Method for modifying intensity profile of bessel beam by intensity apodization algorithm

Abstract

A method for deforming the machining axis intensity of a Bessel beam through an intensity apodization algorithm is disclosed. The method for deforming the machining axis intensity of a Bessel beam according to the present invention uses an intensity apodization algorithm to deform the intensity in the z-axis direction of the Bessel beam so that a flat-top intensity region exists. Subsequently, using the intensity apodization algorithm, the intermediate region of the Bessel beam, in which the intensity profile in the travel direction (z-axis) has been deformed, is formed into a flat-top shape.

Description

Technology Field

[0001] The present invention relates to a method for deforming the machining axis intensity of a Bessel beam.

[0002] More specifically, the present invention relates to a method for deforming the machining axis intensity of a Bessel beam through an intensity apodization algorithm. Background Technology

[0004] Figure 1 schematically shows the processing axis intensity distribution by a laser with a Gaussian distribution and an axicon lens.

[0005] To cut or drill tens to hundreds of micrometers into transparent or brittle materials, a Bessel beam using an ultrashort infrared laser is typically irradiated onto the target material.

[0006] A Bessel beam made of an axicon lens optical system can process transparent / brittle materials with a size of several micrometers to tens of micrometers and a long depth.

[0007] However, generally, a Bessel beam produced through an axicon lens with a laser having a Gaussian beam profile as in (a) of Fig. 1 has an intensity distribution similar to a Gaussian as in Equation 1 below in the direction of the processing axis, which becomes the form shown in (b) of Fig. 1.

[0008] [Equation 1]

[0009]

[0010] Since the intensity distribution of the deep machining axis is in the form of a Gaussian as shown in (b) of Fig. 1, machining is performed only at an intensity above a certain threshold, and the machining energy varies depending on the position of the machining axis.

[0011] To address these issues, conventional techniques have primarily utilized methods such as forming a laser beam with a long depth of focus (DOF) along the processing axis or employing lenses of specific curvature to modify the intensity of the processing axis. However, in these methods, the realization of processing axis intensity is significantly influenced by the degree of lens processing and the shape and quality of the incident laser beam. Furthermore, limitations on lens curvature processing (such as curvature magnitude and aspherical lens coefficients) make it difficult to achieve the desired processing axis intensity. Additionally, while Bessel beams are commonly used for laser beams with long processing lengths along the processing axis, the typical processing axis intensity distribution of a Bessel beam takes on a Gaussian shape, resulting in varying machinability depending on the processing axis.

[0012] Figure 2 schematically shows an example of converting a Gaussian distribution of the processing axis into a flat-top shape.

[0013] To solve this problem, a method was proposed to convert the Gaussian distribution of the processing axis into a flat-top shape, as shown in the example in Fig. 2.

[0014] In this method, by changing the axicon phase in Fig. 2, the Gaussian intensity distribution (GB) in the direction of the processing axis was converted into a flat-top intensity distribution (MGB).

[0015] However, changing the phase of a Bessel beam with a standard Gaussian distribution alters the angle of the beam refracted from the axicon, resulting in a disadvantage where the size of the Bessel beam at the machining axis changes. Prior art literature

[0017] Published Patent Application No. 10-2017-0019855 (Feb. 22, 2017) US Patent Application US 11,548,093 B2 (Issued Jan. 10, 2023) The problem to be solved

[0018] The problem that the present invention aims to solve is to provide a method for making the intensity of a machining axis uniform while solving the problems of the prior art.

[0019] In particular, the problem that the present invention aims to solve is to provide a method for deforming the machining axis intensity of a Bessel beam, which can transform the machining axis intensity distribution of the Bessel beam into a flat-top shape or a desired shape through an Intensity Apodization Algorithm. means of solving the problem

[0021] To solve the above problem, the method for deforming the processing axis intensity of a Bessel beam according to an embodiment of the present invention deforms the intensity profile of the Bessel beam in the direction of travel (z-axis direction) using an intensity apodization algorithm defined by the following equations (1) to (5).

[0023] Equation (1)

[0024] Equation (2)

[0025] Equation (3)

[0026] Equation (4)

[0027] Equation (5)

[0028] In Equations 1 to 5,

[0029] ρ: Position of the vertical axis of the Bessel beam's direction of travel

[0030] z: Position of the Bessel beam's direction of travel

[0031] I(ρ): Intensity distribution of the incident beam

[0032] I0: Incident beam intensity reference

[0033] w0: Size of the incident laser beam

[0034] P(z): Intensity distribution in the direction of the machining axis to be determined

[0035] P0: Reference to intensity strength in the direction of the machining axis to be calculated

[0036] z(ρ): The position in the direction of the processing axis to be determined, corresponding to the incident beam position ρ by the intensity apodization algorithm

[0037] z C : Super Gaussian center when the intensity of the desired machining axis direction is set to a Super Gaussian form

[0038] z0: Super Gaussian magnitude when the intensity in the desired machining axis direction is set to a Super Gaussian form

[0039] α(ρ): The angle at which the incident beam is refracted at position ρ according to the relationship between ρ and z(ρ).

[0040] Φ(ρ): The amount of phase change or curvature in the direction perpendicular to the calculated incident beam refraction angle α(ρ).

[0041] k o: Laser Wave Number

[0042] U(ρ, z=0): Phase and intensity of the electric field of the incident beam. The intensity of the incident laser beam corresponds to the square of the absolute value of the incident beam's electric field.

[0043] Subsequently, a step is performed in which the middle portion of the Bessel beam, in which the intensity profile in the direction of travel (z-axis direction) has been modified using the intensity apodization algorithm, is transformed into a flat-top intensity region.

[0044] The front or rear region of the above Bessel beam can be made identical to the intensity distribution determined by Equation 3 or Equation (6) below.

[0045] A method for deforming the processing axis intensity of a Bessel beam, wherein the front region or rear region of the Bessel beam is identical to the intensity distribution determined by the following equation (3) or equation (6).

[0046] Equation (3)

[0048] Equation (6)

[0049] I(z): Intensity distribution of the incident beam in the z-direction

[0050] I0: Incident beam intensity reference

[0051] z: Position of the Bessel beam's direction of travel

[0052] w0: Size of the incident laser beam

[0053] The step of forming the intermediate region of the Bessel beam, in which the intensity profile in the propagation direction (z-axis direction) is deformed, into a flat-top shape using the above intensity apodization algorithm can be performed through beam propagation simulation.

[0054] The above Bessel beam may be derived from an axicon lens, an axicon phase lens, or a DOE lens.

[0055] A DOE or SLM to which the above-described method is applied may be placed at the rear end of the axicon lens, or a DOE or SLM to which the above-described method is applied may be placed at the rear end of the axicon phase lens or DOE lens, or the axicon lens phase and the phase to which the above-described method is applied may be combined.

[0056] Laser processing of a workpiece can be performed using a Bessel beam having a modified processing axis intensity according to the method described above.

[0058] A Bessel beam according to an embodiment of the present invention for solving the above problem has a processing axis intensity in which the front part exhibits a Gaussian distribution, the middle part exhibits a flat-top shape, and the rear part exhibits a super-Gaussian distribution, or has a processing axis intensity in which the front part exhibits a Gaussian distribution, the middle part exhibits a flat-top shape, and the rear part exhibits a Gaussian distribution.

[0059] The above-mentioned Vessel beam may have a front portion of 5 to 30%, a flat-top shaped middle portion of 40 to 90%, and a rear portion of 5 to 30% in the direction of travel of the Vessel beam.

[0061] The above Gaussian distribution may be a Gaussian distribution by an ideal Bessel beam.

[0062] The processing axis intensity representing the above Gaussian distribution may be due to an axicon lens. The processing axis intensity representing the above flat-top shape may be due to an apodization algorithm and beam propagation simulation. The processing axis intensity representing the above super-Gaussian distribution may be due to an apodization algorithm. Effects of the invention

[0064] According to the present invention, by applying an intensity apodization algorithm to the intensity of the machining axis of a Bessel beam, the intensity distribution in the direction of the machining axis of the Bessel beam can be transformed into a desired form.

[0065] In particular, according to the present invention, by applying an intensity apodization algorithm to the machining axis intensity of a Bessel beam and applying additional beam propagation simulation to form a flat-top region, it is possible to transform the intensity distribution in the machining axis direction of a Bessel beam into a form that includes a flat-top intensity region.

[0066] The effects of the present invention are not limited to those mentioned above, and other unmentioned effects will be clearly understood by those skilled in the art from the detailed description below. Brief explanation of the drawing

[0068] Figure 1 schematically shows the processing axis intensity distribution by a laser with a Gaussian distribution and an axicon lens. Figure 2 schematically shows an example of converting a Gaussian distribution of the processing axis into a flat-top shape. Figure 3 schematically shows the intensity profile of a laser beam passing through an axicon lens. Figure 4 shows (a) an ideal axicon and a super-gaussian z-axis intensity profile, and (b) the phase obtained by the intensity apodization algorithm using the ideal axicon and the super-gaussian z-axis intensity profile. Figure 5 shows the intensity distribution in the z-axis direction of the modified axicon phase using the intensity apodization algorithm according to the present invention. Figure 6a shows an example of removing noise in the flat-top intensity region. Figure 6b shows another example of removing noise in the flat-top intensity region. Figure 7 is a reference diagram for explaining beam propagation simulation. FIG. 8 schematically illustrates examples in which the processing axis intensity of a Bessel beam according to the present invention is deformed. Specific details for implementing the invention

[0069] The advantages and features of the present invention and the methods for achieving them will become clear by referring to the embodiments described below in detail together with the accompanying drawings. However, the present invention is not limited to the embodiments disclosed below but may be implemented in various different forms. These embodiments are provided merely to ensure that the disclosure of the present invention is complete and to fully inform those skilled in the art of the scope of the invention, and the present invention is defined only by the scope of the claims. Throughout the specification, the same reference numerals refer to the same components. In the drawings, the sizes and relative sizes of layers and regions may be exaggerated for clarity of description.

[0070] When an element or layer is referred to as another element or "above" or "on top," it includes not only cases where it is directly above another element or layer, but also cases where another layer or element is interposed in between. On the other hand, when an element is referred to as "directly above" or "immediately above," it indicates that no other element or layer is interposed in between. Furthermore, where it is stated that a component is "connected," "combined," or "connected" to another component, it should be understood that said components may be directly connected or connected to each other, but that another component may be "interposed" between each component, or that each component may be "connected," "combined," or "connected" through another component.

[0071] Spatially relative terms such as "below," "lower," "above," and "upper" may be used to facilitate the description of the relationship between one element or component and another, as illustrated in the drawings. Spatially relative terms should be understood as encompassing different orientations of the element during use or operation, in addition to the orientations illustrated in the drawings. For example, if an element illustrated in the drawings is flipped, an element described as being "below" another element may be placed "above" that other element. Therefore, the exemplary term "below" may encompass both the lower and upper directions.

[0072] The terms used herein are for describing the embodiments and are therefore not intended to limit the invention. In this specification, the singular form includes the plural form unless specifically stated otherwise in the text. As used in this specification, "comprising" and / or "comprising" does not exclude the presence or addition of one or more other components, steps, actions, and / or elements to the mentioned components, steps, actions, and / or elements. Throughout the specification, the same reference numerals refer to the same components.

[0073] The method for deforming the machining axis intensity of a Bessel beam through an intensity apodization algorithm according to a preferred embodiment of the present invention will be described in detail below with reference to the attached drawings.

[0075] Currently proposed intensity profiles with long machining lengths along the machining axis primarily utilize Bessel beams; however, since a Gaussian profile appears along the machining axis, machinability varies depending on the axis. Accordingly, the present invention provides a method for transforming the machining axis intensity of a Bessel beam into a desired shape. In particular, the present invention provides a method for transforming the existing machining axis intensity of a Bessel beam into a desired shape through an Intensity Apodization Algorithm.

[0076] A standard laser beam is incident on a Bessel beam, which is typically used to increase the processing length of a focused laser processing beam. Standard laser beams have a Gaussian intensity distribution, and due to the high coherence of lasers, this intensity distribution is difficult to transform into a different shape. Therefore, when a Bessel beam is applied to a laser with a Gaussian intensity distribution, the intensity distribution along the processing axis of the laser beam exhibits a Gaussian shape.

[0077] In the present invention, when a laser having a general Gaussian distribution is incident, an intensity apodization algorithm is used to create an intensity distribution of a desired shape in the direction of the processing axis of the Bessel beam that is not Gaussian.

[0078] Intensity apodization algorithms are generally used as a technique to modify the beam intensity profile along the same axis (vertical to the direction of beam propagation) after the beam has traveled a certain section, but the present invention proposes a technique to modify the intensity profile along the direction of beam propagation.

[0080] Figure 3 schematically shows the intensity profile of a laser beam passing through an axicon lens.

[0081] As shown in Fig. 3, when the direction of beam propagation is denoted as the z-axis, the intensity profile of the ρ-axis perpendicular to it exhibits a Gaussian distribution in a general laser. Due to this Gaussian distribution, the z-axis (processing axis) intensity profile of the Bessel beam in an optical system using an axicon lens or axicon phase becomes similar to the Gaussian shape described above.

[0083] To transform this z-axis Gaussian distribution into a flat-top or super-Gaussian distribution, the axicon phase can be obtained by utilizing the intensity apodization algorithm as shown in the equation below.

[0084] Equation (3) represents the intensity distribution of the incident beam and the processing axis to be determined, and each intensity is normalized by Equation (2). By Equation (1), the position z(ρ) in the intensity distribution of the processing axis to be determined at position ρ of the incident beam can be obtained. The angle of refraction of the incident beam is calculated by Equation (4) using the obtained z(ρ). The calculated angle of refraction allows for the calculation of the relative phase difference or curvature in the direction perpendicular to the angle of refraction at position ρ. Using the calculated phase difference or curvature, it can be verified through beam propagation simulation whether the electric field U(ρ, z=0) of the intensity and phase of the incident beam is identical to the intensity distribution of the processing axis to be determined.

[0085] Equation (1)

[0086] Equation (2)

[0087] Equation (3)

[0088] Equation (4)

[0089] Equation (5)

[0090] In Equations 1 to 5,

[0091] ρ: Position of the vertical axis of the Bessel beam's direction of travel

[0092] z: Position of the Bessel beam's direction of travel

[0093] I(ρ): Intensity distribution of the incident beam

[0094] I0: Incident beam intensity reference

[0095] w0: Size of the incident laser beam

[0096] P(z): Intensity distribution in the direction of the machining axis to be determined

[0097] P0: Reference to intensity strength in the direction of the machining axis to be calculated

[0098] z(ρ): The position in the direction of the processing axis to be determined, corresponding to the incident beam position ρ by the intensity apodization algorithm

[0099] z C : Super Gaussian center when the intensity of the desired machining axis direction is set to a Super Gaussian form

[0100] z0: Super Gaussian magnitude when the intensity in the desired machining axis direction is set to a Super Gaussian form

[0101] α(ρ): The angle at which the incident beam is refracted at position ρ according to the relationship between ρ and z(ρ).

[0102] Φ(ρ): The amount of phase change or curvature in the direction perpendicular to the calculated incident beam refraction angle α(ρ).

[0103] k o: Laser Wave Number

[0104] U(ρ, z=0): Phase and intensity of the electric field of the incident beam. The intensity of the incident laser beam corresponds to the square of the absolute value of the incident beam's electric field.

[0106] Figure 4 shows (a) an ideal axicon and a super-Gaussian z-axis intensity profile, and (b) the phase obtained from the ideal axicon and a super-Gaussian z-axis intensity profile using an intensity apodization algorithm.

[0107] In order to implement a super-Gaussian profile in the z-axis direction, the angle α(ρ) of the incident beam is obtained using the intensity apodization algorithm defined by the aforementioned equations (1) to (5), and the deformed phase can be obtained through this, and when compared with the ideal axicon phase, it appears as shown in FIG. 4 (a).

[0108] The z-axis intensity of the deformed Bessel beam includes a platform region by using the intensity apodization algorithm according to the present invention.

[0109] Figure 5 shows the intensity distribution in the z-axis direction of the modified axicon phase using the intensity apodization algorithm according to the present invention.

[0110] Specifically, FIG. 5(a) shows a 3D profile of a beam propagation simulation of a deformed axicon phase, and FIG. 5(b) shows a z-axis-centered intensity profile of a beam propagation simulation of a deformed axicon phase.

[0111] Referring to Fig. 5, the intensity distribution in the z-axis direction of the deformed axicon phase can be confirmed through electromagnetic beam propagation simulation of the deformed result of Fig. 4.

[0112] As can be seen in Figure 5, the z-axis intensity profile formed by the modified axicon phase has the same shape as the initially designed super-Gaussian, but it can be seen that noise in the form of oscillation occurs in the flat-top intensity region.

[0113] In other words, in the case of a Bessel beam where the intensity profile in the direction of travel (z-axis direction) is modified using an apodization algorithm, severe oscillation prevents the flat-top intensity region from being properly formed in the middle.

[0114] It is more desirable to minimize such noise through an additional noise removal process.

[0115] Figures 6a and 6b show examples of removing noise in the flat-top intensity region. Specifically, they are simulation results showing no oscillation in the flat-top intensity region due to the modified axicon phase.

[0116] Figure 6a is a profile in which the beginning and end parts of the z-axis intensity profile by an ideal axicon are identical, and only the middle region is made into a flat-top shape.

[0117] Figure 6b is a profile in which the initial part is identical to the z-axis intensity profile by an ideal axicon, but the middle part is a flat-top shape and the rear part is a super-Gaussian shape.

[0118] To create such a profile, the phase is generated using the intensity apodization algorithm above, and then a flat-top z-axis intensity profile without oscillation in the flat-top intensity region can be obtained through beam propagation simulation.

[0119] Figure 7 is a reference diagram for explaining beam propagation simulation.

[0120] Beam propagation simulations generally interpret the phase and intensity of an incident beam as the diffraction of optical electromagnetic waves. As shown in Fig. 7, when an incident beam propagates, it is diffracted according to Fraunhofer's electromagnetic equations, causing the phase and intensity of the beam to change. Mathematically, Fraunhofer's electromagnetic equations are simply summarized as a 2D Fourier transform equation as shown in Equation 7 below, and actual beam propagation simulations are calculated using a computer's mathematical 2D FFT (Fast Fourier Transformation).

[0121] (Equation 7)

[0122] Through this beam propagation simulation, the z-axis intensity profile according to phase change can be calculated, and it is possible to verify a flat-top z-axis intensity profile without oscillation in the flat-top intensity region according to phase change.

[0123] A Bessel beam according to an embodiment of the present invention may have a processing axis intensity in which the front part exhibits a Gaussian distribution, the middle part exhibits a flat top shape, and the rear part exhibits a Gaussian distribution, as shown in the example illustrated in FIG. 6a.

[0124] In addition, the Bessel beam according to an embodiment of the present invention may have a processing axis intensity such that the front part exhibits a Gaussian distribution, the middle part exhibits a flat top shape, and the rear part exhibits a super Gaussian distribution, as shown in the example illustrated in FIG. 6b.

[0125] The Gaussian distribution can be a Gaussian distribution by an ideal Bessel beam.

[0126] Meanwhile, the front or rear region of the Bessel beam can be made identical to the intensity distribution determined by the following equation (3) or equation (6).

[0127] Equation (3)

[0128] (Equation 6)

[0129] I(z): Intensity distribution of the incident beam in the z-direction

[0130] I0: Incident beam intensity reference

[0131] z: Position of the Bessel beam's direction of travel

[0132] w0: Size of the incident laser beam

[0134] In the examples illustrated in FIGS. 6a and 6b, the Bessel beam may have a front portion of 5 to 30%, a flat-top shaped middle portion of 40 to 90%, and a rear portion of 5 to 30% in the Bessel beam direction of travel. This allows for securing a desired or sufficient flat-top shaped middle portion in the Bessel beam direction of travel.

[0136] The processing axis intensity exhibiting a Gaussian distribution may be, for example, due to the intensity distribution of the axicon lens according to FIG. 1. The processing axis intensity exhibiting a flat-top shape may be due to an apodization algorithm and beam propagation simulation. The processing axis intensity exhibiting a super-Gaussian distribution may be due to an apodization algorithm.

[0137] FIG. 8 schematically illustrates examples in which the processing axis intensity of a Bessel beam according to the present invention is deformed.

[0138] The Bessel beam may be derived from an axicon lens, an axicon phase lens, or a DOE lens. In the present invention, a Diffractive Optical Element (DOE) or Spatial Light Modulator (SLM) to which the intensity apodization algorithm according to the present invention described above is applied may be additionally arranged.

[0139] For example, as shown in FIG. 8(a), the intensity of the processing axis of the Bessel beam can be modified by placing a DOE or SLM (620) with an intensity apodization algorithm applied at the rear end of the axicon lens (610). Additionally, as shown in FIG. 8(b), the intensity of the processing axis of the Bessel beam can be modified by placing a DOE or SLM (620) with an intensity apodization algorithm applied at the rear end of the axicon phase lens or DOE lens (630). Furthermore, as shown in FIG. 8(c), a combination (640) of the axicon lens phase and the phase with an intensity apodization algorithm applied can be used.

[0141] Although embodiments of the present invention have been described above with reference to the attached drawings, the present invention is not limited to the above embodiments and can be manufactured in various different forms, and those skilled in the art will understand that the present invention can be implemented in other specific forms without changing the technical concept or essential features of the present invention. Therefore, the embodiments described above should be understood as illustrative in all respects and not restrictive.

Claims

Claim 1 A step of modifying the intensity profile of the Bessel beam's direction of travel (z-axis) using an intensity apodization algorithm defined by the following equations (1) to (5); and Equation (1) Equation (2) Equation (3) Equation (4) Equation (5). In Equations 1 to 5, ρ: position in the direction of the vertical axis of the Bessel beam's propagation direction; z: position in the direction of the Bessel beam's propagation direction; I(ρ): intensity distribution of the incident beam; I0: reference to the intensity of the incident beam; w0: magnitude of the incident laser beam; P(z): intensity distribution in the direction of the processing axis to be determined; P0: reference to the intensity of the processing axis to be determined; z(ρ): position in the direction of the processing axis to be determined corresponding to the incident beam position ρ by the intensity apodization algorithm. C : Super-Gaussian center z0 when the intensity in the direction of the machining axis to be calculated is set in a Super-Gaussian form : Super-Gaussian magnitude α(ρ) when the intensity in the direction of the machining axis to be calculated is set in a Super-Gaussian form : Angle at which the incident beam is refracted at position ρ according to the relationship between ρ and z(ρ) : Phase change amount or curvature k in the direction perpendicular to the calculated incident beam refracting angle α(ρ) o: Laser wave number U(ρ, z=0): phase and intensity of the electric field of the incident beam. The intensity of the laser beam of the incident beam corresponds to the square of the absolute value of the electric field of the incident beam; a method for deforming the processing axis intensity of a Bessel beam, comprising the step of forming the intermediate region of the Bessel beam, in which the intensity profile in the propagation direction (z-axis) is deformed, into a flat-top shape using the intensity apodization algorithm. Claim 2 A method for deforming the processing axis intensity of a Bessel beam, wherein, in claim 1, the front region or rear region of the Bessel beam is identical to the intensity distribution determined by the following equation (3) or equation (6). Equation (3) Equation (6) I(z): Intensity distribution in the z-direction of the incident beam I0: Intensity of the incident beam Reference z: Direction of travel of the Bessel beam Position w0: Magnitude of the incident laser beam Claim 3 In claim 1, the step of forming the intermediate region of the Bessel beam, in which the intensity profile of the direction of travel (z-axis) is deformed into a flat-top shape using the intensity apodization algorithm is performed through beam travel simulation, a method for deforming the processing axis intensity of a Bessel beam. Claim 4 A method for deforming the processing axis intensity of a Bessel beam, wherein, in claim 1, the Bessel beam is derived from an axicon lens, an axicon phase lens, or a DOE lens. Claim 5 A method for deforming the processing axis intensity of a Bessel beam, wherein a DOE or SLM is disposed at the rear end of an axicon lens to which the method according to any one of claims 1 to 4 is applied, or a DOE or SLM is disposed at the rear end of an axicon phase lens or a DOE lens to which the method according to any one of claims 1 to 4 is applied, or an axicon lens phase and a phase to which the method according to any one of claims 1 to 4 is applied are combined. Claim 6 A laser processing method in which laser processing is performed on a workpiece using a Bessel beam having a processing axis intensity modified by any one of claims 1 to 4. Claim 7 A Bessel beam having a processing axis intensity in which the front part exhibits a Gaussian distribution, the middle part exhibits a flat-top shape, and the rear part exhibits a super-Gaussian distribution, or the front part exhibits a Gaussian distribution, the middle part exhibits a flat-top shape, and the rear part exhibits a processing axis intensity in which the rear part exhibits a Gaussian distribution. Claim 8 In claim 7, the above-mentioned Vessel beam is a Vessel beam having, in the direction of travel of the Vessel beam, a front portion of 5 to 30%, a flat-top shaped middle portion of 40 to 90%, and a rear portion of 5 to 30%. Claim 9 In claim 7, the processing axis intensity representing the Gaussian distribution is due to an axicon lens, the processing axis intensity representing the flat-top shape is due to an apodization algorithm and beam propagation simulation, and the processing axis intensity representing the super-Gaussian distribution is due to an apodization algorithm, a Bessel beam.

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