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Directional backlight module based on pixelated nano-gratings
Optics Communications 459 (2020) 125034
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Directional backlight module based on pixelated nano-gratings Yunli Zhang a,b , Donghui Yi a,b , Wen Qiao a,b ,∗, Linsen Chen a,b,c a
School of Optoelectronic Science and Engineering & Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006, China b Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province & Key Lab of Modern Optical Technologies of Education Ministry of China, Soochow University, Suzhou 215006, China c SVG Optronics, Co., Ltd, Suzhou 215026, China
ARTICLE
INFO
Keywords: Directional backlight Pixelated nanogratings Glasses-free 3D display
ABSTRACT A directional backlight is of great interest in the field of glasses-free 3D display, privacy display, and energy efficient display. In this paper, a directional backlight module including a LED light bar, a collimating lens, a diffuser, and a waveguide is proposed. The waveguide is covered by nanogratings with a density gradience to optimize the illumination uniformity and to preserve the angular divergence of the emitted light. The proposed directional backlight achieved a divergence angle of ±6.17◦ and a uniformity of 88%. The directional backlight based on pixelated nanogratings features good uniformity, thin form factor, low cost, and large tolerance of the fabrication process, thus can be used in the illumination of glass-free 3D display, privacy display, and energy efficient display.
1. Introduction Conventional backlight modules that are widely used in liquid crystal display (LCD) panels has the advantage of thin form factor, easy assembly, wide viewing angle, high light efficiency, and uniform illumination over the entire panel [1,2]. However, in many applications, such as glasses-free 3D display, privacy display, and energy efficient display, a directional backlight is highly desirable [3–9]. For example, in our previous work, we proposed a holographic 3D display technology with reduced refreshable data by separating the amplitude and the phase information. Under a collimated illumination, we have achieved a viewing angle of 40 degrees with 9-view horizontal motion parallax [10–12]. In the proposed 3D display system, the angular divergence in horizontal direction of the illumination plays an important role in the elimination of crosstalk and ghost images. K. Käläntär et al. studied a directional backlight structured with micro features and an inverted prism film. The backlight has achieved a luminance cone of ±9◦ , and a uniform spatial distribution of 90% [13– 16]. Fuji company proposed a cylindrical lens array that works with a shadow mask to provide a directional backlight [17]. Yi-Jun Wang et al. proposed a directional backlight with two groups of micro-prism arrays. The backlight offered ±4◦ of FWHM on both directions [18]. He later demonstrated a directional backlight with tunable viewing angle by a striped diffuser [19]. Most recently, Chen designed a directional backlight module with inverse prisms to control the viewing angle within 100◦ in the horizontal direction and 35◦ in the vertical direction. The uniformity was 82% in the system [20].
Despite the great efforts that researchers have made, the design and fabrication of directional backlight is still very hard, especially for the applications that demand narrow angular divergence of illumination. In addition, because of the high sensitivity of human vision to light intensity variation, the requirement on the uniformity of the illumination is quite high. Moreover, the form factor should be considered for the application of display. A thin flat form is always desirable so that the directional backlight module can be incorporated within a flat display system. Last but not the least, the potential of mass production and low cost should always be considered for a design that can be employed to the industry [21,22]. In this paper, we propose an edge-lit directional backlight with a LED light source, a diffuser, a collimating lens, and a waveguide. We first designed a diffuser with the micro cylindrical lens arrays to improve the illumination uniformity. We further propose a waveguide with pixelated nanogratings to redirect light to the normal direction above the screen. The directional backlight module based on the pixelated nanogratings has an angular divergence of ±6.17◦ , and a uniformity of 95.7% in the 𝑥-direction and 86.8% in the 𝑦-direction. 2. Theory 2.1. The systematic design The directional backlight module proposed in this paper is composed of a collimated LED light source, a diffuser, and a waveguide.
∗ Corresponding author. E-mail address: [email protected] (W. Qiao).
https://doi.org/10.1016/j.optcom.2019.125034 Received 14 September 2019; Received in revised form 23 November 2019; Accepted 27 November 2019 Available online 3 December 2019 0030-4018/© 2019 Elsevier B.V. All rights reserved.
Y. Zhang, D. Yi, W. Qiao et al.
Optics Communications 459 (2020) 125034
The schematic diagram of the edge-lit directional backlight module is shown in Fig. 1. In what follows, x-y plane is the plane where the rectangular waveguide is laid, x direction refers to the direction that the light propagates within the waveplate, y direction refers to the direction where the LED light bar is laid, and z direction is normal to the waveguide. Because LEDs have the advantages of high brightness, good uniformity, long lifetime, and low cost, so they are widely adopted in lighting and illumination [23]. The light rays from a LED light bar passes through a cylindrical lens to collimate the light in the z direction. Then the collimated light travels through a diffuser to mix up the illumination gap between LEDs. Next, the one-directional collimated light beam is coupled within the waveguide. A small bundle of light ray leaks from the waveguide when the total internal reflection is disrupted by the pixelated nanogratings. Finally, successive light beams are coupled out from the waveguide by nanogratings and propagate in the z direction without changing the angular divergence of the light beam. Here, angular divergence is an angular measure of the increment in light beam diameter with distance. The divergence angle is evaluated by FWHM and also refers to the viewing angle in the directional backlight. For a desired emission angle from the waveguide, the period of the grating can be calculated by the grating equation [24]: 𝑑(𝑛1 sin 𝜃 ± 𝑛2 sin 𝜑) = 𝑘𝜆
waveguide, light intensity decreases as more and more light are coupled out by the nanogratings. Therefore, it is necessary to gradually tune the light efficiency of the nanogratings to achieve uniform illumination across the display screen. The tunable parameters include: the diffraction efficiency, the pixel size and the pixel density of the pixelated nanogratings. Here we optimized the illumination uniformity by varying the pixel distribution of nanogratings along the x direction. The light efficiency per region 𝑒 is determined by the structural parameters of nanogratings, including the pixel size, depth, the inclination angle, the groove profile, as well as the pixel density of the nanograting. Assume the total intensity of the incident light that coupled from the light source is I. When the incident light is diffracted by the nano-grating in the first region, the intensity of the emitted light is 𝐼1 ’ is: 𝐼1′ = 𝐼 ⋅ 𝑒
(2)
The intensity 𝐼2 ’ of the light that propagates along the waveguide, and diffracted by nanogratings in the second region is governed by: 𝐼2′ = 𝐼 ⋅ 𝑒 ⋅ (1 − 𝑒)
(3)
Similarly, the intensity 𝐼𝑚 ’ of the light that propagates along the waveguide, and diffracted by nanogratings in the 𝑚th region can be calculated by:
(1)
𝐼𝑚′ = 𝐼 ⋅ 𝑒(1 − 𝑒)𝑚−1
where 𝑛1 is the refractive index of air, 𝑛2 is the refractive index of the waveguide, 𝜃 is the incident angle of the light, 𝜑 is the diffraction angle of the light, 𝑘 is the diffraction order, and d is the period of the nanograting. From Eq. (1), we calculate that the period of the grating is 513 nm when the incident angle is 45◦ and the diffracted light escaped from the waveguide travels in the z direction. From Eq. (1), the emission angle of the diffracted light is affected only by the period of the nanogratings and the incident angle. In prior art [18–20,25], micro-prisms are widely used in waveguides to break the total internal reflection for directional illumination. The surface profile of the micro-prisms, including the base angle, the vertex angle, and the smoothness of the inclined surface, plays an important role in the light manipulation. However, surface profile can hardly be 100% preserved in mass production. As a result, the angular divergence of illumination will be significantly broadened, especially for a large panel. In comparison, the surface profile of the nanogratings, such as sine shape or rectangular shape, will not influence the propagating direction of the incident light, providing a large tolerance in fabrication process.
(4)
Consider the total light efficiency 𝑆𝐼 that extracted by the nanogratings over the entire waveguide: 𝑆𝐼 = 1 − (1 − 𝑒)𝑚
(5)
Since the structural parameter of nanogratings, such as the groove profile and the inclination angle, cannot be easily tuned in fabrication process, we choose to vary the pixel density. For simplicity, we divide the nanogratings along the x direction into multiple regions and further assume that the nanogratings are evenly distributed within a region. Moreover, we assume that the intensity of diffracted light increases linearly as the pixel density. To increase the light efficiency, a design with a large number of nanogratings is preferable. As illustrated by Fig. 3(a), when the diffraction efficiency of nanograting is 25% and the pixel size is 40 μm, the light efficiency per region is around 0.2% and the number of pixelated nanogratings should be larger than 1000 for the total light efficiency of 80%. The simulated spatial distribution of nanogratings along the x direction is shown in Fig. 3(b). From the curve, the pixel density of nanogratings increases dramatical as the distance from the LED light increases. Moreover, the light efficiency can be improved by increasing the total number of nanogratings in the waveguide. However, the maximum number of the nanogratings is limited by the maximum pixel density at the edge far from the LED light to prevent overlapping effect between pixels. The number of pixels is set to be 2000. The light efficiency by simulation is 85%.
2.2. The design of diffuser Here we adopted a LED array for illumination. To minimize the variation in light intensity caused by the gap between LEDs, we adopted a diffuser comprised of micro cylindrical lens array. We built a model of LEDs (Lighttools, Synopsis) and seek for the optimized structure for light diffusion (Fig. 2(a-b)). By comparing the irradiance pattern with different vector height and period, we find the optimized micro cylindrical lens structure with a vector height of 50 μm and a period of 100 μm. For the light beam travels in the x direction within the waveguide, as shown in Fig. 2(c-f), the angular divergence of the irradiance expended from ±15◦ to ±60◦ in y direction. The insertion of the diffuser does not affect the intensity distribution along z direction.
3. Experimental results 3.1. Fabrication of nanogratings in the waveguide The fabrication process of nanogratings is conducted by a homemade lithography system (NANOCRYSTAL200, SVG Optronics) as described in the previous work [26]. Briefly, a glass substrate with a thickness of 1 mm and a size of 20 cm×15 cm was pre-cleaned and was coated by a spinner with positive photoresist (RJZ-390, RUIHONG Electronics Chemicals) at the thickness of 1 μm. The nanogratings patterned by interference lithography system was fully developed NaOH solvent. The patterned nanogratings on a waveguide is shown in Fig. 4(a), with a depth of 200 nm. As shown in Fig. 4(b), the pixel size of the nanograting is 40 μm × 40 μm, and the period of the nanograting is 517 nm. Although the
2.3. The design of pixelated nanogratings As aforementioned, pixelated nanogratings are adopted to break total internal refection, and redirect the light to travel along the z direction in space. The amount of light that diffracted from a pixel is determined by the total intensity of the incident light, the pixel size, and the diffraction efficiency. When the light propagates in the 2
Y. Zhang, D. Yi, W. Qiao et al.
Optics Communications 459 (2020) 125034
Fig. 1. The schematic diagram of directional backlight module.
Fig. 2. (a-b)The model of diffuser built in simulation. light distribution of single LED light source (c-d) without diffuser and (e-f) with diffuser.
Electronics Chemicals). After reflow process at a temperature of 90 ◦ C, the patterned cylindrical lens array was electroplated to form a Nickel master mold. Then the micropatterned structures in the Ni mold were transferred to a PET film with a thickness of 180 μm by UV nanoimprinting. The period of the micro cylindrical lens in the PET diffuser is 100 μm and the vector height is 50 μm. We built up the edge-lit directional backlight module as shown in Fig. 5. Here we used a LED light bar that is comprised of 28 LED chips (5730) to form an illumination area of 100 mm × 2 mm. The angular divergence of the LED light source is about ±60◦ [27]. We collimate the LED light in one direction by a cylindrical lens. The cylindrical lens
period of the patterned nanograting is slightly different from the target period in the calculation, the involved error in terms of the emission angle of the diffracted light is within 0.5◦ , which is within the acceptable range of the tolerance. The spatial distribution of nanogratings along the x direction is shown in Fig. 4(d–g). The density of nanogratings increases as the distance from the LED light bar increases. 3.2. System setup The diffuser is patterned by laser direct writing lithography system (Miscan, SVG Optronics) on positive photoresist (RJZ-390, RUIHONG 3
Y. Zhang, D. Yi, W. Qiao et al.
Optics Communications 459 (2020) 125034
Fig. 3. The simulated distribution of the number of pixels on the guide plate.
Fig. 4. (a) The photo of waveguide patterned with nanogratings. (b-c) SEM image of nano-gratings. (d-g) The microscopic images of nanogratings with varied density across the panel.
has a radius of curvature of 9 mm and reduces the angular divergence in horizontal direction to ±4.46◦ . The width of the cylindrical lens is 10 mm, and the height is 16 mm. The gap between the LED light and the cylindrical lens is 5 mm. The one directional collimated light is couple into the waveguide by a small prism at an angle of 45◦ . The irradiance distribution across the waveguide is evaluated by a CCD camera(ANDONSTAR A7, Maimeiou Electronics Co.). 3.3. Uniformity of the illumination The uniformity of the illumination is defined as the division of maximum intensity by the minimum intensity as follows: 𝑈 (%) =
𝐿(𝑖, 𝑗)𝑚𝑖𝑛 × 100% 𝐿(𝑖, 𝑗)𝑚𝑎𝑥
(6)
where 𝑈 is the uniformity of illumination, 𝐿(𝑖, 𝑗)𝑚𝑖𝑛 is the minimum intensity across the panel, 𝐿(𝑖, 𝑗)𝑚𝑎𝑥 is the maximum intensity. The higher the value of the uniformity, the smaller the variation of intensity within the illuminating area. Fig. 6(a) compared the irradiance distribution along 𝑦-direction before and after inserting a diffuser between the LED light source and the collimating cylindrical lens. The uniformity increased from 34% to 86.8% after the insertion of diffuser. The hotspots caused by the illumination gap between LEDs are greatly eliminated. In Fig. 6(b), the irradiance curve along the 𝑥-direction for pixelated nanogratings evenly distributed in the 𝑥-direction drops dramatically as expected. The uniformation is 9.95%. When the pixel density increases in the 𝑥direction according to the curve illustrated in Fig. 4, the uniformity is increased to 95.7%. According to EBU report [28], the acceptable value of uniformity is 80%. Therefore, the uniformity in both directions has been significantly improved after optimization and is well above the acceptable value.
Fig. 5. Experimental setup of directional backlight module.
3.4. The angular divergence The angular divergence of the illumination is a key parameter for directional backlight. A mask with square holes is placed right in front of the waveguide. The irradiance patterns at multiple height above the waveguide are measured. The angular divergence can be determined by: 𝑊2 − 𝑊1 ) (7) 2⋅𝐿 where 𝛼 is the angular divergence of illumination, 𝑊2 and 𝑊1 are the width of the irradiance pattern at different height. L is the vertical distance between the two measurements (Fig. 7). The angular divergences are measured at 5 spots. The averaged angular divergence is ±6.17◦ . 𝛼 = arctan(
4
Y. Zhang, D. Yi, W. Qiao et al.
Optics Communications 459 (2020) 125034
Fig. 6. (a) the light uniformity with and without diffuser. (b) the light uniformity with and without density gradience of nanogratings.
Fig. 7. (a) the apertures used in the measurement. (b) the schematic diagram of the measurement. (c) The measured width of the irradiance pattern at different height.
Acknowledgments
Ideally, the pixelated nanogratings can keep the high directionality of the light ray without distortion (FWHM < 1◦ for a pixel size of 40 μm). A free-form collimating lens can greatly reduce the angular divergence by providing a well collimated light source. Surface irregularities and second order diffraction may be the minor reasons of the spread of light during propagation.
The work was supported by the Natural Science Foundation of China (NSFC) (61975140, 61575135), the Major Basic Research Project of the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (16KJA510002), the Suzhou Natural Science Foundation of China (SYG201930), and the project of the Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions, China. We also thank the SVG Optronics Corporation for the experimental support.
4. Conclusion The edge-lit directional backlight module studied in this paper can be divided into four parts: a LED light bar, a one-directional diffuser, a cylindrical collimating lens, and waveguide. Firstly, a LED light source with a wavelength of 532 nm is collimated by a flat convex cylindrical lens to provide a collimated illumination with an angular divergence of ±4.46◦ . Secondly, a diffuser with micro cylindrical lens array is used to eliminate the illumination gap by the LED array. Finally, the spatial density of the pixelated nanogratings are optimized to improve the uniformity of the system along the 𝑥-direction. The directional backlight module based on the pixelated nanogratings has an angular divergence of ±6.17◦ in the 𝑥-direction, an uniformity of 95.7% and 86.8% in the x, and 𝑦-direction, respectively. The proposed directional backlight is compatible with the architecture of commercial backlight module, thus can be integrated with most LCD panels in the market. The mass production of diffuser and the waveguide can be conducted by nanoimprinting process, which features high throughput and low cost. With thin form factor and simple assembly, the proposed directional backlight can be used in glasses-free 3D display, privacy display, and energy efficient display.
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CRediT authorship contribution statement Yunli Zhang: Data curation, Writing — original draft. Donghui Yi: Visualization, Investigation. Wen Qiao: Supervision, Writing — review & editing. Linsen Chen: Conceptualization, Methodology.
[8] D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, R.G. Beausoleil, A multidirectional backlight for a wide-angle, glasses-free three-dimensional display, Nature 495 (7441) (2013) 348–351. 5
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[9] T.C. Teng, L.W. Tseng, Design of a bidirectional backlight using a pair of stacked light guide plates for large dual-view and 3D displays, Appl. Opt. 54 (3) (2015) 509–516. [10] W.Q. Wan, W. Qiao, W.B. Huang, M. Zhu, Z.B. Fang, D.L. Pu, Y. Ye, Y.H. Liu, L.S. Chen, Efficient fabrication method of nano-grating for 3D holographic display with full parallax views, Opt. Express 24 (6) (2016) 6203–6212. [11] W.Q. Wan, W. Qiao, W.B. Huang, M. Zhu, Y. Ye, X.Y. Chen, L.S. Chen, Multiview holographic 3D dynamic display by combining a nano-grating patterned phase plate and LCD, Opt. Express 25 (2) (2017) 1114–1122. [12] W. Qiao, W.B. Huang, Y.H. Liu, X.M. Li, L.S. Chen, J.X. Tang, Toward scalable flexible nanomanufacturing for photonic structures and devices, Adv. Mater. 28 (47) (2016) 10353–10380. [13] K. Käläntär, A directional backlight with narrow angular luminance distribution for widening the viewing angle for an LCD with a front-surface light-scattering film, J. Soc. Inf. Disp. 20 (3) (2012) 133–142. [14] K. Käläntär, M. Okada, H. Ishiko, Monolithic block-wised light guide with controlled optical crosstalk for field-sequential color/scanning LCD, in: SID Symposium Digest of Technical Papers, Wiley Online Library, 2009, pp. 1038–1041. [15] K. Käläntär, M. Okada, A monolithic block-wise functional light guide for 2-d dimming LCD backlight, in: SID Symposium Digest of Technical Papers, Wiley Online Library, 2010, pp. 997–1000. [16] K. Käläntär, An intensively lit collimating unit for the realization of a mosaic-structured large-scale RGB backlight, J. Soc. Inf. Disp. 14 (8) (2006) 687–694. [17] A. Yamaguchi, Liquid-crystal display apparatus including a backlight section using collimating plate, Google Patents, US Patent 6, 421, 103, 2002.
6
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Directional backlight module based on pixelated nano-gratings Yunli Zhang a,b , Donghui Yi a,b , Wen Qiao a,b ,∗, Linsen Chen a,b,c a
School of Optoelectronic Science and Engineering & Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006, China b Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province & Key Lab of Modern Optical Technologies of Education Ministry of China, Soochow University, Suzhou 215006, China c SVG Optronics, Co., Ltd, Suzhou 215026, China
ARTICLE
INFO
Keywords: Directional backlight Pixelated nanogratings Glasses-free 3D display
ABSTRACT A directional backlight is of great interest in the field of glasses-free 3D display, privacy display, and energy efficient display. In this paper, a directional backlight module including a LED light bar, a collimating lens, a diffuser, and a waveguide is proposed. The waveguide is covered by nanogratings with a density gradience to optimize the illumination uniformity and to preserve the angular divergence of the emitted light. The proposed directional backlight achieved a divergence angle of ±6.17◦ and a uniformity of 88%. The directional backlight based on pixelated nanogratings features good uniformity, thin form factor, low cost, and large tolerance of the fabrication process, thus can be used in the illumination of glass-free 3D display, privacy display, and energy efficient display.
1. Introduction Conventional backlight modules that are widely used in liquid crystal display (LCD) panels has the advantage of thin form factor, easy assembly, wide viewing angle, high light efficiency, and uniform illumination over the entire panel [1,2]. However, in many applications, such as glasses-free 3D display, privacy display, and energy efficient display, a directional backlight is highly desirable [3–9]. For example, in our previous work, we proposed a holographic 3D display technology with reduced refreshable data by separating the amplitude and the phase information. Under a collimated illumination, we have achieved a viewing angle of 40 degrees with 9-view horizontal motion parallax [10–12]. In the proposed 3D display system, the angular divergence in horizontal direction of the illumination plays an important role in the elimination of crosstalk and ghost images. K. Käläntär et al. studied a directional backlight structured with micro features and an inverted prism film. The backlight has achieved a luminance cone of ±9◦ , and a uniform spatial distribution of 90% [13– 16]. Fuji company proposed a cylindrical lens array that works with a shadow mask to provide a directional backlight [17]. Yi-Jun Wang et al. proposed a directional backlight with two groups of micro-prism arrays. The backlight offered ±4◦ of FWHM on both directions [18]. He later demonstrated a directional backlight with tunable viewing angle by a striped diffuser [19]. Most recently, Chen designed a directional backlight module with inverse prisms to control the viewing angle within 100◦ in the horizontal direction and 35◦ in the vertical direction. The uniformity was 82% in the system [20].
Despite the great efforts that researchers have made, the design and fabrication of directional backlight is still very hard, especially for the applications that demand narrow angular divergence of illumination. In addition, because of the high sensitivity of human vision to light intensity variation, the requirement on the uniformity of the illumination is quite high. Moreover, the form factor should be considered for the application of display. A thin flat form is always desirable so that the directional backlight module can be incorporated within a flat display system. Last but not the least, the potential of mass production and low cost should always be considered for a design that can be employed to the industry [21,22]. In this paper, we propose an edge-lit directional backlight with a LED light source, a diffuser, a collimating lens, and a waveguide. We first designed a diffuser with the micro cylindrical lens arrays to improve the illumination uniformity. We further propose a waveguide with pixelated nanogratings to redirect light to the normal direction above the screen. The directional backlight module based on the pixelated nanogratings has an angular divergence of ±6.17◦ , and a uniformity of 95.7% in the 𝑥-direction and 86.8% in the 𝑦-direction. 2. Theory 2.1. The systematic design The directional backlight module proposed in this paper is composed of a collimated LED light source, a diffuser, and a waveguide.
∗ Corresponding author. E-mail address: [email protected] (W. Qiao).
https://doi.org/10.1016/j.optcom.2019.125034 Received 14 September 2019; Received in revised form 23 November 2019; Accepted 27 November 2019 Available online 3 December 2019 0030-4018/© 2019 Elsevier B.V. All rights reserved.
Y. Zhang, D. Yi, W. Qiao et al.
Optics Communications 459 (2020) 125034
The schematic diagram of the edge-lit directional backlight module is shown in Fig. 1. In what follows, x-y plane is the plane where the rectangular waveguide is laid, x direction refers to the direction that the light propagates within the waveplate, y direction refers to the direction where the LED light bar is laid, and z direction is normal to the waveguide. Because LEDs have the advantages of high brightness, good uniformity, long lifetime, and low cost, so they are widely adopted in lighting and illumination [23]. The light rays from a LED light bar passes through a cylindrical lens to collimate the light in the z direction. Then the collimated light travels through a diffuser to mix up the illumination gap between LEDs. Next, the one-directional collimated light beam is coupled within the waveguide. A small bundle of light ray leaks from the waveguide when the total internal reflection is disrupted by the pixelated nanogratings. Finally, successive light beams are coupled out from the waveguide by nanogratings and propagate in the z direction without changing the angular divergence of the light beam. Here, angular divergence is an angular measure of the increment in light beam diameter with distance. The divergence angle is evaluated by FWHM and also refers to the viewing angle in the directional backlight. For a desired emission angle from the waveguide, the period of the grating can be calculated by the grating equation [24]: 𝑑(𝑛1 sin 𝜃 ± 𝑛2 sin 𝜑) = 𝑘𝜆
waveguide, light intensity decreases as more and more light are coupled out by the nanogratings. Therefore, it is necessary to gradually tune the light efficiency of the nanogratings to achieve uniform illumination across the display screen. The tunable parameters include: the diffraction efficiency, the pixel size and the pixel density of the pixelated nanogratings. Here we optimized the illumination uniformity by varying the pixel distribution of nanogratings along the x direction. The light efficiency per region 𝑒 is determined by the structural parameters of nanogratings, including the pixel size, depth, the inclination angle, the groove profile, as well as the pixel density of the nanograting. Assume the total intensity of the incident light that coupled from the light source is I. When the incident light is diffracted by the nano-grating in the first region, the intensity of the emitted light is 𝐼1 ’ is: 𝐼1′ = 𝐼 ⋅ 𝑒
(2)
The intensity 𝐼2 ’ of the light that propagates along the waveguide, and diffracted by nanogratings in the second region is governed by: 𝐼2′ = 𝐼 ⋅ 𝑒 ⋅ (1 − 𝑒)
(3)
Similarly, the intensity 𝐼𝑚 ’ of the light that propagates along the waveguide, and diffracted by nanogratings in the 𝑚th region can be calculated by:
(1)
𝐼𝑚′ = 𝐼 ⋅ 𝑒(1 − 𝑒)𝑚−1
where 𝑛1 is the refractive index of air, 𝑛2 is the refractive index of the waveguide, 𝜃 is the incident angle of the light, 𝜑 is the diffraction angle of the light, 𝑘 is the diffraction order, and d is the period of the nanograting. From Eq. (1), we calculate that the period of the grating is 513 nm when the incident angle is 45◦ and the diffracted light escaped from the waveguide travels in the z direction. From Eq. (1), the emission angle of the diffracted light is affected only by the period of the nanogratings and the incident angle. In prior art [18–20,25], micro-prisms are widely used in waveguides to break the total internal reflection for directional illumination. The surface profile of the micro-prisms, including the base angle, the vertex angle, and the smoothness of the inclined surface, plays an important role in the light manipulation. However, surface profile can hardly be 100% preserved in mass production. As a result, the angular divergence of illumination will be significantly broadened, especially for a large panel. In comparison, the surface profile of the nanogratings, such as sine shape or rectangular shape, will not influence the propagating direction of the incident light, providing a large tolerance in fabrication process.
(4)
Consider the total light efficiency 𝑆𝐼 that extracted by the nanogratings over the entire waveguide: 𝑆𝐼 = 1 − (1 − 𝑒)𝑚
(5)
Since the structural parameter of nanogratings, such as the groove profile and the inclination angle, cannot be easily tuned in fabrication process, we choose to vary the pixel density. For simplicity, we divide the nanogratings along the x direction into multiple regions and further assume that the nanogratings are evenly distributed within a region. Moreover, we assume that the intensity of diffracted light increases linearly as the pixel density. To increase the light efficiency, a design with a large number of nanogratings is preferable. As illustrated by Fig. 3(a), when the diffraction efficiency of nanograting is 25% and the pixel size is 40 μm, the light efficiency per region is around 0.2% and the number of pixelated nanogratings should be larger than 1000 for the total light efficiency of 80%. The simulated spatial distribution of nanogratings along the x direction is shown in Fig. 3(b). From the curve, the pixel density of nanogratings increases dramatical as the distance from the LED light increases. Moreover, the light efficiency can be improved by increasing the total number of nanogratings in the waveguide. However, the maximum number of the nanogratings is limited by the maximum pixel density at the edge far from the LED light to prevent overlapping effect between pixels. The number of pixels is set to be 2000. The light efficiency by simulation is 85%.
2.2. The design of diffuser Here we adopted a LED array for illumination. To minimize the variation in light intensity caused by the gap between LEDs, we adopted a diffuser comprised of micro cylindrical lens array. We built a model of LEDs (Lighttools, Synopsis) and seek for the optimized structure for light diffusion (Fig. 2(a-b)). By comparing the irradiance pattern with different vector height and period, we find the optimized micro cylindrical lens structure with a vector height of 50 μm and a period of 100 μm. For the light beam travels in the x direction within the waveguide, as shown in Fig. 2(c-f), the angular divergence of the irradiance expended from ±15◦ to ±60◦ in y direction. The insertion of the diffuser does not affect the intensity distribution along z direction.
3. Experimental results 3.1. Fabrication of nanogratings in the waveguide The fabrication process of nanogratings is conducted by a homemade lithography system (NANOCRYSTAL200, SVG Optronics) as described in the previous work [26]. Briefly, a glass substrate with a thickness of 1 mm and a size of 20 cm×15 cm was pre-cleaned and was coated by a spinner with positive photoresist (RJZ-390, RUIHONG Electronics Chemicals) at the thickness of 1 μm. The nanogratings patterned by interference lithography system was fully developed NaOH solvent. The patterned nanogratings on a waveguide is shown in Fig. 4(a), with a depth of 200 nm. As shown in Fig. 4(b), the pixel size of the nanograting is 40 μm × 40 μm, and the period of the nanograting is 517 nm. Although the
2.3. The design of pixelated nanogratings As aforementioned, pixelated nanogratings are adopted to break total internal refection, and redirect the light to travel along the z direction in space. The amount of light that diffracted from a pixel is determined by the total intensity of the incident light, the pixel size, and the diffraction efficiency. When the light propagates in the 2
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Optics Communications 459 (2020) 125034
Fig. 1. The schematic diagram of directional backlight module.
Fig. 2. (a-b)The model of diffuser built in simulation. light distribution of single LED light source (c-d) without diffuser and (e-f) with diffuser.
Electronics Chemicals). After reflow process at a temperature of 90 ◦ C, the patterned cylindrical lens array was electroplated to form a Nickel master mold. Then the micropatterned structures in the Ni mold were transferred to a PET film with a thickness of 180 μm by UV nanoimprinting. The period of the micro cylindrical lens in the PET diffuser is 100 μm and the vector height is 50 μm. We built up the edge-lit directional backlight module as shown in Fig. 5. Here we used a LED light bar that is comprised of 28 LED chips (5730) to form an illumination area of 100 mm × 2 mm. The angular divergence of the LED light source is about ±60◦ [27]. We collimate the LED light in one direction by a cylindrical lens. The cylindrical lens
period of the patterned nanograting is slightly different from the target period in the calculation, the involved error in terms of the emission angle of the diffracted light is within 0.5◦ , which is within the acceptable range of the tolerance. The spatial distribution of nanogratings along the x direction is shown in Fig. 4(d–g). The density of nanogratings increases as the distance from the LED light bar increases. 3.2. System setup The diffuser is patterned by laser direct writing lithography system (Miscan, SVG Optronics) on positive photoresist (RJZ-390, RUIHONG 3
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Optics Communications 459 (2020) 125034
Fig. 3. The simulated distribution of the number of pixels on the guide plate.
Fig. 4. (a) The photo of waveguide patterned with nanogratings. (b-c) SEM image of nano-gratings. (d-g) The microscopic images of nanogratings with varied density across the panel.
has a radius of curvature of 9 mm and reduces the angular divergence in horizontal direction to ±4.46◦ . The width of the cylindrical lens is 10 mm, and the height is 16 mm. The gap between the LED light and the cylindrical lens is 5 mm. The one directional collimated light is couple into the waveguide by a small prism at an angle of 45◦ . The irradiance distribution across the waveguide is evaluated by a CCD camera(ANDONSTAR A7, Maimeiou Electronics Co.). 3.3. Uniformity of the illumination The uniformity of the illumination is defined as the division of maximum intensity by the minimum intensity as follows: 𝑈 (%) =
𝐿(𝑖, 𝑗)𝑚𝑖𝑛 × 100% 𝐿(𝑖, 𝑗)𝑚𝑎𝑥
(6)
where 𝑈 is the uniformity of illumination, 𝐿(𝑖, 𝑗)𝑚𝑖𝑛 is the minimum intensity across the panel, 𝐿(𝑖, 𝑗)𝑚𝑎𝑥 is the maximum intensity. The higher the value of the uniformity, the smaller the variation of intensity within the illuminating area. Fig. 6(a) compared the irradiance distribution along 𝑦-direction before and after inserting a diffuser between the LED light source and the collimating cylindrical lens. The uniformity increased from 34% to 86.8% after the insertion of diffuser. The hotspots caused by the illumination gap between LEDs are greatly eliminated. In Fig. 6(b), the irradiance curve along the 𝑥-direction for pixelated nanogratings evenly distributed in the 𝑥-direction drops dramatically as expected. The uniformation is 9.95%. When the pixel density increases in the 𝑥direction according to the curve illustrated in Fig. 4, the uniformity is increased to 95.7%. According to EBU report [28], the acceptable value of uniformity is 80%. Therefore, the uniformity in both directions has been significantly improved after optimization and is well above the acceptable value.
Fig. 5. Experimental setup of directional backlight module.
3.4. The angular divergence The angular divergence of the illumination is a key parameter for directional backlight. A mask with square holes is placed right in front of the waveguide. The irradiance patterns at multiple height above the waveguide are measured. The angular divergence can be determined by: 𝑊2 − 𝑊1 ) (7) 2⋅𝐿 where 𝛼 is the angular divergence of illumination, 𝑊2 and 𝑊1 are the width of the irradiance pattern at different height. L is the vertical distance between the two measurements (Fig. 7). The angular divergences are measured at 5 spots. The averaged angular divergence is ±6.17◦ . 𝛼 = arctan(
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Optics Communications 459 (2020) 125034
Fig. 6. (a) the light uniformity with and without diffuser. (b) the light uniformity with and without density gradience of nanogratings.
Fig. 7. (a) the apertures used in the measurement. (b) the schematic diagram of the measurement. (c) The measured width of the irradiance pattern at different height.
Acknowledgments
Ideally, the pixelated nanogratings can keep the high directionality of the light ray without distortion (FWHM < 1◦ for a pixel size of 40 μm). A free-form collimating lens can greatly reduce the angular divergence by providing a well collimated light source. Surface irregularities and second order diffraction may be the minor reasons of the spread of light during propagation.
The work was supported by the Natural Science Foundation of China (NSFC) (61975140, 61575135), the Major Basic Research Project of the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (16KJA510002), the Suzhou Natural Science Foundation of China (SYG201930), and the project of the Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions, China. We also thank the SVG Optronics Corporation for the experimental support.
4. Conclusion The edge-lit directional backlight module studied in this paper can be divided into four parts: a LED light bar, a one-directional diffuser, a cylindrical collimating lens, and waveguide. Firstly, a LED light source with a wavelength of 532 nm is collimated by a flat convex cylindrical lens to provide a collimated illumination with an angular divergence of ±4.46◦ . Secondly, a diffuser with micro cylindrical lens array is used to eliminate the illumination gap by the LED array. Finally, the spatial density of the pixelated nanogratings are optimized to improve the uniformity of the system along the 𝑥-direction. The directional backlight module based on the pixelated nanogratings has an angular divergence of ±6.17◦ in the 𝑥-direction, an uniformity of 95.7% and 86.8% in the x, and 𝑦-direction, respectively. The proposed directional backlight is compatible with the architecture of commercial backlight module, thus can be integrated with most LCD panels in the market. The mass production of diffuser and the waveguide can be conducted by nanoimprinting process, which features high throughput and low cost. With thin form factor and simple assembly, the proposed directional backlight can be used in glasses-free 3D display, privacy display, and energy efficient display.
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CRediT authorship contribution statement Yunli Zhang: Data curation, Writing — original draft. Donghui Yi: Visualization, Investigation. Wen Qiao: Supervision, Writing — review & editing. Linsen Chen: Conceptualization, Methodology.
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