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Curr. Opt. Photon. 2021; 5(5): 500-505

Published online October 25, 2021 https://doi.org/10.3807/COPP.2021.5.5.500

## Wide-fan-angle Flat-top Linear Laser Beam Generated by Long-pitch Diffraction Gratings

Mu Hyeon Lee1, Taesu Ryu1, Young-Hoon Kim2, Jin-Kyu Yang1,3

1Department of Optical Engineering, Kongju National University, Cheonan 31080, Korea
2United Science Institute Co. Ltd., Daejeon 34013, Korea
3Institute of Application and Fusion for Light, Kongju National University, Cheonan 31080, Korea

Corresponding author: jinkyuyang@kongju.ac.kr, ORCID 0000-0002-7907-2626

Received: June 10, 2021; Revised: July 22, 2021; Accepted: July 26, 2021

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

We demonstrated a wide-fan-angle flat-top irradiance pattern with a very narrow linewidth by using an aspheric lens and a long-pitch reflective diffraction grating. First, we numerically designed a diffraction- based linear beam homogenizer. The structure of the Al diffraction grating with an isosceles triangular shape was optimized with 0.1-mm pitch, 35.5° slope angle, and 0.02-mm radius of the rounding top. According to the numerical results, the linear uniformity of the irradiance was more sensitive to the working distance than to the shape of the Al grating. The designed Al grating reflector was fabricated by using a conventional mold injection and an Al coating process. A uniform linear irradiance of 405-nm laser diode with a 100-mm flat-top length and 0.176-mm linewidth was experimentally demonstrated at 140-mm working distance. We believe that our proposed linear beam homogenizer can be used in various potential applications at a precise inspection system such as three-dimensional morphology scanner with line lasers.

Keywords: Aspherical lens, Beam homogenizer, Grating, Line laser, Numerical modeling

OCIS codes: (050.0050) Diffraction and gratings; (080.1753) Computation methods; (140.3300) Laser beam shaping; (140.5960) Semiconductor lasers

The laser technology is one of widely used modern optical technologies in science and industry due to the non-divergence and coherence of the radiative light. Typically, the intensity distribution of laser beam has a Gaussian profile which provides high energy concentration. This strong point-like distribution is disadvantageous for a certain applications, for example, illuminations and material treatment. Recently, laser beam forming with uniform intensity distribution has been attractive not only in various industrial applications, but also in scientific research. Many optical systems were proposed for forming the laser light from the point-like Gaussian function to the flat-top function, for example, Powell lens, a refractive optical system and a cylindrical lens arrays with lenses [15]. Here, we propose a new method to make a wide-fan-angle uniform linear line beam with narrow linewidth by using a long-period reflective grating system with aspheric lens, which shows around 100 mm flat-top line within 0.1 mm linewidth at 140mm working distance. We believe this wide-fan-angle linear laser beam with narrow linewidth has a great potential as a precise laser source for three-dimensional morphology scanning.

### II. DESIGN AND SIMULATIONS

Typically, multi-mode lasers are homogenized by cylindrical lens array and a subsequent focusing lens. Thus, uniform linear light fields can be produced by transmission-type beam mixing [4, 5]. In this paper, we propose a new concept of linear beam homogenizer, reflection-type linear beam forming system. The proposed optical system consists of an aspherical lens and a long-pitch diffraction grating with an isosceles triangle. The commercial optical design software, LightTools (Synopsis, CA, USA) is used to design the grating structure and to optimize the optical system for ultra-wide flat-top linear beam forming [6]. Figure 1 shows the schematic view of a linear beam homogenizer by with a reflective grating system. In the simulation, a laser diode (LD) with an elliptical Gaussian irradiance is used as a light source, with emission wavelength of 405 nm and divergence angle of 1.92° in the vertical direction and 4.16° in the horizontal direction. In order to focus the beam at the screen, a typical optical pick-up laser lens is placed between LD and grating. The parameters of the aspheric lens are shown in Table 1. The Al grating surface is covered with transparent Polycarbonate (PC). The pitch of the diffraction grating is fixed to 0.1 mm which is about 250 times longer than the laser wavelength. The incident angle is set to 83.5°.

TABLE 1 Parameters of aspherical lens in simulationa)

SurfaceCurvature (R)Conic (C)A (4th)B (6th)C (8th)D (10th)
Front84.515−73.339−5.2810e-102.5219e-121.9786e-130
Rear−10.589−0.82856−2.0896e-5−8.8326e-107.9933e-113.2016e-13

a)The refractive index of lens is set to 1.5607.

Figure 1.Schematics of a linear beam homogenizer. (a) Schematic view of linear beam-forming optical setup with grating geometry, and (b) xz-cut view of schematics with optical system design parameters. The left inset in (b) indicates the cut view of Al grating with an isosceles triangular shape.

Before the design of grating shape, the distance between LD and aspherical lens (l1) was optimized for obtaining narrow linewidth on the screen. In the simulation, the emission surface of LD was fixed to 5 µm × 5 µm. From the simulation, when l1 was 17.9303 mm, the LD beam was focused at a distance of 170 mm from the lens.

In order to optimize a grating geometry, we numerically investigated intensity distribution of the reflected beam on the long-pitch triangular-shape Al grating as shown in Fig. 1. The distance from the lens to the grating (l2) was fixed at 30 mm. The screen was placed at a distance of 140 mm from the normal direction of the grating. In the simulation, we considered diffraction of the incident beam from the Al grating, with direction determined by the equation below [7],

sinθm+sinθi=mλnΛ,m=0,±1,±2,±3,,

where n is the refractive index of the materials in the incident side and m is the order of diffraction. Also, θi and θm are the incidence angle and the m-th order diffraction angle, respectively. In consideration of limited computation power, the total number of rays was set to 100,000 and a hundred diffraction orders from −59th to 40th were considered. Here, we assume that diffraction efficiency of all the order is constant because the pitch of the grating is much longer than the wavelength of the beam [5]. In addition, reflectivity and transmittance at the interface between PC and air was set as 50% to consider multiple reflections in the PC layer.

Figure 2.Dependence of uniformity of linear beam with grating angle. (a) Irradiance pattern in the screen generated by long-pitch reflective diffraction grating, (b) relative intensity distribution with different grating angle along the x-axis, (c) distribution along the y-axis, and (d) flat-top length and FWHM as a function of grating angle. The insets of (b) and (c) show the definitions of flat-top length and FWHM.

Figure 3.Dependence of uniformity of linear beam with grating curvature. (a) Relative intensity distribution with different radius of top circle of grating along the x-axis, (b) distribution along the y-axis, and (c) flat length and FWHM as a function of grating angle.

Finally, the irradiance patterns were numerically studied by changing the distance, z between grating and screen. In this simulation, the pitch, the top radius, and the slope angle of the grating were fixed to 0.1 mm, 0.02 mm, and 35.5°, respectively. Figure 4(a) shows the change of the relative distribution of irradiance pattern along the center of a linear beam when the distance z changes. As the distance increases, the intensity becomes strong and narrow. However, as the distance increases more than 150 mm, the intensity becomes weak without shape change. It implies that the irradiance is focused on the screen at a distance of about 150 mm, and this is well matched with the cross-sectional intensity distribution shown in Fig. 4(b). For further understanding, the flat-top length and FWHM of a linear irradiance pattern were calculated. According to Fig. 4(c), the uniformity of the irradiance pattern is sensitive to the distance between grating and screen, and the optimum value of the distance is 140 nm where the flat-top length is 110 nm and the FWHM is 0.06 mm.

Figure 4.Dependence of uniformity of linear beam with distance between grating and screen. (a) Relative intensity distribution with different distance, z between grating and screen along the x-axis, (b) distribution along the y-axis, and (c) flat length and FWHM as a function of distance, z.

### III. FABRICATION AND MEASUREMENTS

The Al grating reflector was fabricated by using a conventional mold injection and Al coating process. The inset of Fig. 5(c) shows the scanning electron microscopy (SEM) image of the cross-sectional view of a fabricated grating sample before Al coating. According to the SEM image, the pitch, top curvature, and angle of the grating are about 0.1 mm, 0.0357 mm and 37.5°, respectively as designed before. Figure 5(a) shows the irradiance pattern of the 405-nm laser diode and the experimental setup. The angle between the grating and the incident laser beam was set to 6.5° and the distance between the grating and the screen was 140 mm. The intensity distribution of an irradiance pattern at the screen was measured by a Si-photodetector with motor stage and a beam profiler. Figure 5(b) shows a captured image of an irradiance pattern by the beam profiler. There are multi laser spots along the y-axis, which could be removed by adjusting the incident angle of LD along the y-axis carefully. According to the intensity distribution along the x-axis in Fig. 5(c), the intensity variation from x = −50 mm to 50 mm was within ±10%, which agrees well with numerical results. By fitting the intensity distribution along the y-axis with a Gaussian function as shown in Fig. 5(d), the linewidth of the linear irradiance pattern was estimated about 0.184 mm, which is three times wider than numerical results (FWHM). If the angle of incidence and the distance from LD to lens are carefully adjusted, the linewidth could be close to the numerical results. The importance of the precise angular alignment of the LD and the aspheric lens was confirmed by tolerance simulation, where the 1% angular error arises the 3% linewidth error.

Figure 5.Experimental results. (a) Pictures of irradiance pattern of the 405-nm laser diode (upper) and experimental setup (lower), (b) image of a captured irradiance pattern by the beam profiler, (c) measured intensity distribution of irradiance pattern along the x-axis, and (d) distribution along the y-axis. The inset of (c) shows SEM image of a fabricated sample.

The most common method to generate the linear beam is cylindrical lens, but the irradiance distribution of a linear beam is not uniform and a fan angle is narrow [8]. Since Powell’s paper, the Powell lens has been used as an efficient optical component to make a flat-top line beam with a wide fan angle, but it is expensive [1, 8]. Our proposed method, a grating-based linear homogenizer, provides an ultra-wide fan angle with a very large flat-top region. To understand how efficient our grating-based linear beam is, uniformity and cross-sectional shape of irradiance pattern were numerically compared with those from plano-convex circular cylindrical lens and Powell lens. In this simulation, the light source and the aspherical lens were set as those at previous simulations. In the case of a cylindrical lens, the radius of a circular surface was set to 2.857 mm. According to the irradiance profile along the x-axis shown in Fig. 6(c), the intensity is strong at the center. The FWHM of the linear irradiance is about 0.09 mm [see in Fig. 6(d)]. If the curvature of the circular cylinder lens increases, the intensity of the irradiance at the center decreases and becomes a flat-top, but the linewidth increases. In the case of a Powell lens, we assumed that the front surface profile of the Powell lens follows polynomials of x as below:

Figure 6.Comparison of line uniformity generated by various linear beam homogenizers. (a) Schematic view of linear irradiance generated by cylindrical lens and (b) by Powell lens, (c) relative intensity distributions with various linear homogenizers along the x-axis, and (d) distributions along the y-axis.

z(x)=a0+a2x2+a4x4,

where a0 = 30, a2 = 0.2, a4 = −0.03, respectively. Here, z is the distance from the aspheric lens and x is the distance from the optic axis of the system. From numerical results shown in Fig. 6, the irradiance distribution appears symmetrically with two maximums along the x-axis and one maximum along the y-axis. In addition, the linewidth is about 0.12 mm. When a2 decreases, the intensity at the center increases and becomes a flat-top distribution along the x-axis, however, the length of the flat-top region becomes small. Therefore, the grating-based linear homogenizer is more powerful for making a wide-fan-angle and narrow linear irradiance pattern, simultaneously.

We numerically and experimentally demonstrated a wide-fan-angle flat-top linear laser beam with a very narrow linewidth by using an aspheric lens and a long-pitch diffraction grating. The aspheric lens focuses the emitted light from a 405 nm laser diode on the screen and the Al grating with a long-pitch isosceles triangular shape diffracts the light to form a uniform linear irradiance pattern. First, we numerically investigated the dependence of the irradiance pattern on the shape of the Al grating and system parameters. According to the numerical results, the linear uniformity of the irradiance was more sensitive to the working distance than to the shape of the Al grating. The structural parameters of a triangular Al grating were optimized with 0.1-mm pitch, 37.5° slope angle, and 0.02-mm radius of the rounding top. Based on numerical design, the Al grating reflector was fabricated by using a conventional mold injection and Al coating process. By using fabricated samples, we experimentally performed a uniform linear irradiance of 405-nm laser diode, which had a 100-mm flat-top length and 0.176-mm linewidth on the screen. The proposed grating-based linear homogenizer shows better performance of wide-fan-angle and narrow linear irradiation pattern than typical linear homogenizers such as cylindrical circular lens and Powell lens. We believe this wide-fan-angle linear laser beam with narrow linewidth has a great potential for application of precise line lasers such as three-dimensional morphology scan.

This work was supported by the Technology Development Program (S2719427) funded by the Ministry of SMEs and Startups (MSS, Korea).

1. I. Powell, “Design of a laser beam line expander,” Appl. Opt. 26, 3705-3709 (1987).
2. P. W. Rhodes and D. L. Shealy, “Refractive optical systems for irradiance redistribution of collimated radiation: their design and analysis,” Appl. Opt. 19, 3545-3553 (1980).
3. J. A. Hoffnagle and C. M. Johnson, “Design and performance of a refractive optical system that converts a Gaussian to a flattop beam,” Appl. Opt. 39, 5488-5499 (2000).
4. O. Homburg, D. Hauschild, F. Kubacki and V. Lissotschenko, “Efficient beam shaping for high-power laser applications,” Proc. SPIE 6216, 621608 (2006).
5. Y. V. Miklyaev, A. Krasnaberski, M. Ivanenko, A. Mikhailov, W. Imgrunt, L. Aschke and V. N. Lissotchenko, “Efficient diffractive optical elements from glass with continuous profiles,” Proc. SPIE 7913, 79130B (2011).
6. Z. Wang, G. Zhu, Y. Huang, X. Zhu and C. Zhu, “Analytical model of microlens array system homogenizer,” Opt. Laser Technol. 75, 214-220 (2015).
7. J. E. Harvey and R. N. Pfisterer, “Understanding diffraction grating behavior: including conical diffraction and Rayleigh anomalies from transmission gratings,” Opt. Eng. 58, 087105 (2019).
8. C.-Y. Wang, Q.-C. Tan and R.-H. Guo, “Design and optimization of a linear laser beam,” Lasers Eng. 27, 373-381 (2014).

### Article

#### Article

Curr. Opt. Photon. 2021; 5(5): 500-505

Published online October 25, 2021 https://doi.org/10.3807/COPP.2021.5.5.500

## Wide-fan-angle Flat-top Linear Laser Beam Generated by Long-pitch Diffraction Gratings

Mu Hyeon Lee1, Taesu Ryu1, Young-Hoon Kim2, Jin-Kyu Yang1,3

1Department of Optical Engineering, Kongju National University, Cheonan 31080, Korea
2United Science Institute Co. Ltd., Daejeon 34013, Korea
3Institute of Application and Fusion for Light, Kongju National University, Cheonan 31080, Korea

Correspondence to:jinkyuyang@kongju.ac.kr, ORCID 0000-0002-7907-2626

Received: June 10, 2021; Revised: July 22, 2021; Accepted: July 26, 2021

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

### Abstract

We demonstrated a wide-fan-angle flat-top irradiance pattern with a very narrow linewidth by using an aspheric lens and a long-pitch reflective diffraction grating. First, we numerically designed a diffraction- based linear beam homogenizer. The structure of the Al diffraction grating with an isosceles triangular shape was optimized with 0.1-mm pitch, 35.5° slope angle, and 0.02-mm radius of the rounding top. According to the numerical results, the linear uniformity of the irradiance was more sensitive to the working distance than to the shape of the Al grating. The designed Al grating reflector was fabricated by using a conventional mold injection and an Al coating process. A uniform linear irradiance of 405-nm laser diode with a 100-mm flat-top length and 0.176-mm linewidth was experimentally demonstrated at 140-mm working distance. We believe that our proposed linear beam homogenizer can be used in various potential applications at a precise inspection system such as three-dimensional morphology scanner with line lasers.

Keywords: Aspherical lens, Beam homogenizer, Grating, Line laser, Numerical modeling

### I. INTRODUCTION

The laser technology is one of widely used modern optical technologies in science and industry due to the non-divergence and coherence of the radiative light. Typically, the intensity distribution of laser beam has a Gaussian profile which provides high energy concentration. This strong point-like distribution is disadvantageous for a certain applications, for example, illuminations and material treatment. Recently, laser beam forming with uniform intensity distribution has been attractive not only in various industrial applications, but also in scientific research. Many optical systems were proposed for forming the laser light from the point-like Gaussian function to the flat-top function, for example, Powell lens, a refractive optical system and a cylindrical lens arrays with lenses [15]. Here, we propose a new method to make a wide-fan-angle uniform linear line beam with narrow linewidth by using a long-period reflective grating system with aspheric lens, which shows around 100 mm flat-top line within 0.1 mm linewidth at 140mm working distance. We believe this wide-fan-angle linear laser beam with narrow linewidth has a great potential as a precise laser source for three-dimensional morphology scanning.

### II. DESIGN AND SIMULATIONS

Typically, multi-mode lasers are homogenized by cylindrical lens array and a subsequent focusing lens. Thus, uniform linear light fields can be produced by transmission-type beam mixing [4, 5]. In this paper, we propose a new concept of linear beam homogenizer, reflection-type linear beam forming system. The proposed optical system consists of an aspherical lens and a long-pitch diffraction grating with an isosceles triangle. The commercial optical design software, LightTools (Synopsis, CA, USA) is used to design the grating structure and to optimize the optical system for ultra-wide flat-top linear beam forming [6]. Figure 1 shows the schematic view of a linear beam homogenizer by with a reflective grating system. In the simulation, a laser diode (LD) with an elliptical Gaussian irradiance is used as a light source, with emission wavelength of 405 nm and divergence angle of 1.92° in the vertical direction and 4.16° in the horizontal direction. In order to focus the beam at the screen, a typical optical pick-up laser lens is placed between LD and grating. The parameters of the aspheric lens are shown in Table 1. The Al grating surface is covered with transparent Polycarbonate (PC). The pitch of the diffraction grating is fixed to 0.1 mm which is about 250 times longer than the laser wavelength. The incident angle is set to 83.5°.

TABLE 1. Parameters of aspherical lens in simulationa).

SurfaceCurvature (R)Conic (C)A (4th)B (6th)C (8th)D (10th)
Front84.515−73.339−5.2810e-102.5219e-121.9786e-130
Rear−10.589−0.82856−2.0896e-5−8.8326e-107.9933e-113.2016e-13

a)The refractive index of lens is set to 1.5607..

Figure 1. Schematics of a linear beam homogenizer. (a) Schematic view of linear beam-forming optical setup with grating geometry, and (b) xz-cut view of schematics with optical system design parameters. The left inset in (b) indicates the cut view of Al grating with an isosceles triangular shape.

Before the design of grating shape, the distance between LD and aspherical lens (l1) was optimized for obtaining narrow linewidth on the screen. In the simulation, the emission surface of LD was fixed to 5 µm × 5 µm. From the simulation, when l1 was 17.9303 mm, the LD beam was focused at a distance of 170 mm from the lens.

In order to optimize a grating geometry, we numerically investigated intensity distribution of the reflected beam on the long-pitch triangular-shape Al grating as shown in Fig. 1. The distance from the lens to the grating (l2) was fixed at 30 mm. The screen was placed at a distance of 140 mm from the normal direction of the grating. In the simulation, we considered diffraction of the incident beam from the Al grating, with direction determined by the equation below [7],

$sinθm+sinθi=mλnΛ,m=0,±1,±2,±3,…,$

where n is the refractive index of the materials in the incident side and m is the order of diffraction. Also, θi and θm are the incidence angle and the m-th order diffraction angle, respectively. In consideration of limited computation power, the total number of rays was set to 100,000 and a hundred diffraction orders from −59th to 40th were considered. Here, we assume that diffraction efficiency of all the order is constant because the pitch of the grating is much longer than the wavelength of the beam [5]. In addition, reflectivity and transmittance at the interface between PC and air was set as 50% to consider multiple reflections in the PC layer.

Figure 2. Dependence of uniformity of linear beam with grating angle. (a) Irradiance pattern in the screen generated by long-pitch reflective diffraction grating, (b) relative intensity distribution with different grating angle along the x-axis, (c) distribution along the y-axis, and (d) flat-top length and FWHM as a function of grating angle. The insets of (b) and (c) show the definitions of flat-top length and FWHM.

Figure 3. Dependence of uniformity of linear beam with grating curvature. (a) Relative intensity distribution with different radius of top circle of grating along the x-axis, (b) distribution along the y-axis, and (c) flat length and FWHM as a function of grating angle.

Finally, the irradiance patterns were numerically studied by changing the distance, z between grating and screen. In this simulation, the pitch, the top radius, and the slope angle of the grating were fixed to 0.1 mm, 0.02 mm, and 35.5°, respectively. Figure 4(a) shows the change of the relative distribution of irradiance pattern along the center of a linear beam when the distance z changes. As the distance increases, the intensity becomes strong and narrow. However, as the distance increases more than 150 mm, the intensity becomes weak without shape change. It implies that the irradiance is focused on the screen at a distance of about 150 mm, and this is well matched with the cross-sectional intensity distribution shown in Fig. 4(b). For further understanding, the flat-top length and FWHM of a linear irradiance pattern were calculated. According to Fig. 4(c), the uniformity of the irradiance pattern is sensitive to the distance between grating and screen, and the optimum value of the distance is 140 nm where the flat-top length is 110 nm and the FWHM is 0.06 mm.

Figure 4. Dependence of uniformity of linear beam with distance between grating and screen. (a) Relative intensity distribution with different distance, z between grating and screen along the x-axis, (b) distribution along the y-axis, and (c) flat length and FWHM as a function of distance, z.

### III. FABRICATION AND MEASUREMENTS

The Al grating reflector was fabricated by using a conventional mold injection and Al coating process. The inset of Fig. 5(c) shows the scanning electron microscopy (SEM) image of the cross-sectional view of a fabricated grating sample before Al coating. According to the SEM image, the pitch, top curvature, and angle of the grating are about 0.1 mm, 0.0357 mm and 37.5°, respectively as designed before. Figure 5(a) shows the irradiance pattern of the 405-nm laser diode and the experimental setup. The angle between the grating and the incident laser beam was set to 6.5° and the distance between the grating and the screen was 140 mm. The intensity distribution of an irradiance pattern at the screen was measured by a Si-photodetector with motor stage and a beam profiler. Figure 5(b) shows a captured image of an irradiance pattern by the beam profiler. There are multi laser spots along the y-axis, which could be removed by adjusting the incident angle of LD along the y-axis carefully. According to the intensity distribution along the x-axis in Fig. 5(c), the intensity variation from x = −50 mm to 50 mm was within ±10%, which agrees well with numerical results. By fitting the intensity distribution along the y-axis with a Gaussian function as shown in Fig. 5(d), the linewidth of the linear irradiance pattern was estimated about 0.184 mm, which is three times wider than numerical results (FWHM). If the angle of incidence and the distance from LD to lens are carefully adjusted, the linewidth could be close to the numerical results. The importance of the precise angular alignment of the LD and the aspheric lens was confirmed by tolerance simulation, where the 1% angular error arises the 3% linewidth error.

Figure 5. Experimental results. (a) Pictures of irradiance pattern of the 405-nm laser diode (upper) and experimental setup (lower), (b) image of a captured irradiance pattern by the beam profiler, (c) measured intensity distribution of irradiance pattern along the x-axis, and (d) distribution along the y-axis. The inset of (c) shows SEM image of a fabricated sample.

### IV. DISCUSSION

The most common method to generate the linear beam is cylindrical lens, but the irradiance distribution of a linear beam is not uniform and a fan angle is narrow [8]. Since Powell’s paper, the Powell lens has been used as an efficient optical component to make a flat-top line beam with a wide fan angle, but it is expensive [1, 8]. Our proposed method, a grating-based linear homogenizer, provides an ultra-wide fan angle with a very large flat-top region. To understand how efficient our grating-based linear beam is, uniformity and cross-sectional shape of irradiance pattern were numerically compared with those from plano-convex circular cylindrical lens and Powell lens. In this simulation, the light source and the aspherical lens were set as those at previous simulations. In the case of a cylindrical lens, the radius of a circular surface was set to 2.857 mm. According to the irradiance profile along the x-axis shown in Fig. 6(c), the intensity is strong at the center. The FWHM of the linear irradiance is about 0.09 mm [see in Fig. 6(d)]. If the curvature of the circular cylinder lens increases, the intensity of the irradiance at the center decreases and becomes a flat-top, but the linewidth increases. In the case of a Powell lens, we assumed that the front surface profile of the Powell lens follows polynomials of x as below:

Figure 6. Comparison of line uniformity generated by various linear beam homogenizers. (a) Schematic view of linear irradiance generated by cylindrical lens and (b) by Powell lens, (c) relative intensity distributions with various linear homogenizers along the x-axis, and (d) distributions along the y-axis.

$z(x)=a0+a2x2+a4x4,$

where a0 = 30, a2 = 0.2, a4 = −0.03, respectively. Here, z is the distance from the aspheric lens and x is the distance from the optic axis of the system. From numerical results shown in Fig. 6, the irradiance distribution appears symmetrically with two maximums along the x-axis and one maximum along the y-axis. In addition, the linewidth is about 0.12 mm. When a2 decreases, the intensity at the center increases and becomes a flat-top distribution along the x-axis, however, the length of the flat-top region becomes small. Therefore, the grating-based linear homogenizer is more powerful for making a wide-fan-angle and narrow linear irradiance pattern, simultaneously.

### V. CONCLUSION

We numerically and experimentally demonstrated a wide-fan-angle flat-top linear laser beam with a very narrow linewidth by using an aspheric lens and a long-pitch diffraction grating. The aspheric lens focuses the emitted light from a 405 nm laser diode on the screen and the Al grating with a long-pitch isosceles triangular shape diffracts the light to form a uniform linear irradiance pattern. First, we numerically investigated the dependence of the irradiance pattern on the shape of the Al grating and system parameters. According to the numerical results, the linear uniformity of the irradiance was more sensitive to the working distance than to the shape of the Al grating. The structural parameters of a triangular Al grating were optimized with 0.1-mm pitch, 37.5° slope angle, and 0.02-mm radius of the rounding top. Based on numerical design, the Al grating reflector was fabricated by using a conventional mold injection and Al coating process. By using fabricated samples, we experimentally performed a uniform linear irradiance of 405-nm laser diode, which had a 100-mm flat-top length and 0.176-mm linewidth on the screen. The proposed grating-based linear homogenizer shows better performance of wide-fan-angle and narrow linear irradiation pattern than typical linear homogenizers such as cylindrical circular lens and Powell lens. We believe this wide-fan-angle linear laser beam with narrow linewidth has a great potential for application of precise line lasers such as three-dimensional morphology scan.

### ACKNOWLEDGMENT

This work was supported by the Technology Development Program (S2719427) funded by the Ministry of SMEs and Startups (MSS, Korea).

### Fig 1.

Figure 1.Schematics of a linear beam homogenizer. (a) Schematic view of linear beam-forming optical setup with grating geometry, and (b) xz-cut view of schematics with optical system design parameters. The left inset in (b) indicates the cut view of Al grating with an isosceles triangular shape.
Current Optics and Photonics 2021; 5: 500-505https://doi.org/10.3807/COPP.2021.5.5.500

### Fig 2.

Figure 2.Dependence of uniformity of linear beam with grating angle. (a) Irradiance pattern in the screen generated by long-pitch reflective diffraction grating, (b) relative intensity distribution with different grating angle along the x-axis, (c) distribution along the y-axis, and (d) flat-top length and FWHM as a function of grating angle. The insets of (b) and (c) show the definitions of flat-top length and FWHM.
Current Optics and Photonics 2021; 5: 500-505https://doi.org/10.3807/COPP.2021.5.5.500

### Fig 3.

Figure 3.Dependence of uniformity of linear beam with grating curvature. (a) Relative intensity distribution with different radius of top circle of grating along the x-axis, (b) distribution along the y-axis, and (c) flat length and FWHM as a function of grating angle.
Current Optics and Photonics 2021; 5: 500-505https://doi.org/10.3807/COPP.2021.5.5.500

### Fig 4.

Figure 4.Dependence of uniformity of linear beam with distance between grating and screen. (a) Relative intensity distribution with different distance, z between grating and screen along the x-axis, (b) distribution along the y-axis, and (c) flat length and FWHM as a function of distance, z.
Current Optics and Photonics 2021; 5: 500-505https://doi.org/10.3807/COPP.2021.5.5.500

### Fig 5.

Figure 5.Experimental results. (a) Pictures of irradiance pattern of the 405-nm laser diode (upper) and experimental setup (lower), (b) image of a captured irradiance pattern by the beam profiler, (c) measured intensity distribution of irradiance pattern along the x-axis, and (d) distribution along the y-axis. The inset of (c) shows SEM image of a fabricated sample.
Current Optics and Photonics 2021; 5: 500-505https://doi.org/10.3807/COPP.2021.5.5.500

### Fig 6.

Figure 6.Comparison of line uniformity generated by various linear beam homogenizers. (a) Schematic view of linear irradiance generated by cylindrical lens and (b) by Powell lens, (c) relative intensity distributions with various linear homogenizers along the x-axis, and (d) distributions along the y-axis.
Current Optics and Photonics 2021; 5: 500-505https://doi.org/10.3807/COPP.2021.5.5.500

TABLE 1 Parameters of aspherical lens in simulationa)

SurfaceCurvature (R)Conic (C)A (4th)B (6th)C (8th)D (10th)
Front84.515−73.339−5.2810e-102.5219e-121.9786e-130
Rear−10.589−0.82856−2.0896e-5−8.8326e-107.9933e-113.2016e-13

a)The refractive index of lens is set to 1.5607.

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Wonshik Choi,
Editor-in-chief