Design method for diffractive elements and manufacturing method for diffractive elements

Abstract

A method for designing a diffractive element according to the present invention is a method for, using a computer, designing a diffractive element (10) for phase-modulating incident light, and comprises: a step for determining an electric field distribution on an emission surface of the diffractive element with respect to spherical waves that are collected in a range between a first distance and a second distance from the emission surface on a straight line perpendicular to the emission surface; a step for calculating, as the electric field distribution on the emission surface of the diffractive element, a first electric field distribution by multiplying the electric field distribution on the emission surface with respect to the spherical waves by Exp[-jkzcosφB] where z is a coordinate on the straight line, k is a wave number of emitted light from the emission surface, and φB is a convergent angle which the emitted light forms with the straight line, and integrating the solution thereof in the range; and a step for determining the depth of surface asperities of the diffractive element on the basis of the electric field distribution on the emission surface of the diffractive element.　Consequently, the present invention can provide a method for designing a diffractive element capable of keeping the diameter and power of emitted light by a predetermined 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 for performing scanning of emitted light, etc., a so-called head part, are issues. 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 the laser processing device.

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

[0004] FIG. 10 shows a schematic diagram of an optical system when imaging is performed using a conventional diffractive element 40. Light incident on the diffractive element 40 (arrow 1 in the figure indicates the incident direction) exits from the exit surface P0 of the diffractive element 40, and the exit light of the diffractive element 40 (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 approximately coincides with the direction in which the light emitted from the DOE 40 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 we let the z-coordinate on P0 be z0=0 and the z-coordinate on P1 be z1, then from Kirchhoff's diffraction integral formula, the relationship between u0 and u1 can be 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 single point, and is expressed by equations (2) to (4).

[0009]

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[0010]

number

[0011]

number

[0012] Here, j is the imaginary unit and k is the wavenumber of light. (1+cosθ) / 2 is the inclination factor, which represents the dependence of the field intensity at each point on the imaging plane on the emission angle of the field intensity from the DOE emission plane to each point.

[0013] Since the right-hand side of equation (1) is a convolution integral of u0 and g, taking the Fourier transform of both sides of equation (1) gives us 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]

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

[0019]

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[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 DOE40 using the electric field distribution u0 on the DOE emission surface P0.

[0023] Here, DOE40 is a transmissive type, a rectangular dielectric with a uniform refractive index distribution, and the uneven shape on DOE40 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 DOE40, 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 11 shows the relationship between the thickness of the transmissive DOE 40 and the phase of light at the DOE exit surface 42. 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 40 is denoted as d, and the DOE 40 in optical path A43 is assumed to be thinner than the DOE 40 in optical path B44 by a step difference (thickness) of d. Point b is a point on the optical axis at the DOE exit surface 42 of optical path B44, and point a is the intersection of the plane containing the exit surface 42 of optical path B44 and the optical axis of optical path A43. In addition, the dotted line in the figure represents the equiphase plane 45 between optical path A43 and optical path B44.

[0026] As shown in Figure 11, when a plane wave is incident (in the direction of arrow 46), 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 DOE40, respectively; λ1 and λ0 are the wavelengths of light inside and outside the DOE40, respectively; and λ is the wavelength of light in a vacuum.

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

[0030]

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[0031] Assuming that the light incident on the DOE incident surface 41 is a plane wave, the phase at the DOE exit surface 42 is determined by the amount of recess (step difference in unevenness) d from the DOE exit surface 42. The phase difference Δφ of u0 can be expressed in terms of the angle of deviation 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 42 is represented by d(x, y).

[0034] If L0 is the thickness from the DOE ingress surface 41 to the DOE exit surface 42 (the reference thickness of DOE 40), then the thickness L(x, y) of DOE 40 is expressed by equation (11).

[0035]

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[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]

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[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 the steps of: determining the electric field distribution on the output surface of the diffraction element for a spherical wave focused in a range between a first distance and a second distance from the output surface on a straight line perpendicular to the output surface of the diffraction element; and setting the coordinate on the straight line to z, the wavenumber of the light emitted from the output surface to k, and the convergence angle that the light makes with the straight line to φ B When this is the case, Exp[-jkzcosφ B The method comprises the steps of: multiplying the electric field distribution on the emission surface for the spherical wave by ] and integrating over the range to calculate a first electric field distribution as the electric field distribution on the emission surface of the diffraction element; and determining the depth of the irregularities on the surface of the diffraction element based on the electric field distribution on the emission surface of the diffraction element.

[0043] Furthermore, the present invention relates to a method for designing a diffraction element that phase modulates incident light, using a computer, comprising the steps of: determining the electric field distribution on the output surface for a spherical wave focused in a range between a first distance and a second distance from the output surface on a straight line perpendicular to the output surface of the diffraction element; and defining the coordinate on the straight line as z, the wavenumber of the light emitted from the output surface as k, and the convergence angle that the light makes with the straight line as φ B When this is the case, Exp[-jkzcosφ B The method comprises the steps of: multiplying the electric field distribution on the emission surface for the spherical wave by ] and summing them up within the range to calculate a first electric field distribution as the electric field distribution on the emission surface of the diffraction element; and determining the depth of the irregularities on the surface of the diffraction element based on the electric field distribution on the emission surface of the diffraction element. [Effects of the Invention]

[0044] 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]

[0045] [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 flowchart illustrating a design method for a diffraction element according to a second embodiment of the present invention. [Figure 5] Figure 5 is a diagram illustrating a design method for a diffraction element according to a second embodiment of the present invention. [Figure 6A]Figure 6A is a diagram illustrating the effects of the design method for a diffraction element according to a second embodiment of the present invention. [Figure 6B] Figure 6B is a diagram illustrating the effects of the design method for a diffraction element according to a second embodiment of the present invention. [Figure 7] Figure 7 is a diagram illustrating the effects of the design method for a diffraction element according to a second embodiment of the present invention. [Figure 8A] Figure 8A is a diagram illustrating the effects of the design method for a diffraction element according to a second embodiment of the present invention. [Figure 8B] Figure 8B is a diagram illustrating the effects of the design method for a diffraction element according to a second embodiment of the present invention. [Figure 9] Figure 9 is a flowchart illustrating a design method for a diffraction element according to a third embodiment of the present invention. [Figure 10] Figure 10 is a diagram illustrating a conventional design method for diffraction elements. [Figure 11] Figure 11 is a diagram illustrating a conventional design method for diffraction elements. [Modes for carrying out the invention]

[0046] <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.

[0047] 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.

[0048] In the design method for the diffraction element (DOE) 10 according to this embodiment, two points on the z-axis (z α and z β The electric field distribution u0 (first electric field distribution) on the emission surface P0 of the diffraction element 10, which focuses (images) light between the two points, 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.

[0049] Fig. 1 shows a schematic diagram of an optical system when imaging is performed using the diffractive element 10 in the present embodiment. Light incident on the diffractive element 10 (arrow 1 in the figure indicates the incident direction) exits from the exit surface P0 of the diffractive element 10, and the exit light of the diffractive element 10 (arrow 2 in the figure indicates the exit direction) is condensed as a bright line 3_1 in the region between two points (z α and z β ) on the z-axis. Here, the exit light of the diffractive element 10 has a first electric field distribution u0.

[0050] Here, the x, y, and z axes represent the respective axes of the Cartesian coordinate system, and the DOE exit surface P0 is parallel to the xy plane.

[0051] Assuming that the coordinates of an arbitrary point on the z-axis in Fig. 1 are (0, 0, z1) and the coordinates of a point on the DOE exit surface are (x, y, 0), the electric field distribution u 0、z1 ’(x, y) on the DOE exit surface when condensing light at (0, 0, z1) is represented by Equation (13) from Equation (12).

[0052]

Equation

[0053] Here, u1(x, y) is the electric field distribution on a plane parallel to the DOE exit surface including (0, 0, z1).

[0054] u1(x, y) is actually represented by a function having a predetermined spread (for example, a Gaussian function, a Bessel function, etc.). Here, for simplicity of calculation, when approximating u1(x, y) with a δ function, u 0、z1 ’(x, y) is represented by Equation (14).

[0055]

Equation

[0056] From Equation (13), as shown in Fig. 1, from z α to z βThe electric field u0(x, y) on the DOE surface when a set of bright spots (emission line) is formed between these points is approximated by equation (15). Here, u 0、z1 '(x, y) to u 0、z Let's represent it in terms of (x, y).

[0057]

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[0058] Equation (15) will be explained in detail below. First, we consider a Bessel beam as a beam that maintains a beam spot diameter over a long distance along the z-axis.

[0059] Figure 2 shows the propagation of light from the diffracting element (DOE) 10 when a Bessel beam is formed with the z-axis as the center of the main lobe. The Bessel beam is centered on the z-axis at the same angle φ B It is formed when light at a certain angle (hereinafter referred to as the "convergence angle") is propagated. The Bessel beam has a main lobe and side lobes, with the center of the z-axis being the center of the main lobe, and annular side lobes formed around the z-axis.

[0060] 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 (16) (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).

[0061]

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[0062] Thus, φ B 2r is the diameter of the beam on the z-axis (full width at half maximum). B These are the parameters related to the following: Here, k and λ are the wavenumber and wavelength of the propagating light (the light emitted from the diffraction element 10), respectively.

[0063] Next, let's consider the phase of light along the z-axis.

[0064] The length of the phase 2π of light on the z-axis is 1 / cosφ of the wavelength λ. B times (λ / cosφ) B Therefore, the effective wave number k on the z axis is cosφ B times(kcosφ B Therefore, the absolute value of the phase of light on the z-axis is kcosφ. B It changes according to this.

[0065] Therefore, the relative difference between the phase of light at any point on the z-axis and the phase at the intersection of the DOE emission plane and the z-axis is -kzcosφ B That is the case.

[0066] Therefore, z on the z axis α from z β When a set of bright spots (emission line) is formed between these points, the electric field u0(x, y) on the DOE surface is given by equation (15) as follows: Exp[-jkzcosφ B ] is the electric field distribution on the output surface for a spherical wave focused at a predetermined point on the z axis u 0、z Multiply by (x, y) and z α ~z β It is obtained by integrating (summing) with respect to . Here, Exp[x] represents Napier's number e raised to the power of x.

[0067] Figure 3 shows a flowchart illustrating the design method of the diffraction element 10 according to this embodiment.

[0068] First, the electric field distribution on the emission surface of the diffraction element 10 with respect to bright spots in a spherical wave focused to a predetermined distance (range) from the emission surface is calculated using equation (14) (step S11).

[0069] Next, within the predetermined range (z α ~z β In ), the electric field distribution on the emission surface for each bright spot of the spherical wave is given by -kzcosφ B Taking into account the phase difference, the first electric field distribution u0(x, y) is calculated using equation (15) (step S12).

[0070] In equation (15), g(x, y) ≈ e -jkr If it can be approximated in this way, then u0(x, y) can be expressed by equation (17).

[0071]

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[0072] Using the electric field distribution u0(x, y) on the DOE emission surface obtained in this way, the thickness L(x, y) of the diffraction element 10 is calculated for each coordinate (x, y) on the DOE emission surface using equations (18) and (19) (which are the same as equations (10) and (11), respectively), and the surface structure (undulation shape) of the diffraction element 10 is designed (step S13).

[0073]

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[0074]

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[0075] In this embodiment, two points (z α and z βBy deriving the electric field distribution at the emission surface of the diffracting element based on the integral value of the image formation between the two points, the surface structure (undulation structure) of the diffracting element is designed, so that the diameter and power of the emission lines can be kept approximately the same for a predetermined length (range) in the direction of light propagation (z direction). Here, "approximately the same" 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, it may be within a range where the beam diameter changes by about -10% to +13%, or within a range where the normalized beam power density fluctuates within about 2.5 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 100W, which is the rust removal laser power that is normally used. Note that "normalized beam power density" is the beam power density when the total power of the light emitted from the DOE is 1W.

[0076] <Method for manufacturing a diffraction element> Based on the surface structure of the diffraction element 10 designed as described above, the diffraction element 10 is manufactured. The diffraction element 10 is composed of a plate member made of a transparent material such as ZnS or quartz. The surface structure of the designed diffraction element 10 is formed on the surface of the plate member by known microfabrication. This manufactures the diffraction element 10 according to this embodiment.

[0077] <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.

[0078] In the diffraction element designed and manufactured in this embodiment, a finite range (for example, z α ~z β The beam diameter and intensity can be limited to a constant level, allowing irradiation only to the desired area. Therefore, the desired shape can be processed, and safety can be ensured as the beam will not irradiate objects other than those being processed or rust-removed, or the human body.

[0079] 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).

[0080] 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.

[0081] <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 Figures 4 to 8B. Figure 4 shows a flowchart illustrating the design method for the diffraction element 20 according to this embodiment.

[0082] In the first embodiment, integration was used to calculate the electric field distribution u0 on the DOE emission surface, as shown in equation (15).

[0083] In this embodiment, in order to simplify the calculation of the electric field distribution u0 by computer, the emission line on the optical axis (z axis) is treated discretely as multiple bright spots, and the electric field distribution u obtained from each bright spot is calculated. 0、Zn We will now explain how to calculate the electric field distribution u0 (first electric field distribution) on the DOE emission surface by summing these values.

[0084] Figure 5 shows a schematic diagram of the optical system when imaging is performed using the diffractive element 20 in this embodiment. Light incident on the diffractive element 20 (arrow 1 in the figure indicates the direction of incidence) is emitted from the emission surface P0 of the diffractive element 20, and the emitted light from the diffractive element 20 (arrow 2 in the figure indicates the direction of emission) is focused as multiple (N) bright spots 3_2, 1 to 3_2, N on the z-axis. Here, the emitted light has a first electric field distribution u0.

[0085] Each of the bright points 3_2, 1 to 3_2, and N are located on N image planes P. n(However, n = 1 to N, and N is an integer greater than or equal to 2.) P n (where n=1 to N) are all planes and parallel to the DOE emission plane (plane) P0. Here, the imaging plane P n This is within a predetermined range (z=z1~z N ) will be assigned to.

[0086] P n The center coordinates of the bright spot above are (0, 0, z n (where n=1 to N), then, similar to the first embodiment, a point on the z-axis (0, 0, z n ) The electric field distribution on the DOE emission surface that forms a bright spot centered on u 0、zn (x, y) is expressed by equation (20).

[0087]

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[0088] From equation (20), the image plane P n The electric field u0(x, y) on the DOE surface that images a bright spot on (n=1~N) is approximated by equation (21).

[0089]

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[0090] In equation (21), g(x, y) ≈ e -jkr If it can be approximated as such, then u0(x, y) can be expressed by equation (22).

[0091]

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[0092] Here, r n This is expressed by equation (23).

[0093]

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[0094] Thus, in the design method for the diffraction element 20 according to this embodiment, as shown in Figure 4, first, the electric field distribution on the emission surface of the diffraction element 20 is calculated for bright spots in a spherical wave focused at a predetermined distance from the emission surface (N imaging surfaces arranged within a predetermined range) (step S21).

[0095] Next, the electric field distribution on the emission surface for the bright spot of the spherical wave at each of the N imaging surfaces arranged within a predetermined range is given by -kzcosφ B Taking into account the phase difference, the first electric field distribution u0(x, y) is calculated by adding them together using equation (21) (step S22).

[0096] Using the electric field distribution u0(x, y) on the DOE emission surface obtained in this way, the thickness L(x, y) of the diffraction element 20 is calculated for each coordinate (x, y) on the DOE emission surface using equations (18) and (19), similar to the first embodiment, and the surface structure (undulation shape) of the diffraction element 20 is designed (step S23).

[0097] 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.

[0098] <Effects> The effects of the design method and manufacturing method of the diffraction element according to this embodiment will be explained.

[0099] Figure 6A shows the simulation results of the beam diameter and peak power density (maximum power density) of the optical beam intensity distribution (square of the electric field intensity) when using the diffraction element 20 designed and manufactured in this embodiment.

[0100] In the simulation of the light beam intensity distribution, the range of emission lines was defined, and the electric field distribution u0 on the DOE emission surface was calculated using equation (21). Using this electric field distribution u0, the light beam intensity distribution at imaging was calculated based on equation (1).

[0101] Here, bright spots were positioned on the z-axis at distances z = 5 μm to 1000 mm from the DOE emission surface.

[0102] The adjacent imaging planes P used when calculating the electric field distribution u0 on the DOE emission surface. n and P n+1 The spacing was set to 5 μm.

[0103] For comparison, Figure 6B shows the simulation results of the theoretical full width at half maximum and peak power density (maximum power density) of a Gaussian beam when using a lens as a conventional method. The focal length was set to 849 mm so that the beam diameter at the beam waist is approximately the same as when using the diffracting element 20. In the figure, the horizontal axis z represents the distance from the principal point on the lens exit side.

[0104] The incident beam to the diffracting element (DOE) 20 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.

[0105] 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 set to 1W.

[0106] 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.

[0107] In conventional optical systems using lenses with a Gaussian beam, as shown in Figure 6B, a beam with a diameter of approximately 126 μm is maintained only for a length of 75.6 mm with a beam diameter variation in the range of approximately 133 μm to 189 μm.

[0108] On the other hand, in this embodiment, as shown in Figure 6A, a beam with a diameter of approximately 126 μm is maintained over a length of 950 mm between 50 mm and 1000 mm, with a beam diameter change in the range of -10% to +13%.

[0109] Thus, according to the design method of this embodiment, it is possible to design a diffraction element that can maintain the beam diameter over a distance approximately 13 times longer than that of a conventional optical system using lenses.

[0110] Furthermore, regarding the peak power density of the light beam, which is important for rust removal and processing, in conventional optical systems using lenses, the range in which the fluctuation of the maximum power density of the light beam is kept within approximately 2.5 times is 84.2 mm in length.

[0111] On the other hand, in this embodiment, the range in which the fluctuation of the maximum power density of the light beam is within approximately 2.5 times is a length of 750 mm between z = 200 mm and z = 950 mm.

[0112] Thus, according to the design method of this embodiment, it is possible to design a diffraction element that can maintain the maximum power density of the light beam by suppressing fluctuations in the maximum power density of the light beam by about nine times compared to conventional optical systems using lenses.

[0113] Figure 7 also shows the simulation results for the full width at half maximum and peak power density (maximum power density) of a Bessel beam, which is one type of non-diffracted light, when using an axicon lens as a conventional method. The calculations were performed in the same manner as the simulations described above (Figures 6A and 6B).

[0114] In conventional optical systems using lenses and a Bessel beam, a beam with a diameter of approximately 126 μm is maintained over a length of 1500 mm with a beam diameter variation ranging from -2.5% to +1.2%.

[0115] Furthermore, regarding the peak power density of the light beam, the range in which the variation in the maximum power density of the light beam remains within approximately 2.5 times is 650 mm in length. Moreover, it gradually decreases with increasing distance z, reaching 1E+5 W / m at z=1500 mm. 2 It is to that extent.

[0116] On the other hand, in this embodiment, as shown in Figure 6A, the beam diameter is maintained as described above, and the maximum power density of the optical beam is maintained between z=200mm and 950mm. Furthermore, it decreases sharply above z=950mm, reaching 0.5E+5W / m at z=1500mm. 2 It is to that extent.

[0117] Thus, according to this embodiment, rust removal and processing (welding, cutting) can be performed within a desired range, and outside the desired range (for example, z = 950 mm or more), the peak power density decreases sharply, thereby reducing the impact on people and objects and improving work safety.

[0118] Figures 8A and 8B show the simulation results of the changes in beam diameter (FWHM) and normalized peak power density along the z-axis with respect to the bright spot arrangement range along the z-axis during the design of the diffraction element 20 in this embodiment. The bright spot arrangement range along the z-axis was set to + / -0mm (0.5m), + / -10mm (0.49~0.51m), + / -20mm (0.48~0.52m), + / -30mm (0.47~0.53m), + / -40mm (0.46~0.54m), and + / -50mm (0.45~0.55m) centered around 500mm (0.5m). The calculations were performed in the same manner as described above.

[0119] For example, if the bright spot placement range on the z-axis during the design of the diffractive element is set to + / -40 mm (0.46 to 0.54 m), the beam diameter of the light emitted from the diffractive element is approximately 1.5E-4 m in the range of 0.46 to 0.54 m, and is almost constant. Also, the normalized peak power density is approximately 3E+7 to 7E+7 in the range of 0.46 to 0.54 m, and the variation in the maximum power density of the light beam is within approximately 2.5 times. Similarly, when other bright spot placement ranges are set, the beam diameter of the light is almost constant within the set bright spot placement range, and the variation in the maximum power density of the light beam is within an acceptable range.

[0120] Thus, according to this embodiment, the beam diameter maintenance range and peak power density maintenance range can be achieved as set during the design of the diffracting element, according to the bright spot arrangement range.

[0121] As described above, in this embodiment, by deriving the electric field distribution on the emission surface of the diffractive element based on the sum of the electric field distributions on the emission surface of the diffractive element that produce images on multiple (N) imaging planes arranged within a predetermined range, and designing the surface structure (uneven structure) of the diffractive element, the diameter and maximum power density of the light beam emitted from the diffractive element can be kept substantially the same over a predetermined length (range) in the direction of light propagation (z direction).

[0122] Therefore, the diffracting element manufactured in this embodiment can maintain the diameter of the emitted light and the maximum power density at a desired length in the light propagation direction (z-direction), enabling high-precision processing and rust removal of objects with depth using emitted light (laser light), thus achieving the same effects as in the first embodiment.

[0123] Furthermore, the diffraction element manufactured in this embodiment has a finite range (for example, z α ~z β The beam diameter and intensity can be limited to a constant level, allowing irradiation only to the desired area. Therefore, the desired shape can be processed, and safety can be ensured as the beam will not irradiate objects other than those being processed or rust-removed, or the human body.

[0124] <Third Embodiment> A design method for a diffraction element and a manufacturing method according to a third embodiment of the present invention will be described with reference to Figure 9.

[0125] In the first and second embodiments, a DOE in which a bright spot is imaged was shown as an example. In this embodiment, a DOE in which a desired image is imaged will be described as an example.

[0126] In detail, in the first embodiment, z is z α ~z β (z is z α more than z β The following shows the electric field distribution on the DOE emission surface for which the light intensity distribution on a plane parallel to P0 within the range (below) is approximately equivalent.

[0127] Similarly, in the second embodiment, the imaging plane P n The electric field distribution on the DOE emission surface is shown for each of the light intensity distributions (n=1~N) that are approximately equivalent.

[0128] In this embodiment, a diffraction element (DOE) 30 that forms a two-dimensional shape on the imaging plane will be described. The diffraction element 30 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.

[0129] Figure 9 shows a flowchart illustrating the design method for the diffraction element 30 according to this embodiment.

[0130] First, the imaging plane P n Let q(x, y) be the light intensity distribution that is imaged on (n=1~N) (i.e., all imaging planes P). n (n=1~N) The light intensity distribution to be imaged is the same q(x,y). 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 Let (x, y) be (step S31). 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 cAlternatively, we can write (x, y) = √q(x, y) + j·0, where j represents the imaginary unit.

[0131] Next, the electric field distribution on the emission surface of the diffraction element 30 is calculated for a spherical wave focused on the z-axis at a predetermined distance from the emission surface (step S32).

[0132] Next, a predetermined range (for example, z α ~z β In step S32, the electric field distributions on the emission surface for each spherical wave calculated in step S32 are added together, taking into account that the phase of light changes in the direction of light propagation, to calculate the first electric field distribution u0(x, y) (step S33). Here, "summing up electric field distributions" means calculating the sum of each electric field distribution within a predetermined range, including the integral of the electric field distributions within a predetermined range.

[0133] Steps S32 and S33 are the same as the method for calculating the electric field distribution u0 on the DOE emission surface in the first and second embodiments, and are calculated using equations (15), (17), (21), and (22).

[0134] Next, the electric field distribution u on the DOE emission surface 0、l The (1' electric field distribution) is given by the first electric field distribution u0(x, y) and the second electric field distribution u as shown in equation (24). c It is calculated by performing a convolution integral with (x, y) (step S34). Here, the first electric field distribution u0(x, y) is the electric field distribution on the DOE emission surface for a spherical wave focused to a predetermined range on the optical axis.

[0135]

number

[0136] 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.

[0137] Also, u cThe shape represented by (x, y) can also be a bright spot, as shown in the first embodiment. Therefore, the electric field distribution u on the DOE emission surface in this embodiment 0、l (x, y) includes the electric field distribution u0(x, y) on the DOE emission surface in the first embodiment.

[0138] The resulting electric field distribution u on the DOE exit surface 0、l Using (x, y), the depth d(x, y) of the surface irregularities on the diffraction element 30 is calculated using equation (25).

[0139]

number

[0140] Here, n1 is the refractive index inside the diffraction element 30, n0 is the refractive index outside the diffraction element 30, λ is the wavelength of the propagating light (the light emitted from the diffraction element 30), and arg(u 0、l (x, y) is the electric field distribution u 0、l This is the argument of (x, y).

[0141] Using d(x, y), the thickness L(x, y) of the diffraction element 30 is calculated for each coordinate (x, y) on the DOE emission surface from equation (19), and the surface structure (undulation shape) of the diffraction element 30 is designed (step S35).

[0142] Based on the surface structure of the diffractive element 30 designed in this manner, the diffractive element 30 is manufactured in the same manner as in the first embodiment.

[0143] 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 can be removed as a surface.

[0144] 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).

[0145] 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.

[0146] 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.

[0147] In embodiments of the present invention, the equations that express the electric field distribution as an integral (for example, equations (15) and (17)) include equations that express the electric field distribution as the sum of discrete bright spots (for example, equations (21) and (22)).

[0148] In embodiments of the present invention, the diffraction element is designed using a computer.

[0149] 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]

[0150] 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]

[0151] 10 Diffraction element

Claims

1. A method for designing a diffraction element that phase-modulates incident light using a computer, The steps include determining the electric field distribution on the emission surface of the diffraction element for a spherical wave focused in a range between a first distance and a second distance from the emission surface, along a straight line perpendicular to the emission surface of the diffraction element, Let z be the coordinate on the aforementioned straight line, let k be the wavenumber of the light emitted from the emission surface, and let φ be the convergence angle that the emitted light makes with the aforementioned straight line. Ｂ When this is the case, Exp[-jkzcosφ Ｂ The steps include multiplying the electric field distribution on the emission surface for the spherical wave by ] and integrating over the range to calculate the first electric field distribution as the electric field distribution on the emission surface of the diffraction element, A step of determining 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. A method for designing a diffraction element that phase-modulates incident light using a computer, The steps include determining the electric field distribution on the emission surface of the diffraction element for a spherical wave focused in a range between a first distance and a second distance from the emission surface, along a straight line perpendicular to the emission surface of the diffraction element, Let z be the coordinate on the aforementioned straight line, let k be the wavenumber of the light emitted from the emission surface, and let φ be the convergence angle that the emitted light makes with the aforementioned straight line. Ｂ When this is the case, Exp[-jkzcosφ Ｂ The steps include: multiplying the electric field distribution on the emission surface for the spherical wave by ] and summing them up within the range to calculate the first electric field distribution as the electric field distribution on the emission surface of the diffraction element; A step of determining 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.

3. A step of calculating a second electric field distribution whose intensity is the positive square root of the light intensity distribution that is imaged on a plane perpendicular to the straight line arranged in the range, 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 or claim 2, comprising:

4. The first electric field distribution u ０ (x, y) are calculated using equation (A). A method for designing a diffraction element according to claim 1 or 2. [Math 1]

5. The depth d(x, y) of the surface irregularities of the diffracting element is expressed by equation (B). 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 emitted light, and arg(u ０、ｌ (x, y) is the deflection angle of the electric field distribution on the emission surface of the diffraction element.

6. 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.

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