A system and method for constructing a diffraction-free beam interference field

Abstract

This application discloses a system and method for constructing a diffraction-free beam interference field, belonging to the field of optical manufacturing technology. It includes: splitting the incident beam, configuring the optical path and modulating the phase of each beam to convert each beam into a Bessel beam, and combining this with Bessel beam sidelobe suppression technology to obtain a long focal depth diffraction-free beam with no or suppressed sidelobes; intersecting two long focal depth diffraction-free beams with no or suppressed sidelobes in a target region to ultimately construct a three-dimensional diffraction-free interference field. This application utilizes long focal depth diffraction-free beams with no or suppressed sidelobes for interference, fundamentally reducing the nonlinear error of the interference fringe phase and significantly improving the tolerance and stability of the holographic interference field to optical path position deviations.

Description

Technical Field

[0001] This application relates to the field of optical manufacturing technology, and more specifically to a system and method for constructing a non-diffraction beam interference field. Background Technology

[0002] Large-area, high-precision diffraction gratings possess excellent dispersion, polarization adjustment, phase matching, and beam splitting capabilities. Their applications have expanded beyond traditional spectral analysis, making them crucial components of high-end spectroscopic instruments and vital elements in major scientific projects such as space remote sensing, gravitational wave detection, inertial confinement, and nuclear fusion. Scanning interferometry (SIF) is the preferred method for manufacturing large-area holographic gratings. This technique uses two Gaussian beams, expanded, to interfere at the grating substrate, forming interference field fringes that are exposed onto photoresist. Large-area exposure is achieved using a high-precision two-dimensional motion platform for scanning and stepping, offering advantages such as dynamic exposure and real-time control. However, due to the complex structure of the SIF system, lens adjustment errors and beam waist deviations in the optical path can affect the performance of the resulting interference field. Nonlinear errors in the interference fringe phase can lead to grooved and warped gratings after further exposure, and in severe cases, render the grating unusable.

[0003] Bessel beams possess diffraction-free properties; the diameter and intensity of their central main lobe remain almost constant along the propagation direction, and they are self-healing after being partially blocked. Replacing Gaussian beams with Bessel beams can extend the effective depth of focus from the millimeter level to the hundred-millimeter level, thereby reducing wavefront curvature variation by two orders of magnitude. However, Bessel beams have side lobes, resulting in discontinuous fringe distributions in the interference between two Bessel beams. This prevents the provision of a continuous, scannable exposure field, becoming a direct bottleneck restricting the manufacture of high-precision gratings.

[0004] Therefore, there is an urgent need for a system and method for constructing a diffraction-free beam interference field to solve the problems of nonlinear error in the phase of Gaussian beam interference fringes and discontinuity in Bessel beam interference fringes in existing technologies. Summary of the Invention

[0005] The purpose of this application is to provide a system and method for constructing a diffraction-free beam interference field, which can solve at least one of the aforementioned technical problems. The specific solution is as follows:

[0006] This application provides a system for constructing a diffraction-free beam interference field, comprising: a light source and beam preparation unit, a beam splitting unit, a first interference unit, a second interference unit, and an interference field forming unit arranged sequentially along the optical axis; wherein,

[0007] The light source and beam preparation unit are used to generate a collimated Gaussian beam;

[0008] The beam splitting unit is used to split the collimated Gaussian beam into a first beam and a second beam;

[0009] The first interference unit includes a first compensation plate, a first reflector, and a first phase modulation device, used to sequentially perform optical path compensation, propagation direction adjustment, and optical phase modulation on the first beam, converting the first beam into a first non-diffraction beam; wherein, the first interference unit has Bessel beam sidelobe suppression capability; the first non-diffraction beam is a long focal depth non-diffraction beam with no sidelobes or suppressed sidelobes.

[0010] The first compensation plate is used to adjust the optical path of the first optical path; the first reflector is used to set the propagation direction of the first non-diffraction beam; the first phase modulation device is used to convert the first beam into a Bessel beam with suppressed side lobes.

[0011] The second interference unit includes a second compensation plate, a third compensation plate, a second reflector, and a second phase modulation device, used to sequentially perform optical path compensation, propagation direction adjustment, and optical phase modulation on the second beam, converting the second beam into a second diffraction-free beam; wherein, the second interference unit has Bessel beam sidelobe suppression capability; the second diffraction-free beam is a long focal depth diffraction-free beam with no sidelobes or suppressed sidelobes;

[0012] The second compensation plate and the third compensation plate are used to adjust the optical path of the second optical path; the second reflector is used to set the propagation direction of the second non-diffraction beam; the second phase modulation device is used to convert the second beam into a Bessel beam with suppressed side lobes.

[0013] The interference field forming unit sets an angle between the first and second reflectors, causing the first non-diffraction beam and the second non-diffraction beam to intersect at a set angle in the target area, thereby forming a three-dimensional non-diffraction interference field.

[0014] Furthermore, the light source and beam preparation unit includes a laser and a collimating beam expander assembly, used to provide a collimated Gaussian beam with a preset beam waist radius.

[0015] Furthermore, by adjusting the beam waist radius of the collimated Gaussian beam and the phase distribution generated by the first phase modulator and the second phase modulator, the first non-diffraction beam and the second non-diffraction beam are output.

[0016] Furthermore, by adjusting the beam waist radius of the collimated Gaussian beam, the phase distribution generated by the first phase modulation device and the second phase modulation device is set, thereby suppressing the sidelobe energy of the Bessel beam.

[0017] Furthermore, the first compensation plate, the second compensation plate, and the third compensation plate are parallel plane optical glass, and the effective thickness in the optical path is changed by rotating the angle to achieve the adjustment and matching of the optical path.

[0018] Furthermore, by adjusting the pitch and yaw angles of the first and second reflectors, the first non-diffractive beam and the second non-diffractive beam are made to converge in the target area at a set intersection angle.

[0019] Furthermore, the included angle of intersection satisfies the following condition:

[0020]

[0021] Where θ represents half of the intersection angle; λ represents the wavelength of the non-diffractive beam; p represents the target fringe period; and β represents the cone angle of the Bessel beam.

[0022] Furthermore, the first phase modulation device and the second phase modulation device are axial tapered lenses.

[0023] Furthermore, the first phase modulation device and the second phase modulation device are phase plates or spatial light modulators.

[0024] This application also provides a method for constructing a non-diffraction beam interference field, the method comprising:

[0025] Based on the target grating period and the required depth of focus for interference field without diffraction, the phase distribution required for the device used for phase modulation to generate the Bessel beam is preset.

[0026] The beam waist radius of the collimated Gaussian beam is determined based on the preset phase distribution.

[0027] The intersection angle of the two beams is determined based on the phase distribution of the phase modulation device, the waist radius of the collimated Gaussian beam, the laser wavelength, and the period of the target grating.

[0028] Based on the determined beam waist radius, a collimated Gaussian beam is generated;

[0029] The collimated Gaussian beam is split into a first beam and a second beam.

[0030] The first beam is passed sequentially through the first compensation plate, the first reflector and the first phase modulation device to generate a first diffraction-free beam.

[0031] The second beam is passed sequentially through the second compensation plate, the third compensation plate, the second reflector, and the second phase modulation device to generate a second non-diffraction beam.

[0032] Based on the determined intersection angle, the first and second reflectors are adjusted so that the first non-diffraction beam and the second non-diffraction beam intersect and interfere in the target area, forming a three-dimensional non-diffraction interference field.

[0033] Compared with the prior art, the above-described solutions of this application have at least the following beneficial effects:

[0034] 1. This application discloses a system and method for constructing a diffraction-free beam interference field. Through optical phase modulation, the incident beam is converted into a Bessel beam with diffraction-free characteristics. Furthermore, through parametric co-design, the beam phase is controlled, optimizing the Bessel beam into a long focal depth diffraction-free beam with no sidelobes or suppressed sidelobes, which serves as the interference beam. Utilizing the diffraction-free and long focal depth characteristics of the beam, the constructed interference field achieves wavefront stability in the propagation direction. Under the same optical path position deviation, the nonlinear error of the interference fringe phase is reduced by several orders of magnitude compared to a Gaussian beam, thereby fundamentally improving the accuracy of the holographic interference exposure field and providing a basic guarantee for manufacturing high-precision gratings.

[0035] 2. This application discloses a system and method for constructing a diffraction-free beam interference field. When constructing the interference field, two long focal depth diffraction-free beams with no sidelobes or suppressed sidelobes are used to form a three-dimensional interference field. The constructed interference field exhibits excellent tolerance to mechanical deviations in the optical path. This significantly reduces the requirements for vibration, thermal drift, and assembly accuracy in the holographic interferometry exposure system, thereby improving the robustness and process repeatability of the holographic interferometry exposure system.

[0036] 3. The present application provides a system and method for constructing a diffraction-free beam interference field. After generating a Bessel beam, by introducing Gaussian function envelope modulation and phase control, and by optimizing its radial envelope width parameter, the sidelobe energy of the Bessel beam is effectively suppressed, forming a long focal depth diffraction-free beam with no sidelobes or suppressed sidelobes. The energy is highly concentrated in the central main lobe, and after interference, continuous, clear, and high-contrast fringes can be produced. Attached Figure Description

[0037] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application. It is obvious that the drawings described below are merely some embodiments of this application, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. In the drawings:

[0038] Figure 1 This is a schematic diagram of a system for constructing a non-diffraction beam interference field, provided in an embodiment of this application.

[0039] Figure 2This is a schematic diagram of the principle of the axial cone lens of the Bessel beam provided in the embodiments of this application.

[0040] Figure 3 This is a schematic diagram of the phase plate of a Bessel beam provided in an embodiment of this application.

[0041] Figure 4 This is a flowchart illustrating a method for constructing a diffraction-free beam interference field, as provided in an embodiment of this application.

[0042] Figure 5 This is a schematic diagram of the Bessel beam interference intensity distribution provided in an embodiment of this application.

[0043] Figure 6 This is a schematic diagram showing the overall light intensity comparison between the Bessel beam after sidelobe suppression and the unprocessed Bessel beam provided in the embodiments of this application.

[0044] Figure 7 The figure is a magnified schematic diagram of the sidelobe portion of the Bessel beam after sidelobe suppression and the Bessel beam without sidelobe suppression provided in the embodiment of this application.

[0045] Figure 8 This is a schematic diagram of the light intensity distribution of the Bessel beam after suppressing side lobes, provided in an embodiment of this application.

[0046] Figure 9 This is a schematic diagram of the light intensity cross section at the center of the Bessel beam after suppressing side lobes, as provided in an embodiment of this application.

[0047] Figure 10 This is a schematic diagram of the Gaussian beam interference position deviation in the simulation of nonlinear error of interference fringes provided in the embodiments of this application.

[0048] Figure 11 This is a schematic diagram of the Bessel-Gaussian beam interference position deviation in the simulation of nonlinear error of interference fringes provided in the embodiments of this application.

[0049] Explanation of reference numerals in the attached figures:

[0050] 1. Laser, 2. Collimating and expanding lens group, 3. Beam splitter, 4. First compensation plate, 5. First reflector, 6. First phase modulator, 7. Second compensation plate, 8. Third compensation plate, 9. Second reflector, 10. Second phase modulator, 11. Detector. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0052] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a product or device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a product or device. Without further limitation, an element defined by the phrase "comprising one" does not exclude the presence of other identical elements in the product or device that includes that element.

[0053] The embodiments of this application are described in detail below with reference to the accompanying drawings.

[0054] Example 1:

[0055] like Figure 1 As shown, this application provides a system for constructing a diffraction-free beam interference field, which can provide continuous, clear, and diffraction-free interference fringes to meet the requirements of high-precision grating manufacturing.

[0056] The system specifically includes: a light source and beam preparation unit, a beam splitting unit, a first interference unit, a second interference unit, and an interference field forming unit arranged along the optical axis. The light source and beam preparation unit generates a collimated Gaussian beam. The beam splitting unit splits the collimated Gaussian beam into a first beam and a second beam. The first interference unit includes a first compensation plate 4, a first reflector 5, and a first phase modulation device 6, used to perform optical path compensation, propagation direction adjustment, and optical phase modulation on the first beam, converting it into a first non-diffraction beam. The first compensation plate 4 adjusts the optical path of the first optical path. The first reflector 5 sets the propagation direction of the first non-diffraction beam, and the first phase modulation device 6 converts the first beam into a Bessel beam. The second interference unit includes a second compensation plate 7, a third compensation plate 8, a second reflector 9, and a second phase modulation device 10, used to sequentially perform optical path compensation, propagation direction adjustment, and optical phase modulation on the second beam, converting it into a second non-diffraction beam. The second compensation plate 7 and the third compensation plate 8 adjust the optical path of the second optical path. The second reflector 9 sets the propagation direction of the second non-diffraction beam. The second phase modulator 10 is used to convert the second beam into a Bessel beam. The interference field forming unit sets an angle between the first reflector 5 and the second reflector 9, causing the first and second non-diffractive beams to intersect at a set angle in the target region, thereby forming a three-dimensional non-diffractive interference field. In the technical solution of Embodiment 1 of this application, both the first phase modulator 6 and the second phase modulator 10 are axial-cone lenses, namely, a first axial-cone lens and a second axial-cone lens. In this embodiment, both the first and second non-diffractive beams are long-depth-of-focus non-diffractive beams with no sidelobes or suppressed sidelobes.

[0057] In this embodiment, the light source and beam preparation unit includes a laser 1 and a collimation and beam expanding system. The laser 1 is preferably a single-mode continuous laser 1 that outputs a Gaussian beam. In this embodiment, the collimation and beam expanding system is a collimation and beam expanding lens group 2, which is used to expand and collimate the Gaussian beam emitted by the laser 1 into a parallel Gaussian beam with a larger diameter. By adjusting the collimation and beam expanding lens group 2, the beam waist radius of the output beam can be preset and precisely controlled.

[0058] In this embodiment, the beam splitting unit receives the collimated Gaussian beam from the light source and beam preparation unit, and splits it into two paths, forming two beams at a certain ratio. In this embodiment, the beam splitting unit is a 50:50 beam splitter prism 3, which splits the collimated Gaussian beam into a first beam and a second beam, where the first beam is a transmitted beam and the second beam is a reflected beam.

[0059] The first interference unit includes a first compensation plate 4, a first reflector 5, and a first axial cone lens, used to sequentially perform optical path compensation, propagation direction adjustment, and optical phase modulation on the first beam, converting the first beam into a first diffraction-free beam. The first beam passes sequentially through the first compensation plate 4 and the first reflector 5, and is incident on the first axial cone lens; the first axial cone lens performs optical phase modulation on the first beam, and through coordinated design with the incident beam parameters, directly outputs a first-path Bessel-Gaussian beam with suppressed sidelobes.

[0060] The second interference unit, comprising a second compensation plate 7, a third compensation plate 8, a second reflector 9, and a second axial conical lens, is used to sequentially perform optical path compensation, propagation direction adjustment, and optical phase modulation on the second beam, converting the second beam into a second diffraction-free beam. The second beam passes sequentially through the second compensation plate 7, the third compensation plate 8, and the second reflector 9 before being incident on the second axial conical lens. The second axial conical lens performs optical phase modulation on the second beam and, through coordinated design with the incident beam parameters, directly outputs a second-path Bessel-Gaussian beam with suppressed sidelobes.

[0061] In this embodiment, the first compensation plate 4, the second compensation plate 7, and the third compensation plate 8 are all parallel planar optical glass plates. By rotating the angle of each compensation plate, the effective thickness of the light beam passing through the glass can be changed, thereby fine-tuning the optical path of the optical path to achieve optical path matching between the two light paths. The first reflecting mirror 5 and the second reflecting mirror 9 are planar reflecting mirrors supported by high-precision adjustable mirror frames. By adjusting the pitch and yaw angles of each reflecting mirror, the propagation direction of the output light beam can be precisely set.

[0062] In this embodiment, the optical phase modulation function is achieved by axial cone lenses, namely a first axial cone lens and a second axial cone lens. Figure 2 As shown, the base angle of the cone lens is The refractive index is n. The incident beam is converted into a Bessel beam by utilizing the bottom angle of the axial cone lens.

[0063] In this embodiment, the interference field forming unit includes a first reflecting mirror 5, a second reflecting mirror 9, two Bessel beams, and the intersection region of the two beams' propagation paths, namely, the Bessel beam in the first optical path and the Bessel beam in the second beam. The intersection region is the location of the detector 11. By precisely adjusting the angles of the first reflecting mirror 5 and the second reflecting mirror 9, the two non-diffraction beams emitted from the two axial conical lenses intersect at a set intersection angle in the target region, that is, precisely intersect on the plane where the grating substrate is located. When the Bessel beams meet here, interference automatically occurs, forming a three-dimensional non-diffraction interference field.

[0064] The technical solution of this application embodiment generates a Bessel beam using an axial cone lens, and controls the diffraction-free length and spot size of the Bessel beam by controlling the base angle of the axial cone lens. The optical field expression of the Bessel beam is:

[0065]

[0066] Where A represents the amplitude; k 0 Represents the spatial wave vector of the incident light; Indicates the wavelength of the incident light; The radial wave vector of the beam is denoted by , which determines the period of the beam's transverse interference and directly affects the spot size; r represents the radial coordinate. i Represents the imaginary unit; The z-axis represents the longitudinal wave vector of the beam; z represents the coordinate of the beam propagation direction. α represents the 0th order Bessel function; α represents the base angle of the axial cone lens; n represents the refractive index of the axial cone lens; β represents the cone angle of the Bessel beam.

[0067] This application provides a preferred technical solution. To achieve high-quality interference fringes, it is necessary to suppress the side lobes of the Bessel beam. Gaussian function envelope modulation is achieved by controlling the beam parameters incident on the axial conic lens and the geometric parameters of the axial conic lens. This system coordinates the design of the output beam of the light source and the beam preparation unit, as well as the base angle α of the axial conic lens, i.e., the beam waist radius ω of the Gaussian beam and the base angle α of the axial conic lens. This ensures that the light field of the beam directly output by the axial conic lens is simultaneously modulated by both the Bessel function and the Gaussian function, i.e., the output beam is a Bessel-Gaussian beam. The expression for the light field of a Bessel-Gaussian beam is:

[0068]

[0069] in, Represents the 0th order Bessel function; This represents the radial envelope width, i.e., the waist radius of the Gaussian beam.

[0070] This application provides a preferred technical solution, wherein the first non-diffractive beam and the second non-diffractive beam intersect at a predetermined angle, determined by the period of the grating to be manufactured, i.e., the target grating, and the base angle of the axial conical lens. The specific intersection angle satisfies the following conditions:

[0071]

[0072] Where θ represents half of the intersection angle; λ represents the wavelength of the non-diffractive beam, which is the wavelength of the laser source; p represents the target fringe period, which is the target grating period to be manufactured; α represents the bottom angle of the axial cone lens; and n represents the refractive index of the axial cone lens.

[0073] Example 2:

[0074] Example 2 has the same light source and beam preparation unit, beam splitting unit, first interference unit, second interference unit and interference field forming unit as Example 1; the only difference is that the first phase modulation device 6 and the second phase modulation device 10 are phase plates, namely the first phase plate and the second phase plate; the other device parameters are completely the same as those in Example 1 and will not be repeated.

[0075] The following detailed description focuses only on the unique structure and optical path of the first phase modulator 6 and the second phase modulator 10. The phase plate is a planar optical element with specific microstructures etched or machined on its surface to apply the desired phase distribution as the beam passes through. The phase plate is designed to achieve phase modulation, that is, to convert the incident Gaussian beam into a Bessel beam and suppress the side lobes of the Bessel beam. For example... Figure 3 As shown, D is the diameter of the phase plate, β is the cone angle of the Bessel beam, and the phase expression of the phase plate in this embodiment is as follows:

[0076]

[0077] The expression for the non-diffraction distance of the Bessel beam generated by the phase plate is as follows:

[0078]

[0079] in, This indicates the distance without diffraction.

[0080] The diffraction-free distance of the generated Bessel beam can be calculated and set using theoretical formulas. By appropriately selecting the combination of parameters such as the cone angle β of the Bessel beam and the phase plate size D, customizable diffraction-free distances ranging from millimeters to meters can be achieved to meet the depth-of-focus requirements of different application scenarios.

[0081] In the optical path of this embodiment, the collimated Gaussian beam is split and then incident on the first phase plate and the second phase plate respectively. The phase plate uses the microstructure on its surface to digitally encode and modulate the beam wavefront, replacing the refraction effect of the physical axonocone lens, thereby outputting a Bessel-Gaussian beam with suppressed sidelobes.

[0082] Example 3:

[0083] like Figure 4 As shown, this application provides a method for constructing a diffraction-free beam interference field for manufacturing the exposure interference field of a grating. This application uses a phase modulation device 10 as an example of an axonoconical lens; the same principle applies to a phase plate or spatial light modulator. The construction method includes the following steps:

[0084] Based on the size of the interference spot during grating fabrication, the main lobe size is determined, and the required cone angle β of the Bessel beam is preset. According to Bessel beam theory, assuming the main lobe radius and maximum non-diffraction distance meet the requirements for interference spot size and depth of focus, the cone angle β of the Bessel beam is calculated, and an initial axial-cone lens base angle α is determined. For example, if a larger interference spot and a longer depth of focus are required, a smaller α value is preferred.

[0085] This embodiment of the application achieves optical phase modulation through an axial-cone lens, which converts the incident light into a Bessel beam. Under the condition of satisfying the paraxial approximation, the light field intensity distribution at a certain distance from the axial-cone lens exhibits the form of a zero-order Bessel function, thus generating a Bessel beam. For example... Figure 5 As shown, the horizontal axis represents the direction perpendicular to the fringes in the interference plane, in millimeters; the vertical axis represents the direction parallel to the fringes in the interference plane, in millimeters; the right side of the image shows the normalized light intensity value, with larger numbers indicating brighter colors and higher light intensity at that location.

[0086] By adjusting the bottom angle α of the axial conical lens, the main lobe size and diffraction-free propagation range of the output Bessel beam can be directly set, which is equivalent to the spot size and depth of focus of the Bessel beam. Optical phase modulation is concretized as the control of the axial phase distribution of the incident beam to set the main lobe size and diffraction-free propagation range of the Bessel beam. This enables customized design of the Bessel beam for the exposure light source, allowing the interference field to more flexibly adapt to the grating manufacturing needs of different linewidths and substrate conditions.

[0087] The beam waist radius of the collimated Gaussian beam is determined based on the preset bottom angle of the axial conical lens. The technical solution of this application embodiment is to find the beam waist radius ω of the incident Gaussian beam that achieves the best sidelobe suppression effect of the output beam, based on a pre-selected α.

[0088] The technical solution of this application embodiment, based on the preset bottom angle of the axial cone lens, controls the beam waist radius of the Gaussian beam, i.e., sets the radial envelope width parameter, to apply Gaussian function envelope modulation to the radial optical field distribution of the Bessel beam, thus forming a Bessel-Gaussian beam. Through systematic parameter design, the axial cone lens directly outputs a beam conforming to the Bessel-Gaussian model. The optical field expression of the Bessel-Gaussian beam is:

[0089]

[0090] in, Represents the 0th order Bessel function; Represents the envelope term of the Gaussian function; This represents the radial envelope width, i.e., the waist radius of the Gaussian beam.

[0091] According to the optical field expression of the Bessel-Gaussian beam, by controlling the beam waist radius and the bottom angle α of the Gaussian beam incident on the axial cone lens, the Gaussian function envelope modulation is completed at the same time as the Bessel beam is generated, effectively suppressing the sidelobe energy.

[0092] That is, in order to ensure that the output of the axial-cone lens is the result of interference diffraction between the incident Gaussian beam and its conical phase modulation function, even if the output beam is enveloped... To mitigate the effect of attenuation and suppress side lobes, the required incident conditions need to be determined. This is accomplished by substituting the selected bottom angle of the axial cone lens into a diffraction calculation model that includes the incident beam parameters. Based on the optical field expression for a Bessel beam, the main lobe width of the Bessel beam is actually determined by the Bessel function. The decision is made by The specific value of the main lobe width of the Bessel beam can be obtained.

[0093]

[0094] Therefore, given a fixed incident beam wavelength, the main lobe width of the Bessel beam is only related to the bottom angle of the axial conic lens. The beam waist radius is determined by calculating the main lobe width of the beam generated by the bottom angle of the selected cone lens. This width is then used as a base to determine the beam waist radius. Minor adjustments are made during this process to minimize the intensity ratio of the side lobes to the main lobe in the theoretically simulated output light intensity distribution. At this point, the beam waist radius and the selected cone bottom angle are considered to have achieved optimal coordination.

[0095] In this embodiment, by outputting a defined pair of parameters for the bottom angle of the axial tapered lens and the beam waist radius, the collaborative design ensures that the beam directly output by the axial tapered lens is a Bessel-Gaussian beam with suppressed sidelobes.

[0096] Based on the bottom angle of the axial-cone lens, the beam waist radius, the laser wavelength, and the target grating fringe period, the intersection angle between the first and second non-diffraction beams is determined. The intersection angle satisfies the following condition:

[0097]

[0098] Where θ represents half of the intersection angle; λ represents the wavelength of the non-diffractive beam; p represents the target grating period; α represents the base angle of the axial cone lens; and n represents the refractive index of the axial cone lens.

[0099] Based on the optimal beam waist radius calculated above, adjust the lens spacing in collimating and expanding lens group 2 until the spot size and intensity distribution of the output beam on the measurement surface match the Gaussian beam characteristics corresponding to the calculated beam waist radius.

[0100] Select a first-axis cone lens and a second-axis cone lens with a preset bottom angle of α obtained from calculation.

[0101] The rotation angle of the first compensation plate 4 in the first interference unit is set to initially compensate for the optical path. The first reflecting mirror 5 guides the beam to the first axial cone lens. The first axial cone lens directly outputs a Bessel beam, i.e., the first non-diffraction beam.

[0102] Similarly, a second compensation plate 7, a third compensation plate 8, a second reflector 9, and a second axial conical lens are respectively set in the second interference unit. The second compensation plate 7 and the third compensation plate 8 rotate together to precisely match the optical path between the second optical path and the first optical path. The second reflector 9 guides the beam to the second axial conical lens. The second axial conical lens directly outputs a Bessel beam, i.e., a second non-diffraction beam.

[0103] Two Bessel beams are made to intersect at a set angle in the target area, forming a three-dimensional non-diffraction interference field.

[0104] The Bessel beam intensity distribution exhibits a series of high-energy sidelobes, which cause discontinuities in the subsequent interference fringes. The high energy of the sidelobes is fundamentally due to the infinite radial oscillation characteristic of the Bessel function. Introducing a Gaussian envelope term can suppress the rapid radial attenuation of the beam energy. Setting an appropriate Gaussian beam waist radius can significantly suppress the energy of the sidelobes far from the center while maintaining the brightness of the central main lobe. Within a certain range, a smaller Gaussian beam waist radius results in a stronger suppression effect, but the interference spot size will decrease, affecting exposure efficiency. Therefore, optimization is needed based on the requirements of the exposure process for fringe contrast and exposure efficiency. A comparison between the optimized Bessel-Gaussian beam and the original Bessel beam is shown below. Figure 6 , Figure 7 As shown, Figure 6 The overall light intensity diagram shows the original Bessel beam (red dashed line): a standard Bessel beam without suppression, with a clear side lobe sequence; and the optimized Bessel-Gaussian beam (blue solid line): after introducing a Gaussian envelope, the side lobes are compressed to below 0.05, while the main lobe width remains almost unchanged. Figure 7 The image shown is a magnified view of a portion of the sidelobe, which visually demonstrates the effect of the Gaussian envelope on the suppression of the sidelobe in this application.

[0105] The technical solution of this application embodiment does not involve adding an extra filter to the optical path, but rather achieves the modulation through co-design. The beam waist radius of the Gaussian beam incident on the axial cone lens is controlled so that it satisfies a specific relationship with the base angle of the axial cone lens, thereby ensuring that the output beam field of the axial cone lens naturally conforms to the aforementioned Bessel-Gaussian model. By optimizing the beam waist radius, sidelobe energy can be effectively suppressed, making the beam energy more concentrated on the main lobe. The optimized beam is the Bessel-Gaussian beam used for subsequent interference. Figure 5As shown, the unoptimized pure Bessel beam interference fringes are discontinuous due to sidelobes. However, after optimization using Gaussian function envelope modulation, the sidelobes are suppressed, and the resulting Bessel-Gaussian beam interference fringes are as follows: Figure 8 , Figure 9 As shown, Figure 8 In the image, the brighter the color, the higher the light intensity. The dark area corresponds to the minimum light intensity. You can directly see that the stripes are continuous and the contrast is good, presenting continuous and clear high-quality stripes. Figure 9 As can be seen, the fringe contrast, period, and sidelobes have been suppressed to below 0.05. Gaussian envelope modulation is concretized by suppressing the sidelobe energy of the Bessel beam by setting the radial envelope width. Optimization of the beam energy distribution significantly improves the beam's energy concentration, thereby ensuring that the subsequently formed interference fringes are continuous, clear, and have high contrast, meeting the basic requirements of high-precision exposure.

[0106] In this embodiment, at least two beams of light are required to achieve interference. Therefore, the initial beam from the same laser source is split into two paths by a beam splitter: a first transmitted beam and a second reflected beam, ensuring that the beams have the same center wavelength and a defined coherence length. Each path is equipped with an axonoconical lens to independently generate two Bessel-Gaussian beams. By adjusting the angles of the first reflecting mirror 5 and the second reflecting mirror 9, the propagation directions of the two beams can be set, allowing them to propagate in space at a specific relative incident angle and converge at a predetermined optical path configuration in the same spatial location, i.e., the target region, the plane where the detector 11 is located. To ensure stable interference between the first transmitted beam and the second reflected beam in the interference region, their wavefronts must have a fixed phase relationship at the point of convergence.

[0107] In this embodiment, the pitch and yaw of the first reflecting mirror 5 and the second reflecting mirror 9 are adjusted to precisely control the emission direction of the two beams of light and set the propagation direction. The angle between the emission directions of the two beams of light is the relative incident angle when the two beams of light reach the target area. The period of the interference fringes is determined by setting the relative incident angle. This ensures that the extension lines of the two beams of light after the above-mentioned direction adjustment accurately intersect in the same area within a preset spatial range, thereby forming interference at that location. This achieves the optical path configuration.

[0108] In this embodiment, to ensure stable interference between two beams in the target region, their wavefront coherence must be guaranteed. By introducing a first compensation plate 4, a second compensation plate 7, and a third compensation plate 8 into the optical path to adjust the optical path lengths of the two beams, the optical path difference at the interference point is made much smaller than the coherence length of the light source, thus ensuring a stable and definite phase difference. By adjusting the collimation, the angle of the first reflecting mirror 5, and the wavefront tilt angle of the second reflecting mirror 9, it is ensured that the two beams have flat and parallel wavefronts in the interference region. Adjusting the optical path lengths of the two beams compensates for the phase difference caused by path differences, achieving wavefront matching.

[0109] In this embodiment, the contrast and spatial stability (i.e., coherence stability) of fringes within the interference region are improved through optical path configuration and wavefront matching. This solves the problems of decreased contrast, jitter, or disappearance of interference fringes caused by optical path difference and wavefront distortion.

[0110] The technical solution of this application converts a Gaussian beam into a Bessel beam with non-diffraction characteristics through optical phase modulation. Furthermore, through parametric co-design, the beam waist and bottom angle of the axial conic lens are controlled to optimize it into a Bessel-Gaussian beam with suppressed sidelobes, which serves as the interference source. This solves the inherent problems of short depth of focus and wavefront curvature variation during propagation of Gaussian beams, and also addresses the technical problem of grating groove bending caused by nonlinear phase errors in interference fringes during scanning interference field exposure.

[0111] The effectiveness of the technical solution of this application is verified by constructing a mathematical model. The nonlinear error analysis is performed on the non-diffraction beam interference field constructed by the technical solution of the embodiment of this application and the traditional Gaussian beam interference field.

[0112] The Bessel-Gaussian beam used in this application is insensitive to lateral displacement due to its non-diffraction properties. When there is a lateral positional deviation and an axial optical path difference between the left and right beams, the resulting interference fringe phase nonlinearity error can be simplified to the following expression:

[0113]

[0114] in, This indicates the phase nonlinearity error of the interference fringes; Indicates the lateral coordinates of the grating surface; Indicates the actual interference fringe period; Represents the spatial wave vector of the incident light; This indicates the axial optical path difference.

[0115] In a traditional Gaussian beam interference field, the wavefront curvature of the Gaussian beam changes continuously during propagation, making it extremely sensitive to path errors. Its phase error model is much more complex, considering factors such as the additional phase term caused by beam propagation, the phase difference introduced by the wavefront curvature, and the phase shift caused by geometric position deviations. The interference error of a traditional Gaussian beam interference field is expressed as:

[0116]

[0117] in, This represents the interference error of a conventional Gaussian beam interference field; , , These represent the X, Y, and Z coordinates of the left-side Gaussian beam, respectively. , , These represent the X, Y, and Z coordinates of the right-path Gaussian beam, respectively. This indicates the angle of incidence of the left-path beam relative to the base normal; This indicates the angle of incidence of the right-path beam relative to the base normal; , These represent the positional deviations between the actual and ideal beam waist positions of the left and right beams, respectively; x, y, and z represent the X, Y, and Z coordinates of the base surface position, respectively; R L R R denoted by z, ...

[0118] When the positional deviation of the beams on the left and right sides is 10mm, that is When the beam size is 10 mm, the maximum value of the nonlinear error in the phase of the interference fringes caused by the non-diffraction beam interference field constructed by the technical solution of this application is 10 mm. -9 The error is on the order of nm and can be approximated as 0. The nonlinear error of the interference fringes in a traditional Gaussian beam interference field is 0.1986 nm. Compared to the results of Gaussian beam interference fringes, the nonlinear error of the interference fringes in this application is significantly reduced, such as... Figure 10 , Figure 11 As shown in the figure, the contour lines represent the numerical distribution of nonlinear errors, and the different colored lines represent different magnitudes of nonlinear errors. The red dashed line represents the spot size formed by a Gaussian beam with a beam waist of 0.8 mm at the substrate position. It can be clearly seen that, under the same 10 mm deviation, the error formed by the interference field of a conventional Gaussian beam exhibits a gradient distribution throughout the entire spot size. Within the interference spot size, the maximum nonlinear error reaches 0.1986 nm, substantially affecting the periodic uniformity, such as... Figure 10 As shown; and the interference field of the technical solution of this application, as Figure 11 As shown, the phase error is nearly uniform and zero across the entire spot area, and the fringe period is strictly constant.

[0119] This application proposes a system and method for constructing a diffraction-free beam interference field. Based on the principles of grating diffraction and beam wavefront modulation, it utilizes the non-diffraction characteristics of Bessel beams to establish a Bessel beam interference model and construct a three-dimensional non-diffraction interference field. This not only reduces the nonlinear error of interference fringes caused by the light source, but also enhances the fault tolerance of component position deviations in the two-sided interference optical paths when applied to the fabrication of gratings in a scanning interference field exposure system. This further improves the nonlinear error suppression capability of the system and promotes the development of high-precision gratings.

[0120] This application provides a system and method for constructing a diffraction-free beam interference field for grating fabrication. First, the required cone angle β of the Bessel beam is determined based on the linewidth and depth-of-focus requirements of the target grating, and then the corresponding base angle α of the axial conical lens is calculated. The linewidth determines the main lobe size of the required beam, and the depth-of-focus requirement relates to the diffraction-free propagation length of the beam. The base angle of the axial conical lens is a fundamental geometric parameter determining these diffraction-free characteristics of the output beam. Subsequently, for the determined base angle value of the axial conical lens, the optimal beam waist radius of the collimated Gaussian beam working in conjunction with it is determined through theoretical modeling and numerical optimization. This optimization aims to ensure that the light field distribution of the output beam naturally conforms to the Bessel-Gaussian function model, while achieving optimal suppression of sidelobe energy. Next, based on the determined base angle of the axial conical lens, beam waist radius, laser wavelength, and target grating period, the precise intersection angle between the two beams is calculated.

[0121] Based on the aforementioned collaboratively determined set of parameters for the axial conic lens base angle, beam waist radius, and intersection angle, the optical system is configured. The configuration includes adjusting the collimating and beam-expanding lens group 2 to generate a collimated Gaussian beam with a specific beam waist radius, and selecting an axial conic lens with a corresponding base angle. After splitting the collimated beam, the two beams pass through compensation plates in their respective optical paths to achieve optical path matching, are guided by a reflector to determine their propagation direction, and finally pass through the axial conic lens with the corresponding base angle. During this process, based on the pre-optimized combination of the axial conic lens base angle and beam waist radius, the axial conic lens converts the Gaussian beam into a Bessel beam, and its output beam is a Bessel-Gaussian beam with suppressed sidelobes. The setting of the beam waist radius directly controls the radial envelope width of the beam, thereby determining the level of sidelobe suppression.

[0122] Finally, by adjusting the two reflectors according to the calculated intersection angle, the two optimized Bessel-Gaussian beams intersect at a precisely calculated angle on the target area, i.e., the grating substrate, thus constructing a three-dimensional diffraction-free interference field with long depth of focus and low nonlinear error characteristics. This interference field can be directly used in high-precision scanning interferometry exposure processes to manufacture gratings.

[0123] Finally, it should be noted that the various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems or apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple, and relevant parts can be referred to the method section.

[0124] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A system for constructing an interference field of non-diffracting beams, characterized in that, include: The light source and beam preparation unit is used to generate a collimated Gaussian beam; A beam splitting unit is used to split the Gaussian beam into a first beam and a second beam. The first interference unit includes a first compensation plate, a first reflector and a first phase modulation device, used to sequentially perform optical path compensation, propagation direction adjustment and optical phase modulation on the first beam, and convert the first beam into a first non-diffraction beam. The second interference unit includes a second compensation plate, a third compensation plate, a second reflector, and a second phase modulation device, which are used to sequentially perform optical path compensation, propagation direction adjustment, and optical phase modulation on the second beam, converting the second beam into a second non-diffraction beam. The first interference unit and the second interference unit respectively have Bessel beam sidelobe suppression capability; the first non-diffractive beam and the second non-diffractive beam are respectively long focal depth non-diffractive beams with no sidelobes or suppressed sidelobes; The first compensation plate is used to adjust the optical path of the first optical path; the second compensation plate and the third compensation plate are used to adjust the optical path of the second optical path; the first phase modulation device and the second phase modulation device are respectively used to convert the first beam and the second beam into Bessel beams with suppressed side lobes; The interference field forming unit sets an angle between the first and second reflectors, causing the first non-diffraction beam and the second non-diffraction beam to intersect at a set angle in the target area to form a three-dimensional non-diffraction interference field.

2. The construction system of claim 1, wherein, The light source and beam preparation unit includes a laser and a collimating and expanding lens group, used to provide a collimated Gaussian beam with a preset beam waist radius.

3. The construction system of claim 2, wherein, By adjusting the waist radius of the collimated Gaussian beam and the phase distribution generated by the first phase modulator and the second phase modulator, the first non-diffraction beam and the second non-diffraction beam are output.

4. The construction system of claim 3, wherein, By adjusting the waist radius of the collimated Gaussian beam, the phase distribution generated by the first phase modulation device and the second phase modulation device is set, thereby suppressing the sidelobe energy of the Bessel beam.

5. The construction system of claim 1, wherein, The first compensation plate, the second compensation plate, and the third compensation plate are parallel plane optical glass. By rotating the angle, the effective thickness in the optical path is changed, thereby achieving adjustment and matching of the optical path.

6. The construction system according to claim 1, characterized in that, The first reflector is used to set the propagation direction of the first non-diffraction beam; The second reflector is used to set the propagation direction of the second non-diffraction beam; By adjusting the pitch and yaw angles of the first and second reflectors, the first non-diffractive beam and the second non-diffractive beam are made to converge in the target area at a set intersection angle.

7. The construction system of claim 6, wherein, The intersection angle satisfies the following condition: Where θ represents half of the intersection angle; λ represents the wavelength of the non-diffractive beam; p represents the target fringe period; and β represents the cone angle of the Bessel beam.

8. The construction system according to claim 1, characterized in that, The first phase modulation device and the second phase modulation device are axial tapered lenses.

9. The construction system according to claim 1, characterized in that, The first phase modulation device and the second phase modulation device are phase plates or spatial light modulators.

10. A method for constructing a diffraction-free beam interference field based on the construction system according to any one of claims 1-9, characterized in that, The construction method includes: Based on the target grating period and the required depth of focus for interference field without diffraction, the phase distribution required for the device used for phase modulation to generate the Bessel beam is preset. The beam waist radius of the collimated Gaussian beam is determined based on the preset phase distribution. The intersection angle of the two beams is determined based on the phase distribution of the phase modulation device, the waist radius of the collimated Gaussian beam, the laser wavelength, and the period of the target grating. Based on the determined beam waist radius, a collimated Gaussian beam is generated; The collimated Gaussian beam is split into a first beam and a second beam. The first beam is passed sequentially through the first compensation plate, the first reflector and the first phase modulation device to generate a first diffraction-free beam. The second beam is passed sequentially through the second compensation plate, the third compensation plate, the second reflector, and the second phase modulation device to generate a second non-diffraction beam. Based on the determined intersection angle, the first and second reflectors are adjusted so that the first non-diffraction beam and the second non-diffraction beam intersect and interfere in the target area, forming a three-dimensional non-diffraction interference field.

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