Method for generating staggered superposition double-layer Airy light beam array capable of realizing double focusing

Abstract

The invention discloses a method for generating a staggered superposition double-layer Airy light beam array capable of realizing double focusing, and belongs to the technical field of structured light regulation and control and special light beam generation. Aiming at the problems that the focusing characteristics of light beam arrays in transmission in different superposition modes are difficult to fully reveal in the prior art and the generation of an optical bottle depends on complex phase modulation or multiple optical elements, the method comprises the following steps: constructing a first layer of Airy light beam array and setting regulation and control parameters, constructing a second layer of Airy light beam array with staggered azimuth angles and setting regulation and control parameters, and constructing a second layer of Airy light beam array with staggered azimuth angles; a longitudinal double-focusing structure is realized through staggered superposition of double-layer Airy light beam arrays, and a vortex phase is introduced into double-focusing array light beams to form an optical bottle structure. According to the invention, the structure is simple, the longitudinal double-focusing and optical bottle structure can be realized only through the initial light field structure design, the focusing intensity and the regulation freedom degree are high, and the application of the light beam in the related fields of microscopic imaging, particle capture and the like is expanded.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of structured light regulation and special beam generation, and particularly relates to a method for generating a double-focusing misaligned superimposed double-layer Airy beam array. BACKGROUND

[0002] Structured beams, with their unique spatial structure, have driven numerous innovative breakthroughs in optical manipulation, information transmission, and precision machining. Airy beams, as an important type of structured beams, were first experimentally verified in 2007. Due to their unique properties such as non-diffraction, self-acceleration, and self-healing, Airy beams have received widespread attention. Since then, researchers have introduced circular Airy beams, which exhibit sudden self-focusing due to their ring-shaped structure.

[0003] However, single self-focusing beams have limitations in intensity and tunability, which limits their applicability in complex scenarios. To address this limitation, researchers have proposed various arrays composed of self-focusing beams. Qian et al. studied the self-focusing properties of a ring array Airy beam carrying a vortex array. Liu et al. proposed a chirped multi-Pearcey beam, which utilizes first- and second-order chirp factors to achieve double or multi-focusing control and significantly improves the trapping force on Rayleigh particles. Huang et al. proposed an Airy-derived beam array with optical vortices and studied the self-focusing properties and radiation force of the beam array. Deng et al. introduced a masked Pearcey beam array and studied its properties in linear and nonlinear media. However, these studies do not comprehensively address the flexible control of focal point positions and intensities, and do not fully exploit the focusing properties of beams in the transmission process under different superimposed modes.

[0004] Meanwhile, optical bottles have attracted attention due to their applications in particle trapping and microscopic manipulation. Many methods have been developed to generate optical bottles, including beam interference, Moll technique, Fourier space method, and laser cavity method. Chirped circular / elliptical Pearcey beams and chirped circular / elliptical Airy beams have been used to construct optical bottles due to their chirp-like lens effects. In addition, a multi-optical bottle structure with an anisotropic phase ring Airy Gaussian vortex beam has also been reported. Exploring new types of multi-optical bottle beams can expand their potential applications. The above-mentioned methods for generating optical bottles often rely on complex phase modulation methods or the cooperative action of multiple optical elements, resulting in relatively complex system structures, and the combination of multi-focusing array beams still needs further exploration.

[0005] Based on this, it is necessary to propose a new method for constructing self-focusing beam arrays. By designing the azimuth angle misalignment superposition of the double-layer Airy beam array, a longitudinal double-focusing structure can be realized. Furthermore, vortex phase modulation is introduced to form an optical bottle structure, thus providing a new technical approach for the generation of multi-focusing structure light fields and optical bottles. Summary of the Invention

[0006] To address the limitations of existing methods in fully revealing the focusing characteristics of beam arrays under different superposition schemes during transmission, and the problem that optical bottle generation relies on complex phase modulation or multiple optical elements, this invention proposes a method for generating dual focus by superimposing a double-layer Airy beam array with azimuth angle misalignment. This method achieves dual focus control based solely on the initial optical field structure design, featuring a simple structure, flexible control, and ease of integration with multi-focusing array beam structures. To achieve the above objectives, this invention employs the following technical solutions:

[0007] A method for generating a misaligned superimposed double-layer Airy beam array with dual focusing, the method comprising the following steps:

[0008] Step 1: Construct the first layer of Airy beam array on the initial plane. This array consists of multiple two-dimensional Airy beams, each of which is uniformly distributed along the circumference. During the construction process, the control parameters of the first layer of Airy beam array are set.

[0009] Step 2: Construct a second layer of Airy beam array on the same initial plane. The number of Airy beams in the second layer of Airy beam array is the same as that in the first layer. The overall azimuth angle is rotated and misaligned relative to the first layer by a preset angle. Its control parameters can be the same as or different from those of the first layer.

[0010] Step 3: The first and second layers of Airy beam arrays are superimposed. During the propagation of the double-layer array beams, two focusing planes are formed at different positions, thereby realizing a longitudinal double-focusing structure.

[0011] Step 4: Introduce vortex phase modulation on the basis of longitudinal dual-focusing Airy beam array to form an optical bottle with a hollow structure in the focusing area.

[0012] This invention utilizes a two-dimensional Airy beam to generate dual focusing and an optical bottle through a double-layer misalignment superposition and optical vortex. The principle behind its generation is as follows:

[0013] In paraxial optics, the spatial beam evolving along the z-direction is described by the (2+1)-dimensional potential-free Schrödinger equation in a linear medium, the normalized form of which is:

[0014]

[0015] in, It is the amplitude of the electric field, with the x and y axes relative to any length. Normalization The propagation distance z is relative to Normalization, in which For wave number, For wavelength, .

[0016] A two-dimensional Airy beam on the initial plane can be defined as:

[0017]

[0018] in, Represents the Airy integral, for example , Let be the attenuation coefficient of the Gaussian function. .

[0019] In specific operation of this invention, a first layer of Airy beam array is constructed on the initial plane:

[0020]

[0021]

[0022] Construct a second layer of Airy beam array on the same initial plane:

[0023]

[0024]

[0025] in, Indicates the first layer The corresponding positions of the centers of the Airy beams on the xy plane Indicates the second layer The corresponding positions of the centers of the Airy beams on the xy plane This indicates the number of two-dimensional Airy beams superimposed in each layer. , Indicates the horizontal scale factor. Indicates the radial displacement factor of the first layer; Indicates the radial displacement factor of the second layer. and The relationship is , Indicates the first layer One Airy beam; Indicates the second layer A beam of Airy light This represents the angular difference between two beam arrays.

[0026] By superimposing the first and second layers of the Airy beam array, a double-layer Airy beam array is obtained:

[0027]

[0028] in, It is the normalized constant amplitude of the initial spatial field, ensuring that the maximum peak intensity of the input beam is 1.

[0029] Vortex phase modulation is introduced based on the misaligned superimposed double-layer Airy beam array:

[0030]

[0031] Among them, parameters and These represent the number of optical vortices and the topological charge, respectively. This indicates the position of the J-th vortex. When there is significant double focusing, vortex phase is introduced, and the original double-focusing structure of the misaligned superimposed double-layer Airy beam array becomes an optical bottle structure. As the topological charge number or quantity of vortices increases, the hollow region at the beam center gradually increases. Changes in vortex position do not affect the focusing position of the beam array, but they do affect the annular structure of the focal plane.

[0032] Both the first and second layer Airy beam arrays are composed of multiple two-dimensional Airy beams evenly distributed at equal angles along the circumferential direction.

[0033] The second layer of Airy beam array is offset from the first layer of Airy beam array by rotating the overall azimuth angle;

[0034] The self-focusing intensity and position of the Airy beams in different layers are controlled by adjusting parameters such as the scale factor, displacement factor, interlayer angle difference and amplitude ratio of the corresponding layers, so that the double-layer array beams form a longitudinal double-focusing structure during free space propagation.

[0035] Based on the longitudinal dual-focusing Airy beam array, vortex phase modulation is introduced to form an optical bottle structure in the dual-focusing region.

[0036] Compared with the prior art, the present invention has the following advantages:

[0037] This invention achieves a stable dual-focusing structure by using an azimuth-shifted superposition design for a double-layer Airy beam array, which naturally forms two longitudinally separated focusing planes during free space propagation. This eliminates the need for high-order chirping, complex phase encoding, or nonlinear media, and the focusing mechanism is clear and highly controllable.

[0038] By adjusting the parameters of different layers of the Airy beam array, the position and intensity of each focusing plane can be controlled separately, enabling flexible and precise control of the dual-focusing characteristics, suitable for different application needs.

[0039] By introducing vortex phase modulation on the basis of dual-focusing Airy beam array, a hollow optical bottle structure can be formed in the focusing area. The size and shape of the optical bottle can be adjusted by vortex parameters, thus achieving effective integration of multi-focusing structure and optical bottle structure. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of the misaligned superimposed double-layer Airy beam array of the present invention;

[0041] Figure 2 yes Transmission characteristics of a dual-layer Airy beam array;

[0042] Figure 3 It is the angle difference between different layers Transmission curve of the lower double-layer Airy beam array;

[0043] Figure 4 It is a graph showing the relationship between different stacking quantities M and the focal position and intensity;

[0044] Figure 5 These are transmission curves of a two-layer Airy beam array under different scale factors;

[0045] Figure 6 This is a transmission curve diagram of a double-layer Airy beam array under different displacement factors;

[0046] Figure 7 These are transmission curves of a dual-layer Airy beam array with different amplitude ratios;

[0047] Figure 8 This is a diagram showing the transmission characteristics of a two-layer Airy beam array under different vortex topology charge numbers;

[0048] Figure 9 This is a diagram showing the transmission characteristics of a double-layer Airy beam array with different numbers of vortices;

[0049] Figure 10 This is a diagram showing the transmission characteristics of a double-layer Airy beam array at different vortex positions;

[0050] Figure 11 This is a flowchart of the method of the present invention. Detailed Implementation

[0051] To gain a deeper understanding of this invention, we will provide a comprehensive and detailed description. However, this invention has various implementations and is not limited to the specific examples listed herein. These examples are presented to enhance the overall understanding of the disclosure of this invention. The invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0052] A method for generating a misaligned superimposed double-layer Airy beam array to achieve dual focusing is illustrated in the flowchart below. Figure 11 As shown, it includes the following steps:

[0053] (a) Constructing the first layer of Airy beam array on the initial plane Select the number of beams superimposed displacement factor , scale factor .

[0054] (b) Construct a second layer of Airy beam array on the same initial plane. Its overall azimuth angle has a preset rotational misalignment relative to the first layer, and the number of beams superimposed is selected. displacement factor , scale factor amplitude Interlayer angle difference .

[0055] A schematic diagram of the misaligned superimposed double-layer Airy beam array is shown below. Figure 1 As shown, each circle represents a two-dimensional Airy beam, and beams in different layers are distinguished by different colors. Beams in the same layer are evenly distributed on a circle, forming a regular M-gon structure. Figure 1 The radial offset shown by the dashed line satisfies Interlayer angle difference Therefore, the vertex of the first regular polygon is located at the midpoint of the edge of the second regular polygon, in which case the focusing intensity of the beam array is strongest. and These represent the corresponding positions of the center of the m-th Airy beam in the first and second layers on the xy plane, respectively. Lateral scale factor. Amplitude ratio parameter Displacement factor and interlayer angle difference It can control the beam size, amplitude, focusing position, and focusing intensity in each layer. By changing the parameters of the initial light field, the beam in each layer can be modulated independently, enhancing the flexibility of the initial light field.

[0056] (c) The first and second layer Airy beam arrays are superimposed and propagated in free space. During propagation, the dual-layer Airy beam array forms two focusing planes at different positions, thus achieving a longitudinal double-focusing structure, such as... Figure 2 As shown; changing the interlayer angle difference ,from Figure 3 It can be seen from this that when When the beam intensity increases from zero, it first decreases and then increases, and then... The maximum value is reached at this point; when the number of stacks M is changed, the double-focusing phenomenon of the double-layer Airy beam array gradually disappears and becomes single-focused as M increases, but the focusing intensity increases, and when M increases to a certain value, the position and intensity of the focal point no longer change significantly, such as Figure 4 As shown; while maintaining the scale factor of the first layer Changing the scale factor while keeping it unchanged ,from Figure 5 As can be seen, the position of the first focal plane remains almost unchanged, but as... As the focal plane increases, the position of the second focal plane gradually moves away from the initial plane. As the intensity decreases, the second focal plane gradually approaches the initial plane; changing the displacement factor of the two Airy beam arrays can also control the position and intensity of the two focal planes, such as... Figure 6 As shown, with Or, with the increase of the displacement factor, the focal plane gradually moves away from the initial plane; changing the amplitude ratio of the initial double-layer Airy beam array, as the amplitude ratio increases, the intensity of the first focal plane gradually decreases, and the intensity of the second focal plane gradually increases, but the positions of the two focal planes remain unchanged, such as... Figure 7 As shown.

[0057] (d) Adjusting the initial phase, vortex phase modulation is introduced on the basis of the double-layer Airy beam array, when , , , , , In this case, the original dual-focusing structure of the misaligned superimposed double-layer Airy beam array becomes an optical bottle structure, such as... Figure 8 As shown, Figure 8 (a1-a5) represents the case where the topological charge number of the vortex is 2. Figure 8 (b1-b5) represents the case where the topological charge number of the vortex is 3. Figure 8As can be seen, with the increase of charge number, the hollow region at the center of the beam increases, while the position of the focal plane remains almost unchanged; changing the number of introduced vortices, from Figure 9 It can be seen that the propagation characteristics of beams with 2 and 3 vortex numbers are consistent with those with 2 and 3 topological charge numbers. As the number of vortexes increases, the hollow region at the beam center increases, while the position of the focal plane remains almost unchanged. Changing the vortex position... Changes in the position of the vortex disrupt the annular structure of the focal plane. As the number of vortices increases, the annular structure of the focal plane is further disrupted, but the position of the focal plane remains almost unaffected. Figure 10 As shown.

[0058] Contents not described in detail in this specification are prior art known to those skilled in the art. Although illustrative specific embodiments of the invention have been described above to facilitate understanding by those skilled in the art, it should be understood that the invention is not limited to the scope of the specific embodiments. Various modifications are readily apparent to those skilled in the art as long as they fall within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of this invention are protected.

Claims

1. A method for generating a misaligned superimposed double-layer Airy beam array to achieve dual focusing, characterized in that, The method includes the following steps: Step 1: Construct the first layer of Airy beam array on the initial plane. This array consists of multiple two-dimensional Airy beams, each of which is uniformly distributed along the circumference. During the construction process, the control parameters of the first layer of Airy beam array are set. Step 2: Construct a second layer of Airy beam array on the same initial plane. The number of Airy beams in the second layer of Airy beam array is the same as that in the first layer. The overall azimuth angle is rotated and misaligned relative to the first layer by a preset angle. Its control parameters can be the same as or different from those of the first layer. Step 3: The first and second layers of Airy beam arrays are superimposed. During the propagation of the double-layer array beams, two focusing planes are formed at different positions, thereby realizing a longitudinal double-focusing structure. Step 4: Introduce vortex phase modulation on the basis of longitudinal dual-focusing Airy beam array to form an optical bottle with a hollow structure in the focusing area.

2. The method for generating a double-focused, misaligned, superimposed, two-layer Airy beam array according to claim 1, characterized in that, Step 1 involves constructing the first layer of the Airy beam array on the initial plane, using the following formula: in, Indicates the first layer The corresponding positions of the centers of the Airy beams on the xy plane This indicates the number of two-dimensional Airy beams superimposed in each layer; This represents the lateral scale factor of the first layer. Indicates the radial displacement factor of the first layer. Indicates the first layer A two-dimensional Airy beam.

3. The method for generating a misaligned superimposed double-layer Airy beam array with dual focusing according to claim 2, characterized in that, Step 2 involves constructing a second layer of the Airy beam array on the same initial plane, using the following formula: in, Indicates the second layer The corresponding positions of the centers of the Airy beams on the xy plane This represents the lateral scale factor of the second layer. Indicates the radial displacement factor of the second layer. and The relationship is , Indicates the second layer A two-dimensional Airy beam This represents the angular difference between two beam arrays.

4. The method for generating a double-focused, misaligned, superimposed, two-layer Airy beam array according to claim 3, characterized in that, Step 3 involves superimposing the first and second Airy beam arrays to obtain a double-layer Airy beam array: in, It is the normalized constant amplitude of the initial spatial field.

5. The method for generating a misaligned superimposed double-layer Airy beam array with dual focusing according to claim 4, characterized in that, Step 4 introduces vortex phase modulation on the basis of the misaligned superimposed double-layer Airy beam array: Among them, parameters and These represent the number of optical vortices and the topological charge, respectively. This indicates the position of the Jth vortex; when there is obvious double focusing, the vortex phase is introduced, and the original double focusing structure of the misaligned superimposed double-layer Airy beam array becomes an optical bottle structure.

6. The method for generating a misaligned superimposed double-layer Airy beam array with dual focusing according to claim 5, characterized in that, Both the first and second layer Airy beam arrays are composed of multiple two-dimensional Airy beams evenly distributed at equal angles along the circumferential direction. The second layer of Airy beam array is offset from the first layer of Airy beam array by rotating the overall azimuth angle; The self-focusing intensity and position of the Airy beams in different layers are controlled by adjusting parameters such as the scale factor, displacement factor, interlayer angle difference and amplitude ratio of the corresponding layers, so that the double-layer array beams form a longitudinal double-focusing structure during free space propagation.

7. The method for generating a double-focused, misaligned, superimposed, two-layer Airy beam array according to claim 6, characterized in that, Based on the longitudinal dual-focusing Airy beam array, vortex phase modulation is introduced to form an optical bottle structure in the dual-focusing region.

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