Design method for diffractive elements and manufacturing method for diffractive elements

Abstract

This method for designing a diffractive element, for using a computer to design a diffractive element (10) that modulates the phase of incident light, comprises: a step for calculating an electric field distribution of emitted light on an emission surface of a diffractive element with respect to incident light, the incident light being a Gaussian beam; a step for calculating, as an electric field distribution of a beam approximated by a Bessel-Gaussian beam, an electric field distribution that is obtained by multiplying a Gaussian window by the electric field distribution of the emitted light from the emission surface in a plane that is parallel to the emission surface and positioned at a prescribed distance from the emission surface; a step for calculating a first electric field distribution on the basis of the Kirchhoff diffraction integral theorem, as the electric field distribution on the emission surface of the diffractive element with respect to the electric field distribution of emitted light in the plane; and a step for determining the depth of unevenness in a surface of the diffractive element on the basis of the electric field distribution on the emission surface of the diffractive element.　The present invention can thereby provide a method for designing a diffractive element in which the diameter or power of emitted light can be maintained in a prescribed length.

Description

Technical Field

[0001] The present invention relates to a method for designing a diffractive element used in laser processing, rust removal, etc., and a method for manufacturing the same.

Background Art

[0002] High-power laser devices are widely used in a wide range, such as laser processing devices for cutting, welding, printing, etc. of metals and resins, and rust removal laser devices for rust removal of metals. In this high-power laser device, miniaturization and weight reduction of a part that performs scanning of emitted light, so-called a head part, have been an issue. Therefore, attempts have been made to use a diffractive optical element (Diffractive Optical Element, DOE, hereinafter referred to as "diffractive element" or "DOE") in the head part of a laser processing device.

[0003] In particular, a kinoform is a diffractive element that only modulates the optical phase and does not change the optical intensity. Here, a description will be given of a diffractive element having an uneven structure on the surface of a substrate.

[0004] FIG. 7 shows a schematic diagram of an optical system when imaging is performed using a conventional diffractive element 30. Light incident on the diffractive element 30 (arrow 1 in the figure indicates the incident direction) exits from the exit surface P0 of the diffractive element 30, and the exit light of the diffractive element 30 (arrow 2 in the figure indicates the exit direction) is focused (imaged) on the imaging surface P1.

[0005] Here, it is assumed that P0 and P1 are parallel. Also, the x-axis, y-axis, and z-axis in the figure are axes of a Cartesian coordinate system, and the coordinate origin is on P0. The z-axis is the optical axis and generally coincides with the direction in which the light emitted from the DOE 30 travels. The x-axis and y-axis are orthogonal to the z-axis, and the xy plane is parallel to the P0 plane and the P1 plane. That is, the z-axis is orthogonal to the P0 plane and the P1 plane. u0 and u1 in the figure represent the electric field distributions on P0 and P1, respectively.

[0006] If the z - coordinate on P0 is z0 = 0 and the z - coordinate on P1 is z1, then from the equation of Kirchhoff's diffraction integral, the relationship between u0 and u1 is expressed by Equation (1) (for example, Non - Patent Document 1).

[0007]

Number

[0008] Here, (x0, y0, z0) and (x1, y1, z1) are the coordinates of points on P0 and P1 respectively, j is the imaginary unit, and λ is the wavelength of light. Also, g(·) is the propagation function of light emitted from a point and is expressed by Equations (2) to (4).

[0009]

Number

[0010]

Number

[0011]

Number

[0012] Here, j is the imaginary unit and k is the wave number of light. Here, (1 + cosθ) / 2 is the inclination factor, which shows the emission - angle dependence of the electric - field strength from the DOE emission surface to each point in the electric - field strength on individual points on the imaging plane.

[0013] Since the right - hand side of Equation (I) is the convolution integral of u0 and g, if both sides of Equation (1) are Fourier - transformed, it is expressed by Equation (5).

[0014]

Number

[0015] However, U1, U0, and G are the Fourier transforms of u1, u0, and g, respectively, and u and v represent the spatial frequencies in the x and y directions, respectively.

[0016] From equation (5), U0 is expressed by equation (6).

[0017]

number

[0018] By performing an inverse Fourier transform on both sides of equation (6), we can derive u0 as shown in equation (7).

[0019]

number

[0020] However, F[·] and F -1 [·] represents the Fourier transform and the inverse Fourier transform, respectively.

[0021] In this way, by specifying the electric field distribution u1 on the imaging plane P1 and the z-axis coordinate value z1 of the imaging plane P1, the electric field distribution u0 on the DOE emission plane P0 can be calculated.

[0022] Next, we will explain a method for designing the surface irregularities to be formed on the DOE30 using the electric field distribution u0 on the DOE emission surface P0.

[0023] Here, DOE30 is a transmissive type, a rectangular dielectric with a uniform refractive index distribution, and the uneven shape on DOE30 is formed on one side of the rectangular dielectric and consists of square or rectangular pixels arranged in a grid.

[0024] Light is assumed to enter from a surface with irregularities, or from the opposite surface, and exit from the opposite surface of the incident surface. In such a DOE30, the electric field distribution u0 on the DOE exit surface P0 is formed by the thickness of the dielectric at each pixel (the optical path length from the incident surface to the exit surface). Here, we will explain the case where the DOE does not perform amplitude modulation of the electric field, but only phase modulation (kinoform).

[0025] Figure 8 shows the relationship between the thickness of the transmissive DOE 30 and the phase of light at the DOE exit surface 32. The refractive index inside the DOE is n1, and the refractive index outside the DOE is n0 (1 in air). Also, the step difference in the surface irregularities of the DOE 30 is denoted as d, and the DOE 30 in optical path A33 is assumed to be thinner by a step difference (thickness) d than the DOE 30 in optical path B34. Point b is a point on the optical axis at the DOE exit surface 32 of optical path B34, and point a is the intersection of the plane containing the exit surface 32 of optical path B34 and the optical axis of optical path A33. In addition, the dotted line in the figure represents the equiphase plane 35 between optical path A33 and optical path B34.

[0026] As shown in Figure 8, when a plane wave is incident (in the direction of arrow 36), the phase difference Δφ at point a, with the phase at point b as the reference (=0), is expressed by equation (8).

[0027]

number

[0028] Here, k1 and k0 are the wavenumbers of light inside and outside the DOE30, respectively; λ1 and λ0 are the wavelengths of light inside and outside the DOE30, respectively; and λ is the wavelength of light in a vacuum.

[0029] Solving equation (8) for d, we get equation (9).

[0030]

number

[0031] Assuming that the light incident on the DOE incident surface 31 is a plane wave, the phase at the DOE exit surface 32 is determined by the amount of recess (step difference in unevenness) d from the DOE exit surface 32. The phase difference Δφ of u0 can be expressed in terms of the angle of change of u0 arg(u0), and is expressed by equation (10).

[0032]

number

[0033] Here, since u0 fluctuates on the xy plane, the amount of indentation (step difference in unevenness) from the DOE emission surface 32 is represented by d(x, y).

[0034] If L0 is the thickness from the DOE ingress surface 31 to the DOE exit surface 32 (the reference thickness of DOE 30), then the thickness L(x, y) of DOE 30 is expressed by equation (11).

[0035]

number

[0036] Here, since arg(u0) is usually in the range of 0 to 2π or -π to +π, d is 0 to λ / (n1-n0) or -λ / [2(n1-n0)] to +λ / [2(n1-n0)], respectively.

[0037] Since -jλ is a constant in u0 expressed in equation (7), u0' shown in equation (12) may be used instead of u0 expressed in equation (7).

[0038]

number

[0039] [Non-Patent Document 1] Joseph W. Goodman, "Introduction to Fourier Optics Second Edition", McGROW-HILL Companiews Inc., 1996, pp. 32-53. [Overview of the Initiative] [Problems that the invention aims to solve]

[0040] However, with the method of designing the irregularities formed on the surface of the DOE described above, the only imaging plane for which the electric field generated by the DOE can be designed is P1, and the light emission range on the DOE emission surface P0 that forms the bright spot on the imaging plane P1 is the entire DOE emission surface. Therefore, it is not possible to design the bright spot on the imaging plane P1 to maintain a desired diameter in the optical axis direction.

[0041] Therefore, when a diffraction element designed using the above method is used for laser processing, rust removal, etc., it becomes problematic because the beam diameter cannot be maintained when the beam focus shifts in the direction of the optical axis, resulting in a decrease in accuracy in laser processing, rust removal, etc. [Means for solving the problem]

[0042] To solve the problems described above, the present invention provides a method for designing a diffraction element that phase modulates incident light, using a computer, comprising: a first step of calculating the electric field distribution of the emitted light at the output surface of the diffraction element with respect to the incident light, wherein the incident light is a Gaussian beam; a second step of calculating the electric field distribution obtained by multiplying the electric field distribution of the emitted light from the output surface by a Gaussian window in a plane parallel to the output surface located at a predetermined distance from the output surface, as the electric field distribution of a beam approximated by a Bessel-Gauss beam; a third step of calculating a first electric field distribution as the electric field distribution on the output surface of the diffraction element with respect to the electric field distribution of the emitted light in the plane, based on Kirchhoff's principle of diffraction integration; and a fourth step of determining the depth of the surface irregularities of the diffraction element based on the electric field distribution on the output surface of the diffraction element. [Effects of the Invention]

[0043] According to the present invention, it is possible to provide a method for designing and manufacturing a diffraction element that can maintain the diameter and power of the emitted light at a predetermined length in the direction of light propagation, and can perform high-precision processing, rust removal, etc., on objects with depth using emitted light. [Brief explanation of the drawing]

[0044] [Figure 1] Figure 1 is a diagram illustrating a design method for a diffraction element according to the first embodiment of the present invention. [Figure 2] Figure 2 is a diagram illustrating a design method for a diffraction element according to the first embodiment of the present invention. [Figure 3] Figure 3 is a flowchart illustrating a design method for a diffraction element according to the first embodiment of the present invention. [Figure 4] Figure 4 is a diagram illustrating a design method for a diffraction element according to the first embodiment of the present invention. [Figure 5A] Figure 5A is a diagram illustrating the effects of the design method for a diffraction element according to the first embodiment of the present invention. [Figure 5B] Figure 5B is a diagram illustrating the effects of the design method for a diffraction element according to the first embodiment of the present invention. [Figure 6] Figure 6 is a flowchart illustrating a design method for a diffraction element according to a second embodiment of the present invention. [Figure 7] Figure 7 is a diagram illustrating a conventional design method for diffraction elements. [Figure 8] Figure 8 is a diagram illustrating a conventional design method for diffraction elements. [Modes for carrying out the invention]

[0045] <First Embodiment> A design method for a diffraction element according to the first embodiment of the present invention and a manufacturing method therefor will be described with reference to Figures 1 to 3.

[0046] <Design method for diffractive elements> In this embodiment, the diffraction element 10 is a so-called kinoform that performs only phase modulation and not amplitude modulation of the electric field.

[0047] In the design method for the diffraction element 10 according to this embodiment, the electric field distribution u0 (first electric field distribution) on the emission surface P0 of the diffraction element 10, which focuses (images) light within a predetermined range on the z-axis, is determined, and the surface structure (undulation structure) of the diffraction element 10 is designed. Here, the z-axis of the xyz coordinate system is perpendicular to the DOE emission surface P0, and the coordinate origin is on the emission surface P0.

[0048] Figure 1 shows a schematic diagram of the optical system when imaging is performed using the diffractive element 10 in this embodiment. Light incident on the diffractive element 10 (arrow 1 in the figure indicates the direction of incidence) is emitted from the emission surface P0 of the diffractive element 10, and the emitted light from the diffractive element 10 (arrow 2 in the figure indicates the direction of emission) is directed to two points on the z-axis (for example, z α and z β In the region between ), the light is focused as emission line 3_1. Here, the light emitted from the diffracting element 10 has a first electric field distribution u0.

[0049] Here, the x, y, and z axes represent the axes of the Cartesian coordinate system, and the DOE emission plane P0 lies on the xy-plane.

[0050] This embodiment describes a method for designing a diffraction element that realizes a Bessel-Gaussian beam. A Bessel-Gaussian beam is a type of pseudo-non-diffractive light that can maintain its beam diameter over long distances. First, the Bessel beam, which is the non-diffractive light that forms the basis of the Bessel-Gaussian beam, is explained. Next, the Bessel-Gaussian beam is explained. Finally, a method for designing a diffraction element that realizes a Bessel-Gaussian beam is explained.

[0051] First, let me explain Bessel beams.

[0052] The Bessel beam can maintain the beam spot diameter on the z-axis at a long distance (theoretically, infinite distance). The electric field distribution E B、z (x, y) of this Bessel beam is shown by Equation (13) and includes the Bessel function of the first kind of order zero. This electric field distribution has the maximum intensity on the z-axis and is useful for applications such as condensing light for a rust-removing laser and the like.

[0053]

Equation

[0054] Here, J0 is the Bessel function of the first kind of order zero, r xy =√(x 2 +y 2 ), α = ksinφ B , β = kcosφ B , k is the wave number of light (k = 2π / λ, λ is the wavelength of light), and φ B (hereinafter referred to as the "convergence angle") is a parameter that determines the beam diameter of the main lobe (the lobe with the intensity peak on the z-axis) of the Bessel beam (described later).

[0055] Fig. 2 shows the propagation of light from the diffraction element (DOE) 10 when a Bessel beam with the z-axis as the center of the main lobe is formed. The Bessel beam is formed when light travels at the same angle φ B around the z-axis. The Bessel beam has a main lobe and side lobes, the center of the z-axis is the center of the main lobe, and an annular side lobe is formed around the z-axis.

[0056] In the Bessel beam, as shown in Fig. 2, light is emitted from the exit surface of the diffraction element 10 so as to form an angle φ B with respect to the z-axis at an arbitrary position on the z-axis. That is, light forming an angle φ B with respect to the z-axis is emitted from an arbitrary point on P0.

[0057] At this time, in the region where the light emitted from the diffracting element 10 overlaps, the electric field distribution on a plane parallel to the xy-plane is expressed by equation (13). Here, since J0 is a zero-th order Bessel function of the first kind, it has principal lobes.

[0058] Here, the full width at half maximum (FMAX) of the main lobe of the zero-th order Bessel beam of the first kind is 2r. B and φ B This is expressed by equation (14) (Wei. Ting Chen, Mohammadreza Khorasaninejad, Alexander Y. Zhu, Jaewon Oh, Robert C. Devlin, Aun Zaidi, and Federico Capasso, “Generation of wavelength-independent subwavelength Bessel beams using metasurfaces,” Light & Application, 6, el6259, 2017).

[0059]

number

[0060] Therefore, the FWHM of the desired principal lobe is 2r B Once you determine that value, you can use equation (14) to calculate φ B This is calculated.

[0061] A Bessel beam can be artificially generated by using an axicon lens (conical lens) as the diffraction element 10 and injecting a plane wave or a collimated Gaussian beam into the axicon lens. In this case, as shown in Figure 2, a region of superimposed light is created on the output side of the axicon lens, and a Bessel beam is generated that forms a main lobe on the z-axis of that region.

[0062] Next, we will discuss the Bessel-Gaussian beam. The Bessel-Gaussian beam can limit the range over which the beam diameter of the main lobe of the Bessel beam is maintained.

[0063] Electric field distribution E of a Bessel-Gauss beam BG、z (x, y) is given by equation (15).

[0064]

number

[0065] Thus, the electric field distribution of a Bessel-Gauss beam is given by the Gaussian window function exp[-(r) in the Bessel beam represented by equation (13). xy / w) 2 This is obtained by multiplying by ]. Here, w is the power of the Gaussian window function (square of the electric field strength) relative to the peak power (=1), which is 1 / e 2 This is half the width of the total width. Note that since equation (15) represents the electric field distribution, w in equation (15) is half the width of the total width (half the width) which is 1 / e for the peak value (=1) of the Gaussian window function.

[0066] Finally, we will explain the design method for the diffraction element that realizes the Bessel-Gauss beam. Figure 3 shows a flowchart illustrating the design method for the diffraction element 10 according to this embodiment.

[0067] In describing the design method for the diffraction element 10 according to this embodiment, as shown in Figure 4, the emission surface (plane P0) of the diffraction element 10 includes the origin of the xyz coordinate system, and a plane P1 parallel to plane P0 is positioned at a distance z1 from the origin (0,0,0).

[0068] First, the desired beam diameter 2r B Using equation (14), φ B Calculate the φ. B From the value, α = ksinφ B β=kcosφ B The following is calculated: Here, k is the wavenumber of light (k = 2π / λ, where λ is the wavelength of the incident or emitted light in a vacuum).

[0069] Next, the diffracting element (DOE) 10 that realizes the optical path as shown in Figure 2 has radius w inWhen a collimated Gaussian beam is incident on the incident light, the electric field distribution E of the emitted light on the output surface P0 of the diffraction element 10 with respect to the incident light. Ax (x, y) are calculated using equation (16) (Step S11).

[0070]

number

[0071] Here, r xy =√(x 2 +y 2 ) is. Also, Exp[j(αr xy )] shows the phase distribution that realizes the optical path in Figure 2.

[0072] The electric field distribution represented by equation (16) is obtained by taking an angle φ from any coordinate point on the plane P0 towards the z-axis. B This is the electric field distribution through which light propagates. In this case, the diffracting element has the same function as an axicon lens.

[0073] Next, the electric field distribution E on the plane P1 of the light propagated from the emission surface of the diffracting element 10. B、z1 (x, y) are calculated using Kirchhoff's diffraction integral, as shown in equations (17) to (21) (similar to equations (1) to (4)).

[0074]

number

[0075]

number

[0076]

number

[0077]

number

[0078] Here, instead of equation (17), we may also use the Fourier transform and inverse Fourier transform and calculate using equation (21).

[0079]

number

[0080] Here, g z1 (x, y) is the same as equation (2) but with z1.

[0081] The resulting electric field distribution E on plane P1 B、z1 (x, y) is the approximate electric field distribution of a Bessel beam.

[0082] Next, in order to approximate the electric field distribution of a Bessel-Gaussian beam as the electric field distribution on plane P1, we use the Gaussian (Gaussian window) and E as shown in equation (22). B、z1 Calculate the product of (x, y) (Step S12).

[0083]

number

[0084] Here, w is the radius of the Gaussian window (half of the total width (half-maximum) which is 1 / e of the Gaussian peak). Thus, the electric field distribution E on plane P1. BG、z1 (x, y) is calculated as the electric field distribution of a beam approximated by a Bessel-Gaussian beam.

[0085] Next, the electric field distribution E on the plane P1 shown in equation (22) BG、z1 For (x, y), the electric field distribution E on the plane P0 is BG、z=0 The (x, y) (first electric field distribution) is calculated using the inverse Fourier transform based on Kirchhoff's principle of diffraction integrals, according to equation (23) (step S13).

[0086]

number

[0087] In equation (23), g z1 (x, y) ≈ e -jkr If it can be approximated as E BG、z1 (x, y) can be expressed as follows:

[0088]

number

[0089] The resulting electric field distribution E on the DOE output surface BG、z=0 Using (x, y) (the first electric field distribution), the thickness L(x, y) of the diffraction element 10 is calculated for each coordinate (x, y) on the DOE emission surface using equations (24) and (25) (which are the same as equations (10) and (11), respectively), and the surface structure (undulation shape) of the diffraction element 10 is designed (step S14).

[0090]

number

[0091] Here, n1 is the refractive index inside the diffracting element 10, n0 is the refractive index outside the diffracting element 10, λ is the wavelength of the incident or emitted light in vacuum, and arg(E BG、z=0 (x, y) is the electric field distribution E BG、z=0 This is the argument of (x, y).

[0092]

number

[0093] In this embodiment, the electric field distribution at the emission surface of the diffracting element is derived based on a Bessel-Gauss beam, and the surface structure (undulation structure) of the diffracting element is designed accordingly. This allows the diameter and power of the emission lines to be kept approximately equivalent over a predetermined length (range) in the direction of light propagation (z-direction). Here, "approximately equivalent" includes equivalent values ​​and is sufficient as long as it is within a range that can achieve the accuracy required for laser processing, rust removal, etc., using the beam. For example, as will be described later, the beam diameter may vary by about 1.5 times, such as from 30 μm to 40 μm, or the normalized beam power density may vary within about 5 times. With this level of normalized beam power, for example, rust removal is possible when the total power of the light emitted from the DOE emission surface is about 100 W, which is the typical rust removal laser power. Note that "normalized beam power density" is the beam power density when the total power of the light emitted from the DOE is 1 W.

[0094] <Method for manufacturing a diffraction element> Based on the surface structure of the diffractive element designed as described above, the diffractive element 10 is manufactured. The diffractive element 10 is composed of a plate member made of a transparent material such as ZnS or quartz. The surface structure of the designed diffractive element 10 is formed on the surface of the plate member by known microfabrication. This manufactures the diffractive element 10 according to this embodiment.

[0095] <Effects> The effects of the design method and manufacturing method of the diffraction element according to this embodiment of the present invention will be explained.

[0096] Figure 5A shows the electric field distribution E on the emission surface of the diffracting element (DOE) 10. BG、Z=0 In the light beam generated by this, the total width of the Gaussian window (power density is 1 / e of the peak power density) 2 Figure 5B shows the simulation results of the beam diameter of the optical beam intensity distribution (square of the electric field strength) when the diameter (2w) is varied. Additionally, Figure 5B shows the simulation results of the peak power density (maximum power density) of the optical beam intensity distribution.

[0097] In the simulation of the light intensity distribution of a light beam, the electric field distribution E on the DOE emission surface is given by equations (13) to (23). BG、Z=0 The following was calculated: This electric field distribution E BG、Z=0 Using this method, the light beam intensity distribution at imaging was calculated based on equation (1).

[0098] Furthermore, in this simulation, the resolution in the x-axis and y-axis directions is 5 μm.

[0099] The incident beam to the diffracting element (DOE) 10 and lens used in the simulation had a diameter of 5.1 mm (power density was 1 / e of the peak power density). 2 A Gaussian beam with a diameter of (this is the desired diameter) was used.

[0100] Furthermore, the full width at half maximum (FMAX) of the main lobe of a first-order zero-order Bessel beam is 2r. B 35 μm (φ B The radiant energy was set to 3 mrad. The wavelength of light, λ, was set to 1070 nm.

[0101] In the figure, the horizontal axis, "distance z," represents the distance from the DOE emission surface. The vertical axis, "normalized peak power density," represents the peak power density when the total power of the DOE emitted light is assumed to be 1W.

[0102] Furthermore, the "beam diameter" on the vertical axis is typically 1 / e of the peak power density. 2 The diameter that results in the power density is used, but in this embodiment, the light beam intensity distribution determined by the electric field distribution u0 on the DOE emission surface is not of the Gaussian type, so the full width at half maximum (FWHM) was used.

[0103] Furthermore, the total width 2w of the Gaussian window was varied from 50 μm to 1600 μm.

[0104] As shown in Figure 5A, when the total width 2w of the Gaussian window is 50 μm to 400 μm, the beam diameter is approximately 40 μm only when z is near 0.25 m. On the other hand, when the total width 2w of the Gaussian window is 800 μm, the beam diameter is maintained over a length of 0.2 m between 0.1 m and 0.3 m, with a beam diameter change in the range of approximately 30 μm to 42 μm. Furthermore, when the total width 2w of the Gaussian window is 1600 μm, the beam diameter is maintained over a length of 0.4 m or more (in the range of 0 to 0.4 m or more), with a beam diameter change in the range of approximately 30 μm to 40 μm.

[0105] As shown in Figure 5B, when the total width 2w of the Gaussian window is 50μm to 200μm, the peak power density is 5E8W / m² only when z is near 0.25m. 2 It is approximately as follows. On the other hand, when the total width of the Gaussian window 2w is 400μm, the variation in peak power density is within about 5 times (2E7~1E8W / m). 2 The range within which this range is maintained is approximately 0.04 m in length, between z = 0.22 m and 0.26 m. Furthermore, when the total width of the Gaussian window 2w is 800 μm, the peak power density fluctuation is within approximately 5 times (1E7 to 5E7 W / m²). 2 The range within which the fluctuations fall within this range is approximately 0.18 m in length, between z = 0.12 m and 0.3 m. Furthermore, when the total width of the Gaussian window 2w is 1600 μm, the peak power density fluctuation is within approximately 5 times (1E7 to 5E7 W / m²). 2 The range within which it falls within this range is approximately 0.21m in length, between z = 0.04m and z = 0.25m.

[0106] Thus, the beam diameter and peak power density are maintained over a longer distance in the z-axis direction as the width of the Gaussian window increases. Furthermore, by changing the width of the Gaussian window, the length of the beam diameter and power density that can be maintained in the z-axis direction can be changed.

[0107] <Effects> When applying a Bessel beam to the design method of conventional diffraction elements, the Bessel beam has a constant beam diameter and intensity over an infinite range, so the beam power does not attenuate, which means that areas outside the desired range may be irradiated. As a result, problems arise such as being unable to process the desired shape, or the risk of irradiating objects other than those being processed or rust-removed, or the human body.

[0108] In the diffraction element designed and manufactured in this embodiment, the beam diameter and intensity can be limited to a finite range, allowing irradiation only to the desired area. Therefore, it is possible to process the desired shape, and safety can be ensured as the beam will not irradiate objects other than those being processed or rusted, or the human body.

[0109] Thus, the diffracting element designed and manufactured in this embodiment can maintain the diameter and power of the emitted light within a desired range in the direction of light propagation (z-direction), enabling high-precision processing and rust removal of objects with depth using emitted light (laser light).

[0110] Furthermore, the diffraction element designed and manufactured in this embodiment is small and lightweight (approximately several tens of grams), allowing for a smaller and lighter head section of the laser processing device compared to conventional mechanisms.

[0111] <Second Embodiment> A design method for a diffraction element and a manufacturing method according to a second embodiment of the present invention will be described with reference to Figure 6.

[0112] In the first embodiment, a diffraction element in which a bright spot is imaged was shown as an example. In this embodiment, a diffraction element in which a desired image is imaged will be described as an example.

[0113] In this embodiment, a diffraction element (DOE) 20 that forms a two-dimensional shape on the imaging plane will be described. The diffraction element 20 phase-modulates light emitted from the emission surface with a first' electric field distribution so that the light has an intensity distribution of a second electric field distribution that corresponds to a desired light intensity distribution on the imaging plane.

[0114] Figure 6 shows a flowchart illustrating the design method for the diffraction element 20 according to this embodiment.

[0115] First, let q(x, y) be the light intensity distribution that is imaged onto the imaging plane P1. The electric field strength at this time is √q(x, y), and the electric field distribution with this electric field strength (the second electric field distribution) is u c Determine (x, y) (step S21). c (x, y) is, for example, given that the real part of the electric field is √q(x, y) and the imaginary part is 0, u c Alternatively, we can write (x, y) = √q(x, y) + j·0, where j represents the imaginary unit.

[0116] Next, in the first embodiment, the first electric field distribution E is carried out in the same manner as in steps S11 to S13. BG、z=0 Calculate (x, y) (steps S22-S24).

[0117] Next, the electric field distribution E on the DOE emission surface. BG、z=0、l (The first' electric field distribution) is as shown in equation (26), the first electric field distribution E BG、z=0 (x, y) and the second electric field distribution u c It is calculated by performing a convolution integral with (x, y) (Step S25).

[0118]

number

[0119] Here, S represents the integration range, which could be the range on the DOE exit surface, or the range including the DOE exit surface, etc.

[0120] Also, u c The shape represented by (x, y) can also be a bright spot, as shown in the first embodiment. Therefore, the electric field distribution E on the DOE emission surface in this embodiment BG、z=0、l (x, y) is the electric field distribution E on the DOE emission surface in the first embodiment. BG、z=0 Includes (x, y).

[0121] The resulting electric field distribution E on the DOE output surface BG、z=0、l Using (x, y), the depth d(x, y) of the surface irregularities on the diffraction element 20 is calculated using equation (27).

[0122]

number

[0123] Here, n1 is the refractive index inside the diffraction element 20, n0 is the refractive index outside the diffraction element 20, λ is the wavelength of the incident or emitted light in vacuum, and arg(E BG、z=0、l (x, y) is the electric field distribution E BG、z=0、l This is the argument of (x, y).

[0124] Using d(x, y), the thickness L(x, y) of the diffraction element 20 is calculated for each coordinate (x, y) on the DOE emission surface from equation (25), and the surface structure (undulation shape) of the diffraction element 20 is designed (step S26).

[0125] Based on the surface structure of the diffractive element 20 designed in this manner, the diffractive element 20 is manufactured in the same manner as in the first embodiment.

[0126] Furthermore, in this embodiment, u c If (ξ,η) is a line segment, then when rust removal is performed using a laser, a line segment image is formed, and by moving this image perpendicular to the line segment, rust removal can be performed on a surface.

[0127] As described above, in this embodiment, the electric field distribution at the exit surface of the diffractive element is derived by convolution integration of the sum of the electric field distributions on the diffractive element that image each bright point of an emission line within a predetermined range of a straight line penetrating the diffractive element (the electric field distribution on the diffractive element's exit surface that generates the emission line) and electric field distributions of various shapes, and by designing the surface structure (uneven structure) of the diffractive element, the diameter and power of the light beam emitted from the diffractive element can be kept substantially equal over a predetermined length (range) in the direction of light propagation (z direction).

[0128] Therefore, the diffracting element manufactured in this embodiment can maintain the diameter and power density of the emitted light at a desired length in the light propagation direction (z-direction), enabling high-precision processing and rust removal of objects with depth, regardless of their shape, using emitted light (laser light), thus achieving the same effects as in the first embodiment.

[0129] In the embodiments of the present invention, an example was shown in which the light emitted from the diffracting element is focused in a direction parallel to the optical axis. However, the invention is not limited to this, and the light may be focused on an axis that is not parallel to the optical axis but is approximately parallel. "Approximately coaxial" is acceptable as long as it is within a range that can achieve the accuracy required for laser processing, rust removal, etc., using a beam.

[0130] In embodiments of the present invention, the diffraction element is designed using a computer.

[0131] In the embodiments of the present invention, examples of the structure, dimensions, materials, etc., of each component of the diffraction element are shown, but the invention is not limited to these examples. Any configuration that allows the diffraction element to function and produce the desired effect is acceptable. [Industrial applicability]

[0132] This invention relates to a method for designing and manufacturing a diffraction element in a high-power laser device, and can be applied to laser light processing and rust removal. [Explanation of symbols]

[0133] 10 Diffraction element

Claims

1. A method for designing a diffraction element that phase-modulates incident light using a computer, The first step is to calculate the electric field distribution of the emitted light at the output surface of the diffracting element with respect to the incident light, provided that the incident light is a Gaussian beam. A second step involves calculating the electric field distribution obtained by multiplying the electric field distribution of the light emitted from the emission surface by a Gaussian window in a plane parallel to the emission surface located at a predetermined distance from the emission surface, as the electric field distribution of a beam approximated by a Bessel-Gauss beam. A third step involves calculating a first electric field distribution as the electric field distribution on the emission surface of the diffracting element, based on Kirchhoff's principle of diffraction integration, with respect to the electric field distribution of the emitted light in the aforementioned plane. A fourth step is to determine the depth of the surface irregularities of the diffraction element based on the electric field distribution on the emission surface of the diffraction element. A method for designing a diffraction element equipped with the following features.

2. The steps include: calculating a second electric field distribution whose intensity is the positive square root of the light intensity distribution imaged on the aforementioned plane; The steps include: calculating the electric field distribution on the emission surface of the diffraction element by convolution integral of the second electric field distribution and the first electric field distribution; A method for designing a diffraction element according to claim 1, comprising:

3. In a Cartesian coordinate system in which the emission surface is perpendicular to the z-axis, In the first step described above, the electric field distribution E on the output surface with respect to the incident light is given by equation (A). Ａｘ Calculate (x, y), In the second step described above, the electric field distribution E is calculated using Kirchhoff's diffraction integral. Ｂ、ｚ１ Using (x, y), the electric field distribution E of the emitted light in the plane is given by equation (B). ＢＧ、ｚ１ Calculate (x, y) A method for designing a diffraction element according to claim 1 or 2. [Math 1]

4. The depth d(x, y) of the surface irregularities of the diffracting element is expressed by equation (C). A method for designing a diffraction element according to claim 1 or 2. [Math 2] Here, n １ n is the refractive index inside the diffraction element. ０ λ is the refractive index outside the diffracting element, λ is the wavelength of the incident or emitted light in vacuum, and arg(E) Ｂ、ｚ＝０、ｌ (x, y) is the deflection angle of the electric field distribution on the emission surface of the diffraction element.

5. The method for designing a diffraction element according to claim 1 or claim 2 is provided. A method for manufacturing a diffraction element, characterized by the above.

Images