on the metasurface. The technical solution of this application, by adopting the same Dammann grating phase as in step S2, ensures that the arrayed Bessel beam and the arrayed circular Airy beam have exactly the same array arrangement and sub-beam spacing, creating symmetrical conditions for the precise alignment and splicing of the two arrayed beams in three-dimensional space.

[0064] The excitation phase distribution of an arrayed Bessel beam and the excitation phase distribution of an arrayed circular Airy beam, such as Figure 2 and Figure 3 As shown.

[0065] S4. Construct a composite phase distribution based on the array Bessel beam excitation phase and the array circular Airy beam excitation phase, and encode the composite phase distribution onto the metasurface.

[0066] The technical solution of this application embodiment utilizes polarization multiplexing technology to excite the phase of the array Bessel beam obtained in step S203. The array circular Airy beam excitation phase obtained in step S303 It is applied to two orthogonal polarization channels on the same metasurface.

[0067] S401. Establish the first phase channel corresponding to the left-hand circular polarization state. The first phase channel is used to carry the excitation phase of the array Bessel beam. .

[0068] S402. Establish the second phase channel corresponding to the right-hand circular polarization state. The second phase channel is used to carry the excitation phase of the arrayed circular Airy beam. .

[0069] S403, Excite the phase of the array Bessel beam. Configured to the first phase channel. That is, set so that when the incident light is in a left-handed circularly polarized state, the metasurface should provide phase modulation for the outgoing light. .

[0070] S404. The excitation phase of the arrayed circular Airy beam is configured to the second phase channel. That is, it is set that when the incident light is in a right-handed circularly polarized state, the metasurface should provide phase modulation for the outgoing light. .

[0071] S405. Construct the composite phase distribution based on the first phase channel and the second phase channel. The composite phase distribution enables the metasurface to simultaneously apply corresponding phase modulations to left-handed and right-handed circularly polarized light.

[0072] S406, Excitation phase according to the array Bessel beam and the excitation phase of the arrayed circular Airy beam Determine the transmission phase and geometric phase rotation angle .

[0073] Transmission phase in the embodiments of this application This is achieved by changing the structural dimensions of the metasurface unit cells, such as the length and width of nanopillars. (Transmission phase) Its characteristic is that it produces the same phase delay for both left-handed and right-handed circularly polarized light.

[0074] Geometric phase rotation angle in the embodiments of this application This is achieved by rotating the metasurface element by an angle. When the metasurface element rotates within the plane by an angle value... At that time, the geometric phase produces a left-handed circularly polarized light The phase delay produces a phase delay for right-handed circularly polarized light. Phase delay.

[0075] By making the left-hand circularly polarized light obtain a phase value and The same; similarly, the phase value of right-hand circularly polarized light is obtained as... The same applies; the specific calculation formula is as follows:

[0076]

[0077] S407. The transmission phase calculated based on step S406 and geometric phase rotation angle Determine the structural parameters of the metasurface unit.

[0078] For each metasurface unit, according to the transmission phase The corresponding nanopillar dimensions (length and width) are searched in the pre-defined structure database, and then the unit rotation angle is determined. Set the rotation angle of the nanopillar in the plane.

[0079] S408. Construct the metasurface based on the metasurface unit structure parameters. A complete metasurface device is constructed based on the unit structure parameters determined in step S407, with each unit arranged periodically to form a metasurface array. In this embodiment, the period is 350 nm.

[0080] The technical solution of this application embodiment can achieve parallel loading of two independent phases with only a single-layer metasurface, avoiding alignment errors between two discrete components. At the same time, it realizes independent phase control of orthogonal circular polarization state by utilizing the coordinated design of transmission phase and geometric phase.

[0081] S5. Irradiate the metasurface with incident light to simultaneously excite an array of Bessel beams and an array of circular Airy beams.

[0082] The metasurface constructed in step S408 is illuminated by incident light, and after being modulated by the metasurface, arrayed Bessel beams and arrayed circular Airy beams are simultaneously generated in free space.

[0083] S501. Irradiate the metasurface with a linearly polarized plane wave. The technical solution of this embodiment uses an x-ray linearly polarized plane wave to vertically irradiate the metasurface constructed in step S408, with a wavelength of 1550 nm.

[0084] S502. Decompose the x-linearly polarized plane wave into a left-handed circularly polarized component and a right-handed circularly polarized component.

[0085] S503. The left-hand circularly polarized component is used to excite the array Bessel beam. After passing through the metasurface, the left-hand circularly polarized component is phase-modulated and propagates in free space to form the array Bessel beam. Each sub-beam in the array Bessel beam has diffraction-free propagation characteristics.

[0086] S504. The right-hand circularly polarized component is used to excite an array of circular Airy beams. After passing through the metasurface, the right-hand circularly polarized component undergoes phase modulation and propagates in free space to form an array of circular Airy beams. Each sub-beam in the array of circular Airy beams has the characteristic of automatically converting to Bessel mode after self-focusing.

[0087] The technical solution of this application embodiment can simultaneously activate two orthogonal polarization channels with a single beam of X-ray polarized light, without the need for additional polarization beam splitting or combining elements, making the system structure simple and compact. Furthermore, the initial phase and intensity of the two polarization channels are determined by the same incident light, ensuring excitation synchronization.

[0088] S6. Determine the spatial axial splicing position based on the axial propagation characteristics of the array Bessel beam and the array circular Airy beam, and complete the spatial axial splicing of the array Bessel beam and the array circular Airy beam at the spatial axial splicing position to obtain the target array beam.

[0089] S601. Calculate the axial optical field distribution of the arrayed Bessel beam along the propagation direction. The intensity distribution of the arrayed Bessel beam along the Z-axis propagation direction is simulated using the angular spectrum propagation method. In this embodiment, the axial optical field distribution of the arrayed Bessel beam along the Z-axis propagation direction is calculated using parameters such as wavelength, numerical aperture, and metasurface diameter from S101. It maintains high intensity and quasi-diffraction-free properties within the range.

[0090] S602. Calculate the axial optical field distribution of the arrayed circular Airy beam along the propagation direction. The intensity distribution of the arrayed circular Airy beam along the Z-axis is simulated using the angular spectrum propagation method. The Airy ring inner diameter parameters obtained in step S102 are then used as the basis for the calculation. and trajectory parameters Below, the array of circular Airy beams was calculated to be in... The axial intensity within the interval is extremely low, meaning the light intensity in the region in front of the focal point is approximately zero; Nearby, self-focusing forms a high-intensity light spot. It automatically switches to Bessel propagation mode within the interval.

[0091] S603. Determine the spatial axial splicing position based on the axial optical field distribution of the arrayed Bessel beam obtained in step S601 and the axial optical field distribution of the arrayed circular Airy beam obtained in step S602. Comparing the axial optical field distributions of the arrayed Bessel beam and the arrayed circular Airy beam, it can be seen that the focal depth end of the arrayed Bessel beam is located at... The starting point for the arrayed circular Airy beam to self-focus and begin converting to Bessel mode is also located at... Therefore, the spatial axial splicing position is determined as follows: Place.

[0092] S604. Determine the first propagation interval corresponding to the array Bessel beam. Based on the calculation result of step S601, the first propagation interval is... Within the first propagation interval, the array Bessel beam maintains diffraction-free propagation.

[0093] S605. Determine the second propagation interval corresponding to the arrayed circular Airy beam. Based on the calculation results of step S602 and combined with the splicing position of step S603, the second propagation interval is... Within the second propagation interval, the arrayed circular Airy beam has been converted to Bessel propagation mode.

[0094] S606. Adjust the excitation phase parameters of the circular Airy beam to connect the second propagation interval with the first propagation interval in the propagation direction. The above adjustment was completed in the parameter optimization in step S102, by selecting the Airy ring inner diameter parameter and trajectory parameters as follows: , The starting position where the circular Airy beam self-focuses and converts to Bezier mode falls exactly on The focal depth of the Bessel beam in the array coincides with the focal depth end. If improper parameter selection results in a gap or overlap between the first and second propagation intervals, it is necessary to return to step S102 for re-optimization.

[0095] S607. Based on the first and second propagation intervals after connection, complete the spatial axial splicing of the arrayed Bessel beam and the arrayed circular Airy beam. The first and second propagation intervals are in... The ends are connected to form a cover. The continuous propagation range.

[0096] In the technical solution of this application embodiment, within the continuous propagation range, the first segment (0.88mm to 1.11mm) is the original array Bessel beam, and the second segment (1.11mm to 1.43mm) is the Bessel mode beam converted from a circular Airy beam. The light intensity of the two beams at the splicing position is continuous and smooth, without abrupt changes. The total focal depth of the ultra-long focal depth array beam formed after splicing is 0.55mm, which is 2.39 times the focal depth of the original Bessel beam.

[0097] In the technical solution of this application embodiment, the axial optical field superposition of the arrayed Bessel beam and the arrayed circular Airy beam constitutes beam splicing. Since the left-handed and right-handed circular polarization states are orthogonal, the two arrayed beams will not coherently interfere when they coexist in space, and the total optical field intensity is an incoherent superposition of the intensity of the arrayed Bessel beam and the intensity of the arrayed circular Airy beam.

[0098] An arrayed Bessel beam is generated by excitation from a left-handed circularly polarized component, while an arrayed circular Airy beam is generated by excitation from a right-handed circularly polarized component. Since the left-handed and right-handed circularly polarized states are orthogonal, the two arrayed beams do not coherently interfere when coexisting in space; the total optical field intensity is an incoherent superposition of the intensities of the arrayed Bessel beam and the arrayed circular Airy beam. Therefore, combining the axial optical field distributions of the Bessel beam and the circular Airy beam along the propagation direction constitutes beam splicing.

[0099] The axial propagation of a circular Airy beam exhibits a unique evolutionary pattern: the axial light intensity is approximately zero in the propagation interval before the focal point, and automatically converts to a Bessel propagation mode after passing the focal point. Based on this characteristic, the excitation phase of the Bessel beam is first superimposed with the phase of the Damman grating to obtain the excitation phase of the arrayed Bessel beam; the excitation phase of the circular Airy beam is then superimposed with the phase of the Damman grating to obtain the excitation phase of the arrayed circular Airy beam. Then, the axial light field distribution corresponding to the Bessel beam and the axial light field distribution of the circular Airy beam corresponding to different Airy ring inner diameter parameters and trajectory parameters are constructed. The axial light field distributions of the Bessel beam and each circular Airy beam are combined and calculated along the propagation direction. Based on the uniformity of light intensity in the splicing area obtained from the combined calculation, the optimal Airy ring inner diameter parameters and trajectory parameters are determined. In this embodiment, the optimized Airy ring inner diameter parameter is 0.12 mm, and the trajectory parameter is 0.008.

[0100] Under optimal parameters, the focal point of the arrayed circular Airy beam is located at the end of the focal depth of the arrayed Bessel beam. This ensures that the axial intensity of the arrayed circular Airy beam is approximately zero within the corresponding focal depth range of the arrayed Bessel beam before the focal point, thus not interfering with the propagation of the arrayed Bessel beam. After passing the focal point, the arrayed circular Airy beam automatically switches to Bessel propagation mode, continuing the propagation of the arrayed Bessel beam axially, forming a continuous high-intensity propagation range from 0.88 mm to 1.43 mm. The two beam segments smoothly connect at the splicing interface, achieving an extension of the focal depth of the arrayed Bessel beam from 0.23 mm to 0.55 mm, reaching 2.39 times the original focal depth.

[0101] The technical solution of this application embodiment utilizes the propagation characteristics of a circular Airy beam that automatically converts to a Bessel beam after focal point, realizing seamless relay propagation of two array beams. This breaks through the physical bottleneck of the focal length of a single Bessel beam being limited by the element aperture, and the splicing process does not require additional optical elements, but is completed automatically by the propagation characteristics of the beam itself.

[0102] The technical solution provided in this application uses the angular spectrum propagation method to simulate and verify beam propagation under three incident conditions, such as... Figures 4-6 As shown: like Figure 4 As shown, LCP represents left-handed circularly polarized light. When left-handed circularly polarized light is incident alone, that is, only the first phase channel in step S401 is activated, the metasurface generates an array Bessel beam with an axial depth of focus of 0.23 mm. The array Bessel beam generated by the metasurface exits from the exit surface, that is... Propagation begins at 0mm, in It maintains high intensity and non-diffraction propagation characteristics within the range of [0.88mm, 1.11mm]. When the propagation distance exceeds 1.11mm, the beam intensity decays rapidly, and the focal depth is approximately 0.23mm.

[0103] like Figure 5 As shown, RCP represents right-handed circularly polarized light. When right-handed circularly polarized light is incident alone, that is, only the second phase channel of step S402 is activated, the metasurface generates an array of circular Airy beams. The array of circular Airy beams has extremely low intensity before 1.11 mm, and then converts to Bessel mode after 1.11 mm. Specifically, the array of circular Airy beams in... Within the propagation range up to 1.11 mm, the axial light intensity is extremely low, appearing as a dark area. At approximately 1.11 mm, the beam self-focuses, forming a high-intensity spot, and... 1.11mm to Within the 1.43 mm range, it automatically switches to Bezier propagation mode, exhibiting obvious non-diffraction characteristics.

[0104] like Figure 6 As shown, when X-ray polarized light is incident, that is, when the first phase channel and the second phase channel are activated simultaneously, the arrayed Bessel beam and the arrayed circular Airy beam are generated simultaneously, and in... Automatic stitching was used, achieving a total depth of focus of 0.55 mm. As can be seen from the image, from... to For the depth of focus range of the Bessel beam, from to The two intervals are the Bessel mode intervals after the conversion of the circular Airy beam. The beams are joined end-to-end at 1.11mm to form a continuous high-intensity propagation range from 0.88mm to 1.43mm. The total focal depth after splicing is 0.55mm, which is 2.39 times the focal depth of the original Bessel beam (0.23mm).

[0105] Figures 7-9 The diagram shows a comparison of the transverse cross-sections (xy-sections) of beams generated under three incident conditions: arrayed Bessel beams, arrayed circular Airy beams, and ultra-long depth-of-focus array beams. Figures 7-9 In Each contains 0.88mm 1.0mm 1.2mm and Four propagation positions at 1.43mm, each simultaneously displaying three different transverse cross-sectional shapes of the beam.

[0106] like Figure 7 As shown, Figure 7Figure (a) corresponds to a propagation position of 0.88 mm; Figure (b) corresponds to a propagation position of 1.0 mm; Figure (c) corresponds to a propagation position of 1.2 mm; and Figure (d) corresponds to a propagation position of 1.43 mm. The cross-sectional diagrams of the array Bessel beams show that the focusing effect of each sub-beam is relatively good at z=0.88 mm; to... At 1.2 mm, the light spot intensity significantly decreases, essentially losing its non-diffraction characteristics; to At 1.43mm, the light spot almost completely disappears.

[0107] like Figure 8 As shown, Figure 8 Figure (a) corresponds to a propagation position of 0.88 mm; Figure (b) corresponds to a propagation position of 1.0 mm; Figure (c) corresponds to a propagation position of 1.2 mm; and Figure (d) corresponds to a propagation position of 1.43 mm. The cross-sectional view of the arrayed circular Airy beam shows that... At 0.88mm, the sub-beams are not yet fully focused, and the light intensity is relatively weak; 1.0mm to Within a 1.43 mm range, each sub-beam is focused, the light intensity increases, and the non-diffraction characteristics of the Bessel mode are maintained. This verifies the characteristic of the circular Airy beam to automatically convert to the Bessel propagation mode after self-focusing, with a focal depth range of [1.11 mm, 1.43 mm].

[0108] like Figure 9 As shown, Figure 9 Figure (a) corresponds to a propagation position of 0.88 mm; Figure (b) corresponds to a propagation position of 1.0 mm; Figure (c) corresponds to a propagation position of 1.2 mm; and Figure (d) corresponds to a propagation position of 1.43 mm. The cross-sectional views of the ultra-long depth-of-focus array beam show that... 0.88mm to Throughout the entire 1.43mm propagation range, each sub-beam maintained a regular circular spot. To further verify the beam quality of the stitched ultra-long depth-of-focus array beam at different propagation positions within the depth of focus, the lateral resolution of the stitched ultra-long depth-of-focus array Bessel beam at different propagation positions within the depth of focus was quantitatively analyzed, and the full width at half maximum (FWHM) of individual sub-beams at each axial position was measured. Figure 10 As shown, the ultra-long depth of focus array beam at a typical propagation position, Figure 10Figure (a) corresponds to the light intensity distribution at y=0 in the transverse section with Z=0.88mm; Figure (b) corresponds to the light intensity distribution at y=0 in the transverse section with Z=1.0mm; Figure (c) corresponds to the light intensity distribution at y=0 in the transverse section with Z=1.2mm; Figure (d) corresponds to the light intensity distribution at y=0 in the transverse section with Z=1.3mm; and Figure (e) corresponds to the light intensity distribution at y=0 in the transverse section with Z=1.43mm. At the five propagation positions, the full width at half maximum (FWHM) of the sub-beam is 4.54μm, 3.76μm, 4.5μm, 5.5μm, and 6.72μm, respectively. From the above data, it can be seen that... 0.88mm to Within the 1.2mm range, the full width at half maximum (FWHM) remains essentially constant, and the beam does not exhibit significant lateral broadening after splicing, approaching the theoretical diffraction limit. Simultaneously, the intensity differences between sub-beams within the array are small, and the intensity uniformity is better than 95%. These results demonstrate that the spliced ​​ultra-long depth-of-focus array beam maintains consistent lateral resolution and good uniformity throughout the entire extended depth-of-focus range.

[0109] The ultra-long depth-of-focus array beam generation method provided in this embodiment is based on the metasurface polarization control principle. It constructs a Bessel beam excitation phase, optimizes the phase parameters of a circular Airy beam to obtain the optimal Airy ring inner diameter and trajectory parameters, constructs the circular Airy beam excitation phase based on the optimized parameters, and forms the array phase by superimposing Dammann grating phases. The two array phases are encoded onto a single-layer metasurface using the transmission phase and geometric phase. Two polarization channels are simultaneously excited using linearly polarized light, and axial stitching is completed using the self-focusing and automatic conversion characteristics of the circular Airy beam. The entire technical solution is complete and logically clear, achieving a 2.39-fold extension of depth of focus while maintaining lateral resolution.

[0110] In summary, the technical solution of this application, a method for generating ultra-long depth-of-focus array beams, extends the focal depth of the arrayed Bessel beam from 0.23 mm to 0.55 mm, achieving a 2.39-fold increase, by spatially splicing a Bessel beam and a circular Airy beam along their axes. Simultaneously, utilizing the polarization multiplexing properties of a metasurface, the excitation phases of the arrayed Bessel beam and the arrayed circular Airy beam are integrated into a single-layer metasurface. Combined with the cooperative encoding of the transmission phase and geometric phase, independent phase modulation of the left-hand and right-hand circularly polarized states is achieved. The spliced ​​ultra-long depth-of-focus arrayed Bessel beam exhibits full width at half maximum (FWHM) of each sub-beam approaching the diffraction limit within the extended focal depth range, and the intensity uniformity among the sub-beams within the array is better than 95%. This application achieves a significant extension of focal depth while maintaining a lateral resolution close to the diffraction limit. Furthermore, the single-layer metasurface device has a simple structure and high integration, making it widely applicable in fields such as parallel laser processing of high aspect ratio micro / nano structures, rapid three-dimensional microscopic imaging in scattering media, and long-distance multi-particle optical capture and manipulation.

[0111] Finally, it should be noted that the various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems or apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple, and relevant parts can be referred to the method section.

[0112] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for generating an ultra-long depth-of-focus array beam, characterized in that, Includes the following steps: Construct the excitation phases of the Bessel beam and the circular Airy beam; The Bessel beam excitation phase is superimposed with the Dammann grating phase to obtain the array Bessel beam excitation phase; The excitation phase of the circular Airy beam is superimposed with the phase of the Damman grating to obtain the excitation phase of the arrayed circular Airy beam; A composite phase distribution is constructed based on the excitation phase of the array Bessel beam and the excitation phase of the array circular Airy beam, and the composite phase distribution is encoded into the metasurface. The metasurface is illuminated by incident light, causing it to simultaneously excite an array of Bessel beams and an array of circular Airy beams. The spatial axial splicing position is determined based on the axial propagation characteristics of the array Bessel beam and the array circular Airy beam, and the spatial axial splicing of the array Bessel beam and the array circular Airy beam is completed at the spatial axial splicing position to obtain the target array beam.

2. The method for generating an ultra-long depth-of-focus array beam according to claim 1, characterized in that, The methods for constructing the excitation phase of the Bessel beam and the excitation phase of the circular Airy beam are as follows: The excitation phase of the Bessel beam is determined based on the numerical aperture, metasurface diameter, and incident wavelength. The excitation phase of the circular Airy beam is determined based on the inner diameter parameters and trajectory parameters of the Airy ring.

3. The method for generating an ultra-long depth-of-focus array beam according to claim 2, characterized in that, Before determining the excitation phase of the circular Airy beam based on the inner diameter and trajectory parameters of the Airy ring, the phase parameters of the circular Airy beam are optimized, including the following steps: Construct the axial optical field distribution corresponding to the Bessel beam; Construct the axial optical field distribution of a circular Airy beam corresponding to different Airy ring inner diameter parameters and trajectory parameters; The axial optical field distribution of the Bessel beam is combined with the axial optical field distribution of each of the circular Airy beams for calculation. Based on the combined calculation results, the inner diameter parameters and trajectory parameters of the Airy ring used for spatial axial splicing are determined.

4. The method for generating an ultra-long depth-of-focus array beam according to claim 1, characterized in that, The excitation phase of the Bessel beam is superimposed with the phase of the Dammann grating to obtain the excitation phase of the arrayed Bessel beam, including the following steps: The phase of the Bessel beam excitation is superimposed with the phase of the Damman grating; The phase distribution after superposition is normalized; The normalized phase distribution is used as the excitation phase of the array Bessel beam.

5. The method for generating an ultra-long depth-of-focus array beam according to claim 1, characterized in that, The circular Airy beam excitation phase is superimposed with the Dammann grating phase to obtain the arrayed circular Airy beam excitation phase, including the following steps: The phase of the circular Airy beam excitation is superimposed with the phase of the Damman grating; The phase distribution after superposition is normalized; The normalized phase distribution is used as the excitation phase of the array circular Airy beam.

6. The method for generating an ultra-long depth-of-focus array beam according to claim 1, characterized in that, Constructing a composite phase distribution based on the excitation phase of the arrayed Bessel beam and the excitation phase of the arrayed circular Airy beam includes the following steps: Establish the first phase channel corresponding to the left-handed circular polarization state; Establish the second phase channel corresponding to the right-hand circular polarization state; The excitation phase of the array Bessel beam is configured to the first phase channel; The excitation phase of the arrayed circular Airy beam is configured to the second phase channel; The composite phase distribution is constructed based on the first phase channel and the second phase channel.

7. The method for generating an ultra-long depth-of-focus array beam according to claim 6, characterized in that, Encoding the composite phase distribution onto the metasurface includes the following steps: The transmission phase and geometric phase are determined based on the excitation phase of the array Bessel beam and the excitation phase of the array circular Airy beam. The metasurface unit structure parameters are determined based on the transmission phase and the geometric phase; The metasurface is constructed based on the structural parameters of the metasurface unit.

8. The method for generating an ultra-long depth-of-focus array beam according to claim 1, characterized in that, Irradiating the metasurface with incident light to simultaneously excite an array of Bessel beams and an array of circular Airy beams includes the following steps: The metasurface was irradiated with a linearly polarized plane wave. The linearly polarized plane wave is decomposed into a left-hand circularly polarized component and a right-hand circularly polarized component. The left-hand circularly polarized component is used to excite the array Bessel beam; The right-hand circularly polarized component is used to excite the array of circular Airy beams.

9. The method for generating an ultra-long depth-of-focus array beam according to claim 1, characterized in that, The method for determining the spatial axial splicing position includes the following steps: Calculate the axial optical field distribution of the array Bessel beam along the propagation direction; Calculate the axial optical field distribution of the arrayed circular Airy beam along the propagation direction; The spatial axial splicing position is determined based on the axial optical field distribution of the array Bessel beam and the axial optical field distribution of the array circular Airy beam.

10. The method for generating an ultra-long depth-of-focus array beam according to claim 9, characterized in that, Determining the spatial axial splicing position based on the axial optical field distribution of the arrayed Bessel beams and the arrayed circular Airy beams includes the following steps: Determine the first propagation interval corresponding to the array Bessel beam; Determine the second propagation interval corresponding to the arrayed circular Airy beam; Adjust the excitation phase parameters of the circular Airy beam so that the second propagation interval is connected to the first propagation interval in the propagation direction; Based on the first and second propagation intervals after connection, the spatial axial splicing of the array Bessel beam and the array circular Airy beam is completed.

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