Single substrate dual facet diffractive optical element

Abstract

The application provides a single-substrate double-working-surface diffractive optical element, and relates to the field of beam shaping and diffractive optics technology, which comprises a transparent substrate, a first phase modulation structure formed on the incident side surface of the transparent substrate, and a second phase modulation structure formed on the exit side surface of the transparent substrate; an incident light beam is modulated by the first phase modulation structure and propagates in the transparent substrate, and then forms an intermediate light field at the second phase modulation structure; the energy distribution range of the intermediate light field matches the effective modulation area of the second phase modulation structure; the phase distributions of the first phase modulation structure and the second phase modulation structure are jointly determined so that a light beam modulated by the second phase modulation structure and then focused forms a circular flat-top light spot with a preset uniformity on a nominal focal plane and multiple axial planes symmetrically distributed around the nominal focal plane.

Description

Technical Field

[0001] This application belongs to the field of beam shaping and diffraction optics technology, specifically relating to a single-substrate dual-working-plane diffraction optical element. Background Technology

[0002] In applications such as laser precision machining, medical optical therapy, display lighting, semiconductor manufacturing, and micro / nano fabrication, it is often necessary to shape Gaussian or near-Gaussian beams into flat-topped focal spots with predetermined dimensions, high energy uniformity, and low energy leakage outside the target area. Compared to Gaussian focal spots, circular flat-topped focal spots can provide a more uniform energy distribution within the target area, which is beneficial for improving processing consistency, reducing the heat-affected zone, and improving irradiation quality and process stability. Especially in applications that require simultaneous control over focal spot size, edge quality, and axial working tolerance, obtaining circular flat-topped focal spots with long focal depth and high uniformity has become a crucial technical challenge in the field of beam shaping.

[0003] In existing technologies, common beam shaping schemes include monolithic diffractive optical elements, microlens arrays, refractive homogenizers, and multi-element cascaded shaping structures. Among these, monolithic diffractive optical elements are widely used in laser shaping systems due to their compact structure, ease of integration, and ability to achieve flexible wavefront modulation. However, under the same system aperture, working distance, and incident conditions, when the target focal spot size is further reduced and approaches the diffraction limit, it is often difficult to simultaneously achieve the following multiple indicators using only a single phase modulation surface: high uniformity within the flat-top region, steepness of the edge transition region, low energy leakage outside the target region, and large axial tolerance within the focal plane neighborhood.

[0004] For circular flat-top focal spots, if an ideal hard edge is desired, the spatial frequency components of the target optical field will be richer, placing higher demands on modulation freedom and aperture utilization efficiency. However, in practical systems, due to limitations such as effective aperture, processing accuracy, and manufacturing capabilities, it is often difficult to accurately achieve an ideal hard-edge flat-top focal spot, which can easily lead to edge widening, sidelobe enhancement, and increased energy leakage outside the target area. Meanwhile, when applications require not only a good flat-top effect at the central focal plane but also high uniformity across multiple axial positions in the focal plane neighborhood, traditional shaping design methods that only address a single focal plane often struggle to balance central plane quality and axial expansion performance.

[0005] Furthermore, while existing multi-element shaping solutions can improve design freedom to some extent, they typically employ multiple independently configured modulation elements, requiring additional assembly and alignment processes. This results in a larger system size and greater sensitivity to errors in element spacing and relative position, hindering engineering integration and long-term stable operation. For scenarios requiring a balance between structural compactness, assembly stability, and output light field quality, improving the utilization of the intermediate propagating light field within limited device structures, and further enhancing the joint control capability of the target focal plane and multiple axial planes in its neighborhood, remains a challenge in current technologies. Summary of the Invention

[0006] This application provides a single-substrate dual-working-plane diffractive optical element to solve one of the above-mentioned technical problems.

[0007] The technical solution adopted in this application is as follows: This application provides a single-substrate dual-working-plane diffractive optical element, including a transparent substrate, a first phase modulation structure formed on the incident side surface of the transparent substrate, and a second phase modulation structure formed on the exit side surface of the transparent substrate; After the incident beam is modulated by the first phase modulation structure and propagates within the transparent substrate, an intermediate light field is formed at the second phase modulation structure. The energy distribution range of the intermediate light field matches the effective modulation region of the second phase modulation structure. The phase distribution of the first phase modulation structure and the second phase modulation structure are jointly determined such that the beam modulated by the second phase modulation structure and subsequently focused forms a circular flat-top light spot with a preset uniformity on the nominal focal plane and multiple axial planes symmetrically distributed around the nominal focal plane.

[0008] According to one embodiment of this application, the energy distribution range of the intermediate optical field is matched with the effective modulation region of the second phase modulation structure, so that the main energy distribution of the intermediate optical field is located within the region that the second phase modulation structure can effectively modulate.

[0009] According to one embodiment of this application, the circular flat-top light spot includes a flat-top region and a finite-width edge transition region surrounding the flat-top region, the width of the edge transition region and the allowable leakage threshold outside the target area are jointly constrained in the joint determination process.

[0010] According to one embodiment of this application, the phase distribution of the first phase modulation structure and the second phase modulation structure are further jointly determined as follows: a penalty constraint is applied to the energy percentage outside the effective modulation region of the second phase modulation structure.

[0011] According to one embodiment of this application, the first phase modulation structure and the second phase modulation structure are multi-level stepped microstructures or continuous relief microstructures, which provide a spatial phase delay distribution of 0 to 2π radians at the designed operating wavelength.

[0012] A second aspect of this application provides a method for designing the single-substrate dual-working-plane diffractive optical element, comprising the following steps: Obtain incident beam parameters, working wavelength, transparent substrate thickness and refractive index, subsequent focusing conditions, target radius of the central focal plane, edge transition width, allowable leakage threshold outside the target area, and axial working range; Multiple axial planes are selected symmetrically around the nominal focal plane to establish a circular flat-top target model that includes the central axial plane and non-central axial planes; An initial phase distribution is assigned to the first phase modulation structure and the second phase modulation structure, and the light field distribution of the incident beam after propagation through the first phase modulation structure, the transparent substrate, the second phase modulation structure, and subsequent focusing is calculated on the multiple axial planes. During the iteration process, the circular flat-top target model of the corresponding axial plane is adaptively adjusted according to the defocused light field characteristics on the non-central axial plane. Different evaluation weights are set for different axial planes so that the output quality of the multiple axial planes participates in the joint evaluation according to the preset weights. A design evaluation target is constructed, which is used to take into account the uniformity of the flat-top light spot on multiple axial planes, the depth of focus, the utilization rate of the intermediate light field, and the energy leakage outside the target area. The phase distributions of the first phase modulation structure and the second phase modulation structure are jointly updated according to the comprehensive objective function until the stopping condition is met. The phase distributions of the first phase modulation structure and the second phase modulation structure are output to form corresponding phase modulation structures on both sides of the transparent substrate.

[0013] According to one embodiment of this application, the different evaluation weights are determined based on the axial position of each axial plane relative to the nominal focal plane and / or application requirements.

[0014] According to one embodiment of this application, the design evaluation objective includes evaluating the output quality of each axial plane and determining the axial working range that meets the preset quality requirements based on the evaluation results.

[0015] According to one embodiment of this application, the plurality of axial planes includes a nominal focal plane and an equal number of non-central axial planes respectively disposed on the front and rear sides of the nominal focal plane, such that the total number of the plurality of axial planes is an odd number, the predetermined encirclement energy ratio is 80% to 90%, and the allowable leakage threshold outside the target area does not exceed 20%.

[0016] A third aspect of this application provides a laser beam shaping system, including a laser source, a collimation module, the single-substrate dual-working-plane diffraction optical element, and a subsequent focusing optical assembly; the system is used to shape a Gaussian or near-Gaussian incident beam into a long focal depth circular flat-top focal spot with predetermined uniformity in the nominal focal plane and its neighborhood.

[0017] Due to the adoption of the above technical solution, the beneficial effects achieved by this application are as follows: This application sets a first phase modulation structure and a second phase modulation structure on the incident side surface and the exit side surface of the same transparent substrate, respectively. The incident beam is modulated by the first phase modulation structure and propagates in the transparent substrate. An intermediate light field is formed at the second phase modulation structure and then modulated by the second phase modulation structure. Compared with the shaping method that only uses a single phase modulation surface, this application can improve the degree of freedom of light field control and is more conducive to achieving circular flat-top focal spot shaping.

[0018] This application improves the effective utilization of the intermediate light field by matching the energy distribution range of the intermediate light field with the effective modulation region of the second phase modulation structure, and applies a penalty constraint on the proportion of energy outside the effective modulation region of the second phase modulation structure. This suppresses the outward spread of the intermediate light field and reduces the adverse effects of ineffective energy distribution on the shaping effect.

[0019] This application improves the overall output quality of the circular flat-top focal spot by setting the circular flat-top spot to include a flat-top region and a finite-width edge transition region surrounding the flat-top region, and by constraining the width of the edge transition region with the allowable leakage threshold outside the target region during the joint determination process. This achieves a balance between the uniformity of the flat-top region, the edge transition characteristics, and the energy leakage outside the target region.

[0020] This application selects multiple axial planes symmetrically around the nominal focal plane, and makes the beam modulated by the second phase modulation structure and subsequently focused form a circular flat-topped light spot with a preset uniformity on each of the multiple axial planes. This not only ensures the shaping quality of the central focal plane, but also helps to improve the axial working tolerance in the vicinity of the focal plane, thereby forming a long focal depth working area.

[0021] This application improves the adaptability of multi-axial plane joint design to actual propagation state by adjusting the target model according to the light field output state of multiple axial planes during the design process and making different axial planes participate in joint evaluation according to preset weights. It also improves the overall axial shaping effect while taking into account the quality of the central focal plane. Attached Figure Description

[0022] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart illustrating a method for designing a single-substrate, dual-working-surface diffractive optical element, as provided in an embodiment of this application.

[0023] Figure 2 This is a schematic diagram of the light intensity distribution of a long-focal-depth circular flat-top light spot at the nominal focal plane in a specific embodiment of this application.

[0024] Figure 3 This is a schematic diagram showing the change of light intensity distribution and uniformity of the light beam on the XZ propagation section with propagation distance in a specific embodiment of this application.

[0025] Figure 4 This is a schematic diagram of the enclosing phase distribution of the first phase modulation structure and the second phase modulation structure in a specific embodiment of this application.

[0026] Figure 5 This is a schematic diagram of the phase enveloped by the first phase modulation structure, the phase enveloped by the second phase modulation structure, and the intensity distribution of the focused spot corresponding to the near-diffraction-limited small spot in another specific embodiment of this application.

[0027] Figure 6 This is a schematic diagram showing the structure of a single-substrate dual-working-plane diffractive optical element, the position of the intermediate light field, and the relationship between the nominal focal plane and its front and rear axial planes in a specific embodiment of this application.

[0028] Figure 7 This is a schematic diagram illustrating the principle of forming a circular flat-top light spot including a flat-top region and a controlled edge transition region after the incident light beam is shaped by a dual-working-surface diffraction optical element in a specific embodiment of this application. Detailed Implementation

[0029] To more clearly illustrate the overall concept of this application, a detailed explanation is provided below with reference to the accompanying drawings.

[0030] Many specific details are set forth in the following description to provide a thorough understanding of this application. However, this application may also be implemented in other ways different from those described herein. Therefore, the scope of protection of this application is not limited to the specific embodiments disclosed below. It should be noted that, unless otherwise specified, the embodiments of this application and the features thereof can be combined with each other.

[0031] In this application, unless otherwise expressly specified and limited, the "above" or "below" of the second feature can mean that the first and second features are in direct contact, or that the first and second features are in indirect contact through an intermediate medium. In the description of this specification, references to terms such as "an embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described can be combined in any suitable manner in one or more embodiments or examples.

[0032] Example 1 A single-substrate dual-working-plane diffractive optical element includes a transparent substrate, a first phase modulation structure formed on the incident-side surface of the transparent substrate, and a second phase modulation structure formed on the exit-side surface of the transparent substrate. After the incident beam is modulated by the first phase modulation structure and propagates within the transparent substrate, an intermediate light field is formed at the second phase modulation structure. The energy distribution range of the intermediate light field matches the effective modulation region of the second phase modulation structure.

[0033] Specifically, the incident light beam first enters a first phase modulation structure disposed on the incident-side surface of the transparent substrate. This first phase modulation structure applies a predetermined spatial phase modulation to the incident light beam, causing its wavefront distribution to change after passing through it. It should be noted that the first phase modulation structure primarily functions as a pre-modulator of the incident light beam; its role is not limited to simply changing the beam's propagation direction, but rather to provide an initial modulation basis for the subsequent formation of the desired propagation optical field within the transparent substrate.

[0034] The beam modulated by the first phase modulation structure continues to propagate into the transparent substrate along the propagation direction. Because the spatial phase distribution introduced by the first phase modulation structure undergoes diffraction evolution during propagation, when it reaches the vicinity of the exit surface of the transparent substrate, i.e., the location of the second phase modulation structure, the beam no longer maintains its original energy distribution state at incidence, but instead forms an intermediate light field. This intermediate light field can be understood as the light field to be further modulated located before the second phase modulation structure; it not only includes the energy distribution characteristics formed after propagation but also corresponds to the input light field subsequently finely modulated by the second phase modulation structure.

[0035] The phrase "the energy distribution range of the intermediate optical field matches the effective modulation region of the second phase modulation structure" in this application means that, under predetermined evaluation conditions, the main energy distribution of the intermediate optical field should fall within the region where the second phase modulation structure can effectively implement phase modulation, thereby enabling the second phase modulation structure to effectively act on the main energy portion of the intermediate optical field. In other words, if the distribution range of the intermediate optical field is too small, the effective modulation region of the second phase modulation structure will not be fully utilized, which is detrimental to the subsequent freedom of optical field shaping; if the distribution range of the intermediate optical field is too large, some energy will fall outside the effective modulation region of the second phase modulation structure, resulting in energy spillover, increased ineffective modulation, and a decrease in shaping effect.

[0036] The term "matching" can be further understood as follows: the radius of the encircling energy corresponding to the intermediate optical field at a predetermined encircling energy ratio is not greater than the effective modulation radius of the second phase modulation structure, and not less than the lower limit of the preset ratio of the effective modulation radius. Through this method, the main energy of the intermediate optical field is neither excessively concentrated in the central region of the second phase modulation structure nor significantly exceeds the effective modulation boundary of the second phase modulation structure. This allows the second phase modulation structure to perform sufficient and stable subsequent modulation of the intermediate optical field within its effective region.

[0037] Based on the above configuration, this application does not involve the first phase modulation structure and the second phase modulation structure independently completing the modulation process that is unrelated to each other. Instead, through the synergistic effect between the first phase modulation structure, the propagation process within the transparent substrate, and the second phase modulation structure, an intermediate light field suitable for further modulation is first formed at the second phase modulation structure. Then, the second phase modulation structure performs subsequent modulation on this intermediate light field to achieve joint shaping of circular flat-top light spots on multiple axial planes in the nominal focal plane and its neighborhood.

[0038] It should be noted that the "propagation within a transparent substrate" is not required to be limited to a specific propagation model. As long as the modulation introduced by the first phase modulation structure can form the aforementioned intermediate optical field at the second phase modulation structure after propagation, it should fall within the protection scope of this application. Similarly, the "effective modulation region" is not limited to a specific geometric boundary form; it can be the region where the second phase modulation structure actually undertakes the effective phase modulation function.

[0039] The phase distribution of the first phase modulation structure and the second phase modulation structure are jointly determined such that the beam modulated by the second phase modulation structure and subsequently focused forms a circular flat-top light spot with a preset uniformity on the nominal focal plane and multiple axial planes symmetrically distributed around the nominal focal plane.

[0040] Specifically, the joint determination of the phase distributions of the first and second phase modulation structures means that the phase distributions of the first and second phase modulation structures are not determined separately and in isolation, but rather they are designed as a coupled whole. That is, when determining the phase distribution of the first phase modulation structure, the characteristics of the intermediate optical field formed at the second phase modulation structure after propagation through the transparent substrate must be considered simultaneously; when determining the phase distribution of the second phase modulation structure, the modulation effect pre-introduced by the first phase modulation structure and the target output requirements after subsequent focusing must be considered simultaneously. Through this joint determination method, the first phase modulation structure undertakes the pre-modulation function, while the second phase modulation structure undertakes the subsequent compensation and fine-shaping functions, thereby jointly achieving the expected target optical field output.

[0041] The beam modulated and subsequently focused by the second phase modulation structure refers to a beam that, after passing through the first phase modulation structure, propagating within the transparent substrate, and then being affected by the second phase modulation structure, is further focused by the subsequent focusing optical components to form the desired spot distribution on the target observation plane. In other words, the target light field of interest in this application is not located on the surface of the second phase modulation structure, but rather at the nominal focal plane corresponding to the subsequent focusing and its neighboring axial position. Therefore, the phase distribution of the first and second phase modulation structures is not solely aimed at optimizing the local light field at the intermediate position, but is jointly designed with the multi-plane output effect after final focusing as the constraint objective.

[0042] The nominal focal plane can be understood as the central target focal plane corresponding to the subsequent focusing optical components in the design state, which is usually used as the main design reference plane for a circular flat-top light spot. Based on this nominal focal plane, multiple axial positions are selected before and after the light propagation direction. These axial positions are symmetrically distributed around the nominal focal plane, thus forming multiple axial planes. By simultaneously imposing constraints on the light field distribution on these axial planes, this application does not only pursue the shaping quality at a single focal plane, but also focuses on the output stability and consistency within a certain axial range in the neighborhood of the focal plane.

[0043] The requirement to form circular flat-topped light spots with a predetermined uniformity on the nominal focal plane and multiple axial planes symmetrically distributed around it means that the light spots formed on the central focal plane and the selected multiple non-central axial planes should all meet the predetermined circular flat-top characteristics and achieve the predetermined uniformity requirements. Here, "circular flat-topped light spot" refers to a light spot whose main active area is circularly distributed, and whose light intensity distribution is relatively uniform within the flat-top region. "Preset uniformity" refers to a uniformity evaluation standard predetermined during the design phase based on application requirements, used to measure whether the light intensity fluctuations within the flat-top region on the corresponding axial plane are within the allowable range. In other words, this application requires not only the formation of a circular flat-topped light spot at the central focal plane, but also the maintenance of the basic uniformity characteristics of this circular flat-topped light spot on multiple axial planes in the vicinity of the focal plane.

[0044] Through the above methods, this application effectively establishes a joint shaping mechanism for multiple axial planes. Compared to design methods that only use a single focal plane as the optimization target, this application considers the output results of multiple axial planes simultaneously when determining the phase distribution of the first and second phase modulation structures. This results in a final spot that not only has a good flat-top effect at the nominal focal plane but also maintains high uniformity at forward and backward axial positions at a certain distance from the nominal focal plane. This facilitates the formation of a high-quality working area with a certain extension along the optical axis, namely, a long focal depth circular flat-top spot working area.

[0045] It should be noted that the "multiple axial planes" are not limited to a specific number. As long as they are symmetrically distributed around the nominal focal plane and used to characterize the output quality in the neighborhood of the focal plane, they can fall within the protection scope of this application. The "preset uniformity" is also not limited to a fixed mathematical expression. It can be characterized by corresponding uniformity evaluation indicators according to specific application scenarios. For those skilled in the art, any method that can reflect the uniformity of light intensity of the circular flat-topped light spot on the corresponding axial plane can be used as a specific implementation of the "preset uniformity" in this application.

[0046] Furthermore, the "joint determination" is not limited to a specific solution algorithm. It can be achieved through iterative optimization, numerical solution, constraint search, or other methods that can simultaneously consider the influence of the first phase modulation structure and the second phase modulation structure on the final multi-plane output light field. As long as the beam modulated by the second phase modulation structure and subsequently focused can form a circular flat-top light spot with a predetermined uniformity on the nominal focal plane and multiple axial planes symmetrically distributed around the nominal focal plane, it should be considered to fall within the technical concept of this application.

[0047] In some embodiments of this application, the energy distribution range of the intermediate optical field is matched with the effective modulation region of the second phase modulation structure, so that the main energy distribution of the intermediate optical field is located within the region that the second phase modulation structure can effectively modulate.

[0048] Specifically, after the incident beam modulated by the first phase modulation structure propagates within the transparent substrate and forms an intermediate optical field at the location of the second phase modulation structure, the matching relationship between the intermediate optical field and the second phase modulation structure is further defined. Matching the energy distribution range of the intermediate optical field with the effective modulation region of the second phase modulation structure means that the main energy distribution of the intermediate optical field neither significantly exceeds the effective modulation region of the second phase modulation structure nor significantly contracts to the central part of the effective modulation region, but rather maintains a coordinated relationship with the effective modulation region on a spatial scale. This allows the second phase modulation structure to perform sufficient subsequent modulation of the main energy portion of the intermediate optical field.

[0049] The enclosing energy radius under the predetermined enclosing energy ratio refers to the radius corresponding to the cumulative energy counted outward from the center of the intermediate optical field, based on the intensity distribution of the intermediate optical field at the plane where the second phase modulation structure is located, when the cumulative energy reaches a predetermined proportion of the total energy of the intermediate optical field. This radius can characterize the spatial occupancy range of the main energy of the intermediate optical field at the second phase modulation structure.

[0050] The effective modulation radius of the second phase modulation structure refers to the radius range corresponding to the effective region of the second phase modulation structure that can perform a predetermined phase modulation on the light field incident on that region. Typically, this effective modulation radius corresponds to the boundary of the region where the second phase modulation structure actually performs effective phase modulation. That is, when the main energy distribution of the intermediate light field is within the range defined by this effective modulation radius, the second phase modulation structure can effectively modulate the main part of the intermediate light field; conversely, if the main energy distribution of the intermediate light field significantly exceeds this effective modulation radius, the excess portion is difficult to modulate sufficiently, which can easily lead to energy spillover and a decrease in shaping quality.

[0051] Through the above-described configuration, this embodiment does not simply require the intermediate light field to reach the second phase modulation structure, but further requires that the main energy distribution of the intermediate light field maintains a spatially compatible relationship with the effective modulation region of the second phase modulation structure. This improves the effective utilization of the intermediate light field by the second phase modulation structure, reduces the adverse effects of excessive expansion or contraction of the intermediate light field, and further provides more favorable input conditions for forming a circular flat-topped light spot with predetermined uniformity on the nominal focal plane and its neighboring multiple axial planes after subsequent focusing.

[0052] In some embodiments of this application, the circular flat-top light spot includes a flat-top region and a finite-width edge transition region surrounding the flat-top region, the width of which is jointly constrained by the allowable leakage threshold outside the target area during the joint determination process.

[0053] Specifically, the flat-top region refers to the main area within the target light spot used to achieve the predetermined irradiation, processing, or energy application functions. Within this region, the light intensity distribution should meet a preset uniformity requirement to ensure good consistency in energy deposition within the target area. The edge transition region is located outside the flat-top region and is used to ensure a continuous transition of light intensity distribution from a higher and relatively uniform level within the flat-top region to a lower energy region outside the flat-top region. In other words, the target light spot in this embodiment is not an ideal hard-edged circular flat-top light spot with infinitely steep boundaries, but rather an edge transition region with a controlled width is set around the flat-top region, causing the edge of the target light spot to gradually decrease outward from the flat-top region.

[0054] The term "finite-width edge transition zone" emphasizes that this transition zone has a clearly defined width control meaning; its width is neither infinitely extended nor negligible. If the edge transition zone is too wide, the transition between the flat-top region and the outer low-energy region will be too slow, resulting in an unclear edge contour of the target spot and affecting the effective range of the circular flat-top spot. Conversely, if the edge transition zone is too narrow, even approaching an ideal hard edge, the light intensity will change too drastically at the boundary, increasing the difficulty of light field shaping and easily causing enhanced edge oscillations and increased energy leakage outside the target area. Therefore, in this embodiment, the width of the edge transition zone is not a consequential feature, but rather one of the target parameters involved in the overall design.

[0055] Furthermore, the "allowable leakage threshold outside the target area" refers to the upper limit of energy leakage allowed outside the effective target area corresponding to the target circular flat-top light spot. This threshold is used to characterize the acceptable energy distribution range of the output light field outside the target area. If the proportion of energy outside the target area exceeds this allowable leakage threshold, it indicates that some energy has significantly diffused outside the target area, which will not only reduce the effective energy utilization rate within the target area, but may also adversely affect the processing boundary, irradiation accuracy, or the stability of adjacent areas.

[0056] In this embodiment, the width of the edge transition region and the allowable leakage threshold outside the target area are jointly constrained during the joint determination process. This means that when co-designing the phase distribution of the first phase modulation structure and the second phase modulation structure, the edge transition characteristics of the target spot and the energy leakage outside the target area are not optimized independently, but rather they are incorporated into the design process as interrelated constraints. In other words, how steep or gentle the edge of the target spot is formed is not determined in isolation, but needs to be considered in conjunction with the energy leakage control requirements outside the target area to achieve a balance between edge quality and energy control outside the target area.

[0057] Specifically, if the goal is only to make the edge transition region as narrow as possible, while this may result in a steeper boundary, it usually increases the high spatial frequency components in the light field, thereby increasing the risk of energy diffusion outside the target area and making it difficult to control leakage outside the target area. If the goal is only to minimize leakage outside the target area, the edge transition region may be designed to be too wide. While this may help mitigate edge changes to some extent, it will blur the boundary of the target spot and affect the effective contour of the flat-top region and the edge shaping quality. Therefore, this implementation does not unilaterally pursue infinitely steep edges, nor does it unilaterally pursue an absolute minimum of energy outside the target area. Instead, it constrains the width of the edge transition region with the allowable leakage threshold outside the target area, so that the final target spot maintains a balance between the uniformity of the flat-top region, the edge shaping quality, and the control of energy outside the target area.

[0058] In other words, in this embodiment, the target shape of the circular flat-top beam spot itself already includes preset requirements for edge transition characteristics. These preset requirements are not independent but rather participate in the joint determination of the phase distribution of the first and second phase modulation structures together with the allowable leakage threshold outside the target region. Through this configuration, the final circular flat-top beam spot not only maintains good uniformity within the flat-top region but also forms a controlled transition shape at the edge, keeping energy leakage outside the target region within acceptable limits, thereby improving the overall quality of the beam shaping results.

[0059] The width of the edge transition region can be preset according to application requirements, or used as a design variable for optimization within an allowable range; the allowable leakage threshold outside the target region can also be set according to the requirements of different applications for boundary sharpness, sidelobe suppression capability, or energy utilization. For those skilled in the art, as long as the width of the edge transition region and the allowable leakage threshold outside the target region are considered as interrelated constraints in the process of jointly determining the phase distribution of the first phase modulation structure and the second phase modulation structure, they should all be considered to fall within the scope of the technical concept of this application.

[0060] With the above settings, compared to simply idealizing the target spot as a hard-edged circular flat-top spot, this embodiment is more conducive to taking into account the uniformity of the flat-top area, the quality of the edge contour, and the energy control effect outside the target area. It also provides more reasonable target constraints for forming a long focal depth circular flat-top spot with preset uniformity on the nominal focal plane and multiple axial planes in its neighborhood.

[0061] In one specific implementation, such as Figure 2 As shown, when the incident beam aperture and the target flat-top spot size meet the preset design conditions, a circular flat-top spot can be formed at the nominal focal plane after being modulated by the first phase modulation structure and the second phase modulation structure. Figure 2 The light intensity distribution in the image is used to characterize that the central region of the light spot at the target plane has a relatively uniform intensity distribution, and there is a controlled edge transition region around the flat top region; in this example, the energy ratio of the target region meets the preset requirements.

[0062] Furthermore, such as Figure 3 As shown, the XZ propagation section can be intercepted along the light propagation direction, and the uniformity variation at different axial positions can be statistically analyzed. Figure 3 The cross-sectional light intensity distribution is used to represent the propagation state of a circular flat-topped light spot within a certain axial range before and after the nominal focal plane, and the superimposed uniformity variation curves are used to represent the variation trend of the uniformity of the flat-topped region on each axial plane. Figure 3 It can be seen that by symmetrically setting multiple axial planes around the nominal focal plane and jointly optimizing them, the light spot can maintain a high degree of uniformity within the target axial range, thereby supporting the technical effect of the long focal depth circular flat-top light spot described in this application.

[0063] In some embodiments of this application, the phase distribution of the first phase modulation structure and the second phase modulation structure are further jointly determined as follows: a penalty constraint is imposed on the proportion of energy outside the effective modulation region of the second phase modulation structure.

[0064] Specifically, the phase distributions of the first and second phase modulation structures are jointly determined by imposing a penalty constraint on the energy percentage outside the effective modulation region of the second phase modulation structure. This setting ensures that the joint determination of the phase distributions of the first and second phase modulation structures considers not only the formation effect of the circular flat-top light spot on the nominal focal plane and multiple axial planes, but also the spatial distribution of the intermediate light field at the plane where the second phase modulation structure is located, thereby further improving the effective utilization of the intermediate light field by the second phase modulation structure.

[0065] The "effective modulation region of the second phase modulation structure" refers to the area within the second phase modulation structure capable of performing predetermined phase modulation on the optical field arriving within this region. Typically, this region corresponds to the effective working range where the second phase modulation structure actually performs its modulation function. In other words, the intermediate optical field entering this effective modulation region can receive predetermined phase modulation from the second phase modulation structure, while energy distributed outside this effective modulation region is difficult for the second phase modulation structure to fully utilize, or cannot participate in the subsequent shaping process in the expected manner.

[0066] The "energy percentage outside the effective modulation region" refers to the proportion of energy in the intermediate optical field that falls outside the effective modulation region of the second phase modulation structure within the plane of the second phase modulation structure. This energy percentage characterizes the extent of the outward expansion of the intermediate optical field at the second phase modulation structure and the effectiveness of energy utilization. If this energy percentage is large, it indicates that a significant portion of the intermediate optical field energy falls outside the effective modulation region of the second phase modulation structure. In this case, this portion of energy cannot be sufficiently and effectively phase-modulated, which not only reduces the utilization efficiency of the intermediate optical field by the second phase modulation structure but may also lead to ineffective energy diffusion during subsequent focusing, thus adversely affecting the uniformity, edge quality, and external leakage control of the target circular flat-top spot.

[0067] In this embodiment, "applying a penalty constraint to the energy percentage outside the effective modulation region of the second phase modulation structure" means that when jointly determining the phase distribution of the first and second phase modulation structures, the energy percentage outside the effective modulation region is incorporated as a constraint factor to be suppressed into the overall design process. When the energy percentage outside this region is large, the corresponding design result is adversely affected during the evaluation process; when the energy percentage outside this region is small, the corresponding design result is more likely to be retained or further optimized. In other words, this application does not allow the intermediate optical field to arbitrarily expand outward at the second phase modulation structure, but rather introduces this penalty constraint to make the main energy of the intermediate optical field more inclined to be distributed within the effective modulation region of the second phase modulation structure.

[0068] Through the above setup, it becomes clear that the first phase modulation structure and the second phase modulation structure in this application are not simply connected in series. The first phase modulation structure is not only used for pre-modulation of the incident beam, but also needs to be combined with the propagation process within the transparent substrate to form an intermediate optical field suitable for subsequent modulation at the second phase modulation structure. The second phase modulation structure further performs fine modulation on the intermediate optical field, provided that the main energy of the intermediate optical field falls as close as possible to its effective modulation region. Therefore, imposing a penalty constraint on the proportion of energy outside the effective modulation region is actually a further limitation on the cooperative relationship between the two working surfaces. Its function is to make the joint design result of the first phase modulation structure and the second phase modulation structure more suitable for the actual working capability of the second phase modulation structure.

[0069] The penalty constraint and the aforementioned requirement to match the energy distribution range of the intermediate optical field with the effective modulation region of the second phase modulation structure are both related and have their own emphasis. The aforementioned matching relationship emphasizes the coordination of the main energy distribution range of the intermediate optical field and the effective modulation region of the second phase modulation structure in terms of spatial scale; while the penalty constraint in this embodiment further suppresses the energy distributed outside the effective modulation region from the perspective of energy proportion. That is to say, the former focuses more on constraining the matching between the intermediate optical field and the second phase modulation structure based on the relationship between the enclosing energy radius and the effective modulation radius, while the latter focuses more on further suppressing the spillover of the intermediate optical field from the perspective of overall energy utilization. The combined effect of the two is conducive to improving the effective utilization rate of the intermediate optical field by the second phase modulation structure.

[0070] The penalty constraint can be reflected in the evaluation function, objective function, or constraint function used to jointly determine the phase distribution of the first and second phase modulation structures. For example, when the proportion of energy in the intermediate light field distribution outside the effective modulation region of the second phase modulation structure increases, the corresponding evaluation value decreases or the penalty term increases; conversely, when the proportion of this energy is small, the corresponding evaluation value increases or the penalty term decreases. In this way, the overall design process pursues the output quality of the nominal focal plane and multiple axial planes while also taking into account the utilization efficiency of the intermediate light field at the plane where the second phase modulation structure is located. It should be noted that the penalty constraint is not limited to a fixed mathematical expression; as long as it can suppress and limit the proportion of energy outside the effective modulation region of the second phase modulation structure during the joint design process, it falls within the scope of the technical concept of this application.

[0071] Through the above-described configuration, this embodiment effectively reduces the outward spillover of the intermediate light field at the second phase modulation structure, minimizes the ineffective energy distribution that the second phase modulation structure cannot utilize, and provides more favorable input conditions for forming a circular flat-top light spot with preset uniformity on the nominal focal plane and its neighboring multiple axial planes after subsequent focusing. Compared to schemes that do not constrain the energy ratio outside the effective modulation region of the second phase modulation structure, this embodiment is more conducive to improving the energy utilization efficiency, shaping stability, and overall output quality of the dual-working-plane diffraction optical element.

[0072] In some embodiments of this application, the first phase modulation structure and the second phase modulation structure are multi-level stepped microstructures or continuous relief microstructures, which provide a spatial phase delay distribution of 0 to 2π radians at the designed operating wavelength.

[0073] Specifically, the first phase modulation structure and the second phase modulation structure are multi-level stepped microstructures or continuous relief microstructures, which provide a spatial phase delay distribution of 0 to 2π radians at the designed operating wavelength. Through the above configuration, the first phase modulation structure and the second phase modulation structure can respectively implement predetermined spatial phase modulation on the incident beam and the intermediate optical field in a static micro / nano structure manner, thereby achieving the goal of dual-working-plane collaborative shaping in this application.

[0074] The "multi-level stepped microstructure" can be understood as: forming a surface microstructure with multiple discrete height levels on the surface of the corresponding phase modulation structure. Different height levels correspond to different optical path differences, thereby applying different phase delays to the light beam passing through this region. By designing the step height at each location, a predetermined spatial phase distribution can be formed on the entire surface of the phase modulation structure. The "continuous relief microstructure" can be understood as: forming a surface contour that continuously varies along the spatial position on the surface of the corresponding phase modulation structure, so that the structure height at different positions continuously varies, thereby providing a continuously varying phase delay to the light beam passing through different positions. In other words, regardless of whether a multi-level stepped form or a continuous relief form is used, the essence is to control the optical path of the light beam through the surface morphology of the microstructure to obtain a predetermined spatial phase modulation effect.

[0075] The first and second phase modulation structures are defined in the aforementioned microstructure form, the purpose of which is to enable the phase modulation function to be directly integrated onto both sides of the transparent substrate. Compared to solutions that rely on additional active modulation components or complex variable optical structures, the use of multi-level stepped microstructures or continuous relief microstructures allows the dual-working-surface phase modulation structure of this application to be formed on the transparent substrate in an integrated and static manner, thereby reducing system size, lowering system complexity, and improving the stability and manufacturability of the device in engineering applications.

[0076] The phrase "providing a spatial phase delay distribution of 0 to 2π radians at the designed operating wavelength" means that, under a predetermined operating wavelength, the first and second phase modulation structures can provide phase delay modulation covering a complete phase period range for the beam passing through corresponding positions at different spatial locations on their respective surfaces. In other words, the phase modulation structures do not merely provide limited local phase shifts, but are able to construct the required spatial phase distribution within the range of 0 to 2π radians to meet the need for fine modulation of the incident beam and intermediate optical field.

[0077] Limiting the phase delay distribution to a range of 0 to 2π radians means that the phase modulation amount at different spatial locations can cover any value within a complete cycle. This setting allows the first and second phase modulation structures to have higher degrees of freedom in phase design, thus facilitating the implementation of the first phase modulation structure for the pre-stage modulation of the incident beam, the formation of the intermediate optical field after propagation within the transparent substrate, and the second phase modulation structure for further compensation and fine shaping of the intermediate optical field. Especially when this application requires simultaneously considering the output quality of a circular flat-top beam from both the nominal focal plane and multiple axial planes, insufficient phase modulation range can easily limit the controllability of the dual-working-plane collaborative design, hindering the achievement of the desired shaping effect.

[0078] It should be noted that the "design operating wavelength" refers to the target operating wavelength used in designing the first and second phase modulation structures. At this operating wavelength, the phase delay relationship corresponding to different structural heights can be predetermined, enabling the multi-level stepped microstructure or continuous relief microstructure to achieve a predetermined spatial phase modulation distribution. For different application scenarios, the design operating wavelength can be set according to specific light source conditions; correspondingly, the microstructure parameters of the first and second phase modulation structures can also be adjusted according to the selected design operating wavelength. For those skilled in the art, any spatial phase delay distribution covering the range of 0 to 2π radians achieved through a multi-level stepped microstructure or continuous relief microstructure under the predetermined operating wavelength conditions can be considered a specific implementation method in this application.

[0079] Furthermore, the first phase modulation structure and the second phase modulation structure may employ either a multi-stage stepped microstructure or a continuous relief microstructure, and they are not required to have identical structural forms. In some embodiments, the first phase modulation structure may employ a multi-stage stepped microstructure, and the second phase modulation structure may employ a continuous relief microstructure; in other embodiments, both may employ multi-stage stepped microstructures or both may employ continuous relief microstructures. As long as both can provide the required 0 to 2π radian spatial phase delay distribution at the designed operating wavelength and respectively achieve the corresponding phase modulation function, they should be considered to fall within the scope of the technical concept of this application.

[0080] Through the above-described configuration, this embodiment enables the first and second phase modulation structures to have well-defined and manufacturable structural implementations, and allows them to provide a spatial phase delay distribution that meets the requirements of collaborative shaping of the two working surfaces at the designed operating wavelength. This not only facilitates the achievement of the design goals of this application regarding intermediate light field formation, effective utilization of the second phase modulation structure, and joint shaping of multi-axial planar circular flat-top light spots, but also improves the engineering feasibility and application stability of the device.

[0081] In one specific implementation, such as Figure 4 As shown, the first phase modulation structure and the second phase modulation structure each have corresponding wrapping phase distributions, where grayscale variations can be used to represent spatial phase delays within the range of 0 to 2π radians. The phase distribution of the first phase modulation structure is mainly used for pre-modulation of the incident beam, so that after the beam propagates within the transparent substrate, it forms an intermediate optical field suitable for continued use by the second phase modulation structure; the phase distribution of the second phase modulation structure is used for further compensation and fine shaping based on the intermediate optical field.

[0082] It should be noted that, Figure 4 The first and second phase modulation structures shown are not simple copies of the same phase diagram, but rather differentiated phase distributions determined by the propagation process within the transparent substrate, the effective modulation region of the second phase modulation structure, and the constraints of circular flat-topped light spots on multiple axial planes. This differentiated phase distribution reflects the collaborative modulation relationship between the two working surfaces and helps improve the shaping quality of the multi-axial planes.

[0083] like Figure 1 As shown, a second aspect of this application provides a method for designing the single-substrate dual-working-surface diffractive optical element, comprising the following steps: S1. Obtain incident beam parameters, working wavelength, transparent substrate thickness and refractive index, subsequent focusing conditions, target radius of the central focal plane, edge transition width, allowable leakage threshold outside the target area, and axial working range.

[0084] Specifically, the phrase "acquiring incident beam parameters, working wavelength, transparent substrate thickness and refractive index, subsequent focusing conditions, target radius of the central focal plane, edge transition width, allowable leakage threshold outside the target area, and axial working range" refers to: before jointly designing the phase distribution of the first phase modulation structure and the second phase modulation structure, pre-determining the basic input parameters related to the design of the dual-working-plane diffraction optical element and the subsequent formation of the output light field, so as to serve as the basis for subsequently establishing the target model, calculating the light field propagation process, and constructing optimization constraints.

[0085] The incident beam parameters characterize the initial state of the beam before it enters the first phase modulation structure. In some embodiments, the incident beam parameters may include at least one of the following: beam aperture, amplitude distribution, beam radius, divergence characteristics, incident position, incident direction, and polarization state. By obtaining the incident beam parameters, the original optical field distribution incident on the surface of the first phase modulation structure can be determined, thereby providing input conditions for subsequent calculations of the beam's propagation process after modulation by the first phase modulation structure. Especially in this application, the effect of the first phase modulation structure on the incident beam is closely related to the initial distribution of the incident beam itself; therefore, obtaining the incident beam parameters is one of the fundamental steps in the collaborative design of the two working surfaces.

[0086] The operating wavelength refers to the target beam wavelength targeted when designing the single-substrate dual-working-surface diffractive optical element. Since the phase delay of the beam produced by the first and second phase modulation structures is related to the operating wavelength, and the diffraction evolution characteristics during propagation within the transparent substrate are also related to the operating wavelength, the operating wavelength is a crucial parameter for determining the phase distribution, phase delay, and propagation calculation results. In different implementations, the operating wavelength can be preset according to the specific light source type and application scenario.

[0087] The thickness and refractive index of the transparent substrate are used to characterize the geometric propagation distance and material propagation characteristics of the transparent substrate itself. Specifically, the thickness of the transparent substrate determines the propagation length of the light beam from the first phase modulation structure to the second phase modulation structure; the refractive index of the transparent substrate affects the equivalent optical path and propagation phase change of the light beam as it propagates within the transparent substrate. In other words, the thickness and refractive index of the transparent substrate jointly determine the equivalent propagation characteristics between the first and second phase modulation structures, and further influence the intermediate optical field distribution formed at the second phase modulation structure. Therefore, in this application, the thickness and refractive index of the transparent substrate are not only device structural parameters, but also important design inputs that need to be obtained in advance when jointly determining the phase distribution of the first and second phase modulation structures.

[0088] The subsequent focusing conditions refer to the focusing conditions corresponding to the beam modulated by the second phase modulation structure before forming the target circular flat-top light spot. In some embodiments, the subsequent focusing conditions may include at least one of the following: focal length, aperture, relative position relationship, numerical aperture, and target observation plane setting conditions of the subsequent focusing optical components. By obtaining the subsequent focusing conditions, it is possible to clarify how the beam modulated by the second phase modulation structure forms the final target light field in the nominal focal plane and its neighborhood. This allows the joint design of the first and second phase modulation structures to be guided by the output effect after final focusing, rather than being limited to the local light field state at the plane where the second phase modulation structure is located.

[0089] The target radius of the central focal plane refers to the central design size parameter of the target circular flat-top spot on the nominal focal plane, which characterizes the scale range of the desired circular flat-top spot at the central focal plane. In other words, the target radius of the central focal plane is used to determine the target size of the flat-top region on the central focal plane, and is an important basis for subsequently establishing a circular flat-top target model and evaluating the degree of deviation of the spot size in each axial plane. In this application, the target models of multiple non-central axial planes can be further expanded or updated around the target radius of the central focal plane. Therefore, the target radius of the central focal plane plays the role of a reference parameter in the overall design process.

[0090] The edge transition width characterizes the width range of the edge transition zone outside the flat-top region of the target circular flat-top spot. This parameter reflects the abruptness of the transition from the flat-top region to the outer low-energy region of the target spot. By pre-obtaining the edge transition width, edge morphology constraints can be clearly defined when establishing the target circular flat-top spot model, allowing subsequent design to consider not only the uniformity within the flat-top region but also the edge forming quality. In conjunction with the aforementioned technical solutions, the edge transition width is not used in isolation but participates in the overall design constraints together with the allowable leakage threshold outside the target region.

[0091] The allowable leakage threshold outside the target area refers to the upper limit of energy leakage permitted outside the effective target area corresponding to the target circular flat-top light spot. This parameter is used to limit the degree of energy diffusion of the output light field outside the target area, thereby avoiding excessively high ineffective energy distribution outside the target area. By obtaining this allowable leakage threshold in advance, energy control outside the target area can be incorporated into the overall design process when constructing the comprehensive objective function or constraints, so as to balance the flat-top shaping quality within the target area and the energy suppression effect outside the target area.

[0092] The axial working range refers to the axial range extending forward and backward along the light propagation direction around the nominal focal plane, used to define the focal plane neighborhood range for which output quality needs to be prioritized in this application. In other words, the axial working range corresponds to the axial boundary of the long focal depth working area of ​​interest in this application. By obtaining the axial working range in advance, the selection intervals of these axial planes can be clearly defined when symmetrically selecting multiple axial planes around the nominal focal plane subsequently. This allows the joint optimization process to be carried out for the actual required axial working area, rather than designing arbitrarily distant regions without constraints.

[0093] Therefore, the parameters obtained in this step correspond to the incident conditions, device structure conditions, propagation and focusing conditions, and target output conditions, respectively. These parameters are not isolated but collectively form the fundamental inputs for the subsequent design process of dual-plane diffractive optical elements: the incident beam parameters, operating wavelength, transparent substrate thickness and refractive index, and subsequent focusing conditions are primarily used to determine the light field propagation and modulation process; the target radius of the central focal plane, edge transition width, allowable leakage threshold outside the target region, and axial operating range are primarily used to determine the target light field form and evaluate the constraint range. Obtaining these parameters at the beginning of the design phase provides a unified and clear parameter basis for subsequently establishing a circular flat-top target model, calculating the multi-axial planar light field distribution, and jointly updating the phase distribution of the first and second phase modulation structures.

[0094] In some implementations, the above parameters can be obtained from system presets, manual input, experimental measurements, optical system calibration results, or previous design requirements. For those skilled in the art, any parameters related to incident conditions, propagation conditions, focusing conditions, and target output requirements that can be determined before subsequent joint design should be considered to fall within the scope of the technical concept of this step in this application.

[0095] S2. Select multiple axial planes symmetrically around the nominal focal plane to establish a circular flat-top target model that includes the central axial plane and non-central axial planes.

[0096] Specifically, the phrase "symmetrically selecting multiple axial planes around the nominal focal plane to establish a circular flat-top target model including a central axial plane and non-central axial planes" means that, based on the already determined nominal focal plane and axial working range, the target light field requirements are not only constructed for a single central focal plane, but also, along the light propagation direction, multiple planes corresponding to the axial positions are selected on both sides of the aforementioned nominal focal plane as the center, and target light field models are established for these planes respectively, so that the subsequent joint design of the phase distribution of the first phase modulation structure and the second phase modulation structure can be carried out simultaneously on multiple axial planes.

[0097] The nominal focal plane can be understood as the central design focal plane corresponding to subsequent focusing conditions, which typically serves as the main reference plane for the target circular flat-top light spot. At this nominal focal plane, the design target is usually to form a circular flat-top light spot that meets the target radius, preset uniformity, and edge transition requirements of the central focal plane. Since this application focuses not only on the output quality at the nominal focal plane but also on the output stability within a certain axial range in the neighborhood of the focal plane, multiple axial planes need to be further selected based on the nominal focal plane to characterize the target optical field requirements at different axial positions within the neighborhood of the focal plane.

[0098] The symmetrical selection of multiple axial planes around the nominal focal plane refers to selecting several axial positions in front of and behind the nominal focal plane along the direction of light propagation, such that the selected axial planes are symmetrically distributed relative to the nominal focal plane. In other words, if a plane corresponding to a certain axial offset is selected in front of the nominal focal plane, then another plane with the same axial offset is selected behind the nominal focal plane. This symmetrical selection method allows the established multi-axial plane target model to simultaneously reflect the output requirements on both sides of the nominal focal plane, thus facilitating a more balanced design of the overall axial working area within the focal plane's neighborhood.

[0099] The plurality of axial planes may include a central axial plane and several pairs of non-central axial planes. The central axial plane is the nominal focal plane itself; the non-central axial planes are planes offset along the optical axis relative to the nominal focal plane. By incorporating both the central and non-central axial planes into the target model, this application can, during the design process, focus on the output quality of the central focal plane while simultaneously considering the formation effect of circular flat-top light spots at multiple axial positions in the defocused state.

[0100] The establishment of a circular flat-top target model including a central axial plane and non-central axial planes refers to: pre-setting corresponding target spot shape requirements for the central axial plane and each non-central axial plane, so that the subsequent design process can use these target requirements as a reference to evaluate and adjust the actual light field formed on each axial plane after passing through the first phase modulation structure, transparent substrate propagation, second phase modulation structure, and subsequent focusing. The core of the target model is that: on each selected axial plane, a circular flat-top spot is used as the target output form, and the flat-top area range, uniformity requirements, edge transition characteristics, and energy control requirements outside the target area are described accordingly.

[0101] Specifically, for the central axial plane, the circular flat-top target model typically uses the target radius of the central focal plane as the primary dimensional reference, and combines preset uniformity, edge transition width, and allowable leakage threshold outside the target area to determine the corresponding target spot shape. For non-central axial planes, the circular flat-top target model can be set based on the target model of the central axial plane, according to the actual propagation state corresponding to the axial position change. In this application, the target model of the non-central axial plane does not necessarily have to be exactly the same as that of the central axial plane, but can be adjusted or updated according to subsequent design needs while maintaining the characteristics of the circular flat-top target, so that the target constraints of the non-central axial plane better meet the actual design requirements under defocus conditions.

[0102] Therefore, the multi-axial planar circular flat-top target model established in this step essentially provides a multi-plane target constraint basis for the subsequent joint design of the phase distribution of the dual working surfaces. Compared with the method of establishing a single target model only at the nominal focal plane, this application establishes a circular flat-top target model on both the central axial plane and multiple non-central axial planes simultaneously. This allows the subsequent optimization process to consider the output light field quality at multiple axial positions at the same time, thereby avoiding the situation where the design result performs well only at a single focal plane, while the quality degrades significantly at other positions in the vicinity of the focal plane.

[0103] By employing multiple axial planes symmetrically distributed around the nominal focal plane as modeling objects, the subsequent optimization results can achieve better balance on both sides of the nominal focal plane. In other words, this application does not aim for local improvement in a single defocus direction, but rather for an overall axial performance enhancement around the nominal focal plane. This makes it easier to obtain a long-focal-depth circular flat-top spot that maintains a predetermined uniformity within the nominal focal plane and its neighborhood.

[0104] The number of the plurality of axial planes, the spacing between adjacent axial planes, and the offset of the farthest non-central axial plane relative to the nominal focal plane can be set according to the axial working range and specific application requirements. For those skilled in the art, as long as multiple axial planes can be symmetrically selected around the nominal focal plane and corresponding circular flat-top target models can be established for subsequent joint design of the phase distribution of the dual working surfaces, they should all be considered to fall within the scope of the technical concept of this step of the application.

[0105] S3. Assign an initial phase distribution to the first phase modulation structure and the second phase modulation structure, and calculate the light field distribution of the incident beam on the multiple axial planes after propagation through the first phase modulation structure, the transparent substrate, the second phase modulation structure, and subsequent focusing.

[0106] Specifically, after obtaining the basic parameters required for the design and establishing a circular flat-top target model including the central axial plane and non-central axial planes, the initial phase distribution for starting the joint design process is first set for the first phase modulation structure and the second phase modulation structure, and then the optical field is calculated for the entire dual working surface modulation and propagation process based on the initial phase distribution to obtain the actual output optical field distribution results on each axial plane under the current design state, providing a calculation basis for subsequent phase distribution updates.

[0107] The phrase "assigning initial phase distributions to the first and second phase modulation structures" refers to pre-setting initial spatial phase delay distributions for the first phase modulation structure formed on the incident side surface of the transparent substrate and the second phase modulation structure formed on the exit side surface of the transparent substrate during the initial design phase. This initial phase distribution can be understood as the initial design state adopted at the start of subsequent joint optimization, and its purpose is to provide a starting point for iterative updates of the phase distributions of the first and second phase modulation structures. It should be noted that the initial phase distribution is not limited to a specific form; it can be a zero-phase distribution, a random phase distribution, a phase distribution generated based on empirical rules, a phase distribution imported from existing design results, or other preset phase distribution forms that can serve as the starting condition for iteration.

[0108] The initial phase distribution of the first phase modulation structure can be used to form the initial pre-stage modulation state, so that when the incident beam propagates within the transparent substrate to the location of the second phase modulation structure, a corresponding initial intermediate optical field is generated. The initial phase distribution of the second phase modulation structure is then used to form the initial post-stage modulation state based on this initial intermediate optical field. By simultaneously assigning initial phase distributions to both, the first and second phase modulation structures can be integrated as a whole from the outset in the subsequent design process, rather than determining one phase modulation structure separately and then passively matching the other.

[0109] The phrase "calculating the light field distribution of the incident beam on the multiple axial planes after propagation through the first phase modulation structure, the transparent substrate, the second phase modulation structure, and subsequent focusing" refers to: using the obtained incident beam parameters as input light field conditions, and under the current phase distribution state of the first and second phase modulation structures, calculating the evolution process of the light field in the entire system according to the relationship between beam propagation and phase modulation, thereby obtaining the actual light field distribution results on the nominal focal plane and each non-central axial plane.

[0110] Specifically, the incident beam first acts on the first phase modulation structure. Since the first phase modulation structure has a pre-assigned initial phase distribution, the wavefront distribution of the incident beam changes accordingly after passing through it. Subsequently, the beam modulated by the first phase modulation structure continues to propagate within the transparent substrate. Because parameters such as the thickness, refractive index, and operating wavelength of the transparent substrate are predetermined, the evolution of the optical field after propagation within the transparent substrate can be calculated based on the corresponding propagation conditions, thereby obtaining the intermediate optical field distribution at the location of the second phase modulation structure.

[0111] After obtaining the intermediate optical field, the beam is further acted upon by the second phase modulation structure. Since the second phase modulation structure also possesses the currently assigned initial phase distribution, it introduces a predetermined spatial phase modulation based on the intermediate optical field. The beam modulated by the second phase modulation structure continues to propagate in conjunction with subsequent focusing conditions, forming corresponding actual output optical fields on the nominal focal plane and multiple axial planes symmetrically distributed around it. By calculating the actual output optical fields on these axial planes, the intensity distribution, spot range, flat-top region uniformity, edge transition characteristics, and energy distribution outside the target region on each axial plane under the current phase distribution conditions can be obtained.

[0112] The "light field distribution" in this step can be represented as either a complex amplitude distribution or a light intensity distribution further derived from the complex amplitude. In subsequent design processes, the light field distribution on the multiple axial planes can typically be extracted and analyzed based on the target model and evaluation requirements. For example, the uniformity index of the flat-top region, the bounding energy radius, the edge transition width, and the energy leakage outside the target region can be extracted based on the light intensity distribution to evaluate whether the phase distribution of the current first phase modulation structure and the second phase modulation structure meets the expected requirements.

[0113] Therefore, the core of this step lies in using the current phase distribution assigned to the first and second phase modulation structures as input, and obtaining the actual output light field distribution on multiple axial planes through continuous calculations of the beam's propagation through the first phase modulation structure, the transparent substrate, the second phase modulation structure, and the subsequent focusing process. This calculation result reflects, on the one hand, the effect of the current dual-working-plane phase distribution on the formation of the final target light field, and on the other hand, provides a direct basis for the subsequent adjustment, updating, and optimization of the phase distribution.

[0114] When calculating the light field distribution across multiple axial planes, the local effects of the first or second phase modulation structure are not evaluated independently. Instead, both are incorporated into a unified calculation chain along with the propagation process within the transparent substrate and the subsequent focusing process. The final multi-plane output result guides the evaluation of the current design state. This helps avoid situations where the overall output effect is insufficient due to designing the phase distribution based solely on a local plane.

[0115] The calculation of the optical field distribution can be based on diffraction propagation theory, Fourier optics methods, angular spectrum propagation methods, Fresnel propagation methods, Fraunhofer propagation methods, or other numerical calculation methods that can characterize the relationship between phase modulation and propagation. For those skilled in the art, any calculation of the actual optical field distribution on multiple axial planes after modulation by the dual working surfaces and subsequent focusing, based on the phase distribution of the current first and second phase modulation structures, should be considered within the scope of the technical concept of this step in this application.

[0116] By adopting the above settings, this application can avoid directly updating the phase distribution based on an abstract target during subsequent design processes. Instead, it first obtains the actual output light field on multiple axial planes under the current phase distribution conditions, and then performs subsequent optimization based on the difference between the actual output results and the target model. This is beneficial for improving the targeting and stability of the phase distribution design of dual-working-plane diffraction optical elements, and provides a computational basis for forming a long focal depth circular flat-top light spot with preset uniformity on the nominal focal plane and multiple axial planes in its neighborhood.

[0117] S4. During the iteration process, the circular flat-top target model of the corresponding axial plane is adaptively adjusted according to the defocused light field characteristics of the non-central axial plane.

[0118] Specifically, in the joint design of the phase distribution of the first phase modulation structure and the second phase modulation structure, the target model of the corresponding axial plane can be iteratively adjusted according to the defocused light field characteristics of the non-central axial plane in the current iterative state, so that the target model can be adapted to the current propagation state.

[0119] The "iterative process" can be understood as follows: based on the phase distribution of the current first and second phase modulation structures, the actual optical field distribution on multiple axial planes after dual-working-plane modulation and subsequent focusing is first calculated. Then, based on the difference between the actual optical field distribution and the target model, the phase distribution of the first and second phase modulation structures is updated, and the above calculation and update process is repeated until the stopping condition is met. In this iterative process, the target radius of the non-central axial plane does not always remain unchanged at the initial set value, but participates in the dynamic update process adapted to the current propagation results.

[0120] The term "adaptive adjustment" refers to the fact that the relevant parameters of the target model can be adjusted during the iteration process according to the current light field characteristics, rather than being limited to a single target form that is fixed in advance.

[0121] S5. Set different evaluation weights for different axial planes so that the output quality of the multiple axial planes participates in the joint evaluation according to the preset weights.

[0122] Specifically, when jointly evaluating the output light field of the nominal focal plane and its neighboring multiple axial planes, corresponding evaluation weights can be set according to the positional relationship of each axial plane relative to the nominal focal plane, the importance of the application scenario, or design requirements, so that different axial planes can contribute to the overall evaluation results.

[0123] S6. Construct a design evaluation target, which is used to take into account the uniformity of the flat-top light spot on multiple axial planes, the depth of focus, the utilization rate of the intermediate light field, and the energy leakage outside the target area.

[0124] Specifically, in the joint design of the phase distribution of the first phase modulation structure and the second phase modulation structure, the multi-axial plane output quality, the utilization of the intermediate optical field at the second phase modulation structure, and the energy control outside the target area can be incorporated into the same evaluation framework to provide an evaluation basis for subsequent joint updates of the phase distribution.

[0125] S7. The phase distributions of the first phase modulation structure and the second phase modulation structure are jointly updated according to the comprehensive objective function until the stopping condition is met.

[0126] Specifically, after constructing a comprehensive objective function that includes multi-axial planar uniformity evaluation, depth-of-focus reward, intermediate light field spillover suppression, and energy leakage control outside the target region, the comprehensive objective function is further used as a unified evaluation basis to coordinately adjust the current phase distribution of the first phase modulation structure and the second phase modulation structure, so that the two gradually approach the phase distribution state that can better meet the design target in the continuous iteration process.

[0127] The phrase "jointly updating the phase distributions of the first and second phase modulation structures" means that it's not simply adjusting the phase distribution of the first or second phase modulation structure alone, but rather treating them as an interconnected whole for simultaneous design and coordinated correction. In other words, during each update, the adjustment of the phase distribution of the first phase modulation structure needs to consider its impact on the formation of the intermediate light field after propagation within the transparent substrate; the adjustment of the phase distribution of the second phase modulation structure needs to consider the current intermediate light field distribution and the output results on multiple axial planes after subsequent focusing. This allows the pre-amplification function of the first phase modulation structure and the subsequent compensation and fine-shaping function of the second phase modulation structure to be coordinated and optimized under the same objective constraint.

[0128] The phrase "according to the comprehensive objective function" refers to the following: In the current iteration state, the value of the comprehensive objective function is first calculated based on the multiple axial plane optical field distribution results corresponding to the existing phase distributions of the first and second phase modulation structures. Then, based on the evaluation of the current design results by the comprehensive objective function, the direction and magnitude of the next round of phase distribution adjustment are determined. In other words, the comprehensive objective function in this application not only plays a role in evaluating the merits of the current design but also serves as a basis for guiding the phase distribution update, ensuring that the subsequent update process always revolves around the overall goal of "improving the comprehensive quality of the circular flat-top light spots in each axial plane, expanding the effective depth of focus range, suppressing the spillover of the intermediate optical field at the second phase modulation structure, and reducing energy leakage outside the target area."

[0129] The joint update of the phase distribution is not limited to a fixed update mechanism. In some embodiments, the phase distribution of the first and second phase modulation structures can be modified in parts or entirely based on the changing trend of the comprehensive objective function. In other embodiments, it can be achieved through iterative optimization, constraint solving, numerical search, or other methods that can gradually improve the phase distribution based on the evaluation results of the comprehensive objective function. For those skilled in the art, any coordinated adjustment of the phase distribution of the first and second phase modulation structures based on the comprehensive objective function, so that they gradually change towards a better design state, should be considered to fall within the scope of the technical concept of this step in this application.

[0130] The emphasis on "joint updating" in this application stems from the clear coupling between the first and second phase modulation structures. The phase distribution of the first phase modulation structure not only determines the intermediate optical field morphology after the incident beam propagates within the transparent substrate but also further influences the input optical field state received by the second phase modulation structure. Conversely, the phase distribution of the second phase modulation structure directly affects the output results of the intermediate optical field after subsequent modulation and focusing on the nominal focal plane and multiple non-central axial planes. Therefore, optimizing only one phase modulation structure without simultaneously considering the response relationship of the other phase modulation structure makes it difficult to fully leverage the advantages of the dual-working-plane collaborative design and hinders the overall optimization goal of achieving a long focal depth circular flat-top spot.

[0131] The phrase "until the stopping condition is met" means that the aforementioned joint update process of phase distribution based on the comprehensive objective function is not carried out indefinitely, but ends when a pre-set termination criterion is met. In other words, when the design process reaches the expected optimization level or further iterations are unlikely to produce significant improvements, the phase distribution update can be stopped, and the current phase distributions of the first and second phase modulation structures can be output as the final design result.

[0132] The stopping conditions may include at least one of the following: first, the synthesized objective function reaches a preset target value or a preset convergence range; second, the change in the synthesized objective function between two or more adjacent iterations is less than a preset threshold; third, the change in the phase distribution of the first phase modulation structure and the second phase modulation structure between two or more adjacent iterations is less than a preset threshold; fourth, the number of iterations reaches a preset upper limit. By setting the stopping conditions, unconstrained extension of the design process can be avoided, while ensuring that the joint update of the phase distribution ends in a timely manner after reaching a predetermined stable state or target state.

[0133] In this step, based on the aforementioned target model and design evaluation objectives, the phase distribution of the first phase modulation structure and the second phase modulation structure are jointly updated, so that the finally obtained dual-working-plane diffraction optical element can form a long focal depth circular flat-top light spot with preset uniformity on the nominal focal plane and multiple axial planes in its neighborhood.

[0134] By employing the above-described configuration, this application avoids the problem of local optimization based solely on a single plane, a single evaluation index, or a single phase modulation surface. Instead, it guides the improvement of the phase distribution of the two working surfaces through continuous, coordinated, and constrained refinement using a comprehensive objective function. This, in turn, enhances the stability and convergence of the entire design process, as well as the overall performance of the final output optical field.

[0135] S8. Output the phase distribution of the first phase modulation structure and the second phase modulation structure to form corresponding phase modulation structures on both sides of the transparent substrate.

[0136] Specifically, after jointly updating the phase distributions of the first phase modulation structure and the second phase modulation structure according to the comprehensive objective function and satisfying the stopping condition, the currently obtained phase distributions of the first phase modulation structure and the second phase modulation structure are output as the final design result to guide the formation of corresponding actual phase modulation microstructures on the incident side surface and the exit side surface of the transparent substrate.

[0137] The phrase "outputting the phase distribution of the first phase modulation structure and the second phase modulation structure" can be understood as: providing the spatial phase distribution results, determined through the aforementioned joint design process, that meet the requirements for shaping the circular flat-top light spot of the nominal focal plane and its neighboring multiple axial planes, in a form that can be used for subsequent device fabrication, processing, or layout generation. In other words, the output in this step is no longer an intermediate calculation state in the iterative process, but rather the final phase distribution result that has met the predetermined design requirements and can be used as the basis for actual device implementation.

[0138] Specifically, the phase distribution of the first phase modulation structure corresponds to the spatial phase delay distribution required to be formed on the incident side surface of the transparent substrate; the phase distribution of the second phase modulation structure corresponds to the spatial phase delay distribution required to be formed on the exit side surface of the transparent substrate. Both are final results determined through joint design, and they are not independent of each other, but rather jointly serve the target optical field output required by this application. That is, the output phase distribution of the first phase modulation structure is used to perform predetermined phase modulation on the incident beam in the pre-stage and form an intermediate optical field suitable for subsequent modulation during propagation within the transparent substrate; the output phase distribution of the second phase modulation structure is used to further compensate and finely shape the intermediate optical field so that the subsequently focused beam forms a circular flat-topped spot with a predetermined uniformity on the nominal focal plane and multiple axial planes in its vicinity.

[0139] The phrase "for forming corresponding phase modulation structures on both sides of the transparent substrate" refers to forming corresponding actual microstructure morphologies or equivalent phase modulation structures on the incident and exit surfaces of the transparent substrate, based on the phase distributions of the first and second phase modulation structures output above. In other words, this step not only focuses on obtaining theoretical design results but also aims at the actual fabrication and realization of the device. Through this step, the phase distribution results obtained from the aforementioned joint design can be transformed into a concrete, fabricable, and manufacturable dual-plane diffractive optical element structure.

[0140] The output phase distribution can be further converted into a data format adapted to the processing technology. For example, when the first and second phase modulation structures are implemented using multi-level stepped microstructures, the corresponding continuous phase distribution can be discretized to form structural layout data corresponding to the height of each step. When the first and second phase modulation structures are implemented using continuous relief microstructures, the phase distribution can be converted into corresponding continuous surface contour height distribution data. Therefore, the output phase distribution can be further used in photolithography, etching, imprinting, molding, ion beam processing, laser direct writing, or other micro / nano fabrication processes.

[0141] The "output" is not limited to a single, specific form. For those skilled in the art, any final phase distribution obtained after the joint design of the first and second phase modulation structures, presented in a form usable for subsequent structure formation, layout generation, or device fabrication, should be considered within the scope of the technical concept of this step in this application. For example, the output may be a phase matrix, a phase mapping table, structural height distribution data, discrete step-encoded data, or other data formats capable of characterizing the target phase distribution and used to form the actual modulation structure.

[0142] Furthermore, this step also demonstrates that the method of this application is not merely for abstractly obtaining a certain theoretical light field, but aims to form a practical single-substrate dual-working-plane diffraction optical element. The parameters obtained in the preceding steps, the established target model, the calculated multiple axial plane light field distributions, the extracted enclosing energy radii, the constructed comprehensive objective function, and the executed phase distribution joint update all ultimately converge in the phase distribution output of this step, thus giving the entire design method a clear engineering application objective.

[0143] This application enables the direct application of the dual-working-plane phase distribution results, which meet the design requirements of long focal depth circular flat-top light spots, to the actual structural formation of both sides of a transparent substrate, thereby achieving an effective connection from design to device fabrication. This not only facilitates the transformation of the aforementioned jointly optimized phase distribution into a manufacturable single-substrate dual-working-plane diffractive optical element, but also helps ensure the consistency between the final fabricated device and the design objectives.

[0144] In some embodiments of this application, the different evaluation weights are determined based on the axial position of each axial plane relative to the nominal focal plane and / or application requirements.

[0145] In some embodiments of this application, the design evaluation objective includes evaluating the output quality of each axial plane and determining the axial working range that meets the preset quality requirements based on the evaluation results.

[0146] In some embodiments of this application, the plurality of axial planes includes a nominal focal plane and an equal number of non-central axial planes respectively disposed on the front and rear sides of the nominal focal plane, such that the total number of the plurality of axial planes is an odd number, the predetermined encirclement energy ratio is 80% to 90%, and the allowable leakage threshold outside the target area does not exceed 20%.

[0147] Specifically, having an odd number of axial planes symmetrically distributed about the nominal focal plane means selecting an equal number of non-central axial planes on both sides of the nominal focal plane as the central plane, ensuring that the total number of axial planes is odd. This setting ensures that the nominal focal plane is always retained as the central reference plane, while also taking into account the output quality on both sides of the nominal focal plane, which helps improve the overall balance of axial performance.

[0148] The predetermined enclosing energy ratio of 80% to 90% refers to using 80% to 90% of the total energy as the characterization standard for the main energy distribution range when extracting the enclosing energy radius of each non-central axial plane. This can better reflect the main energy distribution range while avoiding excessive influence from the weak energy distribution at the edges.

[0149] The allowable leakage threshold of no more than 20% outside the target area means that the proportion of energy leakage outside the target area is controlled within 20% of the total energy. This setting allows the majority of energy to be concentrated within the target area, thereby improving energy utilization and edge quality, and enhancing the constraint effect of energy control outside the target area.

[0150] The specific number of axial planes, the specific value of the enclosing energy ratio, and the specific value of the allowable leakage threshold can all be set within the above range according to application requirements. For those skilled in the art, as long as an odd number of axial planes are used and symmetrically distributed about the nominal focal plane, and the enclosing energy ratio and allowable leakage threshold are controlled within the above range, they should all be considered to fall within the protection scope of this application.

[0151] The above settings help improve the symmetry of the multi-plane target model, the stability of the enclosing energy radius extraction, and the energy control effect outside the target area, thereby improving the overall design quality of the long focal length deep circular flat-top spot.

[0152] A third aspect of this application provides a laser beam shaping system, including a laser source, a collimation module, the single-substrate dual-working-plane diffraction optical element, and a subsequent focusing optical assembly; the system is used to shape a Gaussian or near-Gaussian incident beam into a long focal depth circular flat-top focal spot with predetermined uniformity in the nominal focal plane and its neighborhood.

[0153] Example 2 like Figure 6 and Figure 7 As shown, in this embodiment, the first phase modulation structure is formed on the incident side surface of the transparent substrate, and the second phase modulation structure is formed on the exit side surface of the transparent substrate. The incident Gaussian beam or near-Gaussian beam first undergoes energy pre-distribution and wavefront pre-shaping through the first phase modulation structure; the beam modulated by the first phase modulation structure propagates within the transparent substrate and forms a predetermined intermediate light field in front of the second phase modulation structure; the second phase modulation structure performs further phase compensation and fine shaping based on the intermediate light field; after subsequent focusing, a long focal depth, high uniformity circular flat-top focal spot is formed in the target focal plane and its neighborhood.

[0154] Under a set of representative parameters, the operating wavelength, subsequent focusing conditions, target size at the central focal plane, axial working range, number of axial planes, encircling energy ratio, edge transition width, and allowable leakage threshold outside the target area can all be selected within a preset range according to specific light source conditions and application requirements. It should be noted that... Figure 3 The XZ propagation cross section shown can be used to illustrate the propagation trend within and outside the focal plane neighborhood, and its display range is not limited to the actual optimized range. The above parameters are only used to illustrate the design concept of this application and do not constitute a limitation on the scope of protection of this application.

[0155] In another set of small-sized circular flat-top spot design examples, the incident beam aperture, focusing conditions, target flat-top spot size, and edge transition region width can all be set according to specific application requirements to illustrate that this application can be applied to small-sized circular flat-top focal spot shaping scenarios.

[0156] like Figure 5 As shown, in the example of a small-sized circular flat-top focal spot design, after joint modulation by the first phase modulation structure and the second phase modulation structure, a small-sized circular flat-top light spot with a controlled edge transition region can be formed on the target plane. This example illustrates that the dual-working-plane collaborative design of this application is applicable to both long focal depth circular flat-top light spots and small-sized circular flat-top focal spot shaping scenarios. Figure 5 This is for conceptual effect illustration only and does not specify the exact phase distribution, spot size, or uniformity value.

[0157] 1. Overview of the circular flat-top target, its dimensions, and edge transitions. In circularly symmetric focal plane modeling scenarios, the aperture field corresponding to a circular flat-top target typically needs to simultaneously satisfy the requirements of flat-top region uniformity, edge transition quality, and external leakage control in the target area. For smaller or near-diffraction-limited flat-top targets, simply pursuing an ideal hard edge increases the difficulty of implementation; by setting a finite-width edge transition region, a balance can be achieved between edge sharpness and external energy suppression in the target area.

[0158] 2. Realizability limitations of monolithic pure-phase DOEs Under Gaussian or near-Gaussian incident conditions, the degree of freedom for adjustment of a single pure phase DOE is limited, making it difficult to simultaneously achieve small-sized circular flat-top spot, controlled edge transition, low-target region leakage, and axial stability in the focal plane neighborhood under the same structural conditions.

[0159] 3. The mechanism by which the dual-working-face structure forms the intermediate phase distribution This application sets phase modulation structures on two working surfaces of a transparent substrate, so that the modulation introduced by the first phase modulation structure propagates within the substrate and forms an intermediate amplitude-phase distribution that can be further utilized at the second phase modulation structure; the second phase modulation structure continues to modulate based on this intermediate optical field, thereby improving the overall degree of freedom of optical field control.

[0160] 4. The necessity and constraints of non-zero propagation In-substrate propagation between the first and second phase modulation structures should not degenerate to zero propagation, but should enable the preceding phase modulation to form a usable intermediate optical field at the second phase modulation structure; at the same time, the main energy distribution of the intermediate optical field should match the effective modulation region of the second phase modulation structure to avoid underutilization of the effective region or energy spillover.

[0161] 5. Long focal depth multi-plane optimization model In long depth-of-focus design, multiple axial planes can be symmetrically selected around the nominal focal plane, and the output light field of each axial plane can be jointly evaluated. For non-central axial planes, the corresponding target model can be adjusted according to the current defocused light field characteristics, making the multi-plane target constraint more adaptable to the actual propagation state.

[0162] 6. Quality Evaluation and Design Evaluation Objectives During the joint design process, design evaluation targets can be constructed to comprehensively reflect the uniformity of the multi-axial planar flat-top light spot, the depth of focus, the utilization rate of the intermediate light field, and the control of energy leakage outside the target area. The specific evaluation function form can be determined according to different application requirements and is not limited to a fixed mathematical expression.

[0163] 7. Design Steps The design process of this embodiment can be performed according to the steps in the foregoing claims, namely, obtaining design input parameters, establishing a multi-axial plane target model, calculating the current light field distribution, adjusting the target model according to the defocused light field characteristics, setting evaluation weights for different axial planes, constructing design evaluation targets, jointly updating the phase distribution of the two working surfaces, and outputting the corresponding design results.

[0164] 8. Implementation Results This embodiment utilizes the synergistic effect of the first phase modulation structure, propagation within the transparent substrate, and the second phase modulation structure to form a circular flat-top light spot in the target plane and its neighborhood, which is beneficial for balancing the uniformity of the flat-top area, edge transition, axial working tolerance, and energy control outside the target area. Figures 2 to 5 This is for illustrative purposes only and does not limit the specific phase layout, parameter values, or test results.

[0165] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0166] The above description is merely an embodiment of this application and is not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for designing a single-substrate, dual-working-plane diffractive optical element, characterized in that, It includes a transparent substrate, a first phase modulation structure formed on the incident side surface of the transparent substrate, and a second phase modulation structure formed on the exit side surface of the transparent substrate; After the incident beam is modulated by the first phase modulation structure and propagates within the transparent substrate, an intermediate light field is formed at the second phase modulation structure. The energy distribution range of the intermediate light field matches the effective modulation region of the second phase modulation structure. The phase distribution of the first phase modulation structure and the second phase modulation structure are jointly determined such that the beam modulated by the second phase modulation structure and subsequently focused forms a circular flat-top light spot with a preset uniformity on the nominal focal plane and on a plurality of axial planes symmetrically distributed around the nominal focal plane. Includes the following steps: Obtain incident beam parameters, working wavelength, transparent substrate thickness and refractive index, subsequent focusing conditions, target radius of the central focal plane, edge transition width, allowable leakage threshold outside the target area, and axial working range; Multiple axial planes are selected symmetrically around the nominal focal plane to establish a circular flat-top target model that includes the central axial plane and non-central axial planes; An initial phase distribution is assigned to the first phase modulation structure and the second phase modulation structure, and the light field distribution of the incident beam after propagation through the first phase modulation structure, the transparent substrate, the second phase modulation structure, and subsequent focusing is calculated on the multiple axial planes. During the iteration process, the circular flat-top target model of the corresponding axial plane is adaptively adjusted according to the defocused light field characteristics on the non-central axial plane. Different evaluation weights are set for different axial planes so that the output quality of the multiple axial planes participates in the joint evaluation according to the preset weights. A design evaluation target is constructed, which is used to take into account the uniformity of the flat-top light spot on multiple axial planes, the depth of focus, the utilization rate of the intermediate light field, and the energy leakage outside the target area. A comprehensive objective function is constructed that includes multi-axial planar uniformity evaluation, depth-of-focus reward, intermediate light field spillover suppression, and energy leakage control outside the target region; The phase distributions of the first phase modulation structure and the second phase modulation structure are jointly updated according to the comprehensive objective function until the stopping condition is met. The phase distributions of the first phase modulation structure and the second phase modulation structure are output to form corresponding phase modulation structures on both sides of the transparent substrate.

2. The method according to claim 1, characterized in that, The energy distribution range of the intermediate light field is matched with the effective modulation region of the second phase modulation structure, so that the main energy distribution of the intermediate light field is located within the region that the second phase modulation structure can effectively modulate.

3. The method according to claim 1 or 2, characterized in that, The circular flat-top light spot includes a flat-top region and a finite-width edge transition region surrounding the flat-top region. The width of the edge transition region and the allowable leakage threshold outside the target area are jointly constrained during the joint determination process.

4. The method according to claim 1, characterized in that, The phase distributions of the first phase modulation structure and the second phase modulation structure are also jointly determined as follows: a penalty constraint is imposed on the proportion of energy outside the effective modulation region of the second phase modulation structure.

5. The method according to claim 1, characterized in that, The first phase modulation structure and the second phase modulation structure are multi-level stepped microstructures or continuous relief microstructures, which provide a spatial phase delay distribution of 0 to 2π radians at the designed operating wavelength.

6. The method according to claim 1, characterized in that, The different evaluation weights are determined based on the axial position of each axial plane relative to the nominal focal plane and / or application requirements.

7. The method according to claim 1 or 6, characterized in that, The design evaluation objectives include evaluating the output quality of each axial plane and determining the axial working range that meets the preset quality requirements based on the evaluation results.

8. The method according to claim 1, characterized in that, The plurality of axial planes include a nominal focal plane and an equal number of non-central axial planes respectively disposed on the front and rear sides of the nominal focal plane, such that the total number of the plurality of axial planes is an odd number, the predetermined encirclement energy ratio is 80% to 90%, and the allowable leakage threshold outside the target area does not exceed 20%.

9. A laser beam shaping system, characterized in that, The system, implemented using the method of claim 1, includes a laser source, a collimation module, a single-substrate dual-working-surface diffractive optical element manufactured by the method for designing a single-substrate dual-working-surface diffractive optical element, and subsequent focusing optical components; the system is used to shape a Gaussian or near-Gaussian incident beam into a long focal depth circular flat-top focal spot that maintains a predetermined uniformity within the nominal focal plane and its neighborhood.

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