 Proceedings of Engineering and Technology Innovation , vol. 3, 2016, pp. 07 - 09 7 Design of Slim LED Coupler for Collimated Light Source Chun-Hao Sun, Tun-Chien Teng * Department of Mechatronic Engineering, National Taiwan Normal University, Taipei, Taiwan. Received 25 February 2016; received in revised form 28 March 2016; accept ed 16 April 2016 Abstract This study proposed a slim coupler to col- limate the light e mitted fro m an LED, which can be used as a collimated light source. The coupler is substantially a 2-D co mpound parabolic col- lector (CPC); its bottom surface has longitud i- nally e xtending V-groove microstructures thereon. The parabolic side wa lls re flect the propagating light to converge only in the trans- verse direction, but the V-groove mic rostruc- tures reflect the light and make its propagating direction gradually rotates around a central a xis of the CPC. Therefo re, the angular d istribution of the light finally converges after several times of reflection on both side walls and V-groove microstructures. Moreover, the illu minance distribution on the outlet of the V-groove CPC becomes more uniform than a CPC without V-groove mic rostructures. The effects of V-groove microstructures on both angular and illu minance distributions of the light emerging fro m the outlet of the CPC is analyzed, and the feasibility of providing a uniform co llimated light source is verified by conducting simula - tion. Keywor ds : collimation, Coupler, LED, com- pound parabolic collector, illumi- nation 1. Introduction The liquid crystal display (LCD) needs an e xtra p lanar light source such as a backlight. As energy-saving is paid more attention an u l- tra-collimated planar light source (UCPLS) becomes an attractive solution to ra ise energy efficiency of the LCD. The UCPLS concentrates the light toward the observer to avoid waste of energy. Moreover, it is essential for achieving some advanced functions to greatly raise energy efficiency. Severa l typica l designs of UCPLS were proposed. The first is to fabricate a light guide plate (LGP) with special microstructures thereon that directly reflect the light propagating within the LGP into the norma l direct ion [1]. The second is to form grat ing dots on the LGP surface to diffract the light propagating within the LGP into the normal d irect ion. [2]. The third is to utilize an LGP co mposed of a stack of mu ltip le layers of diffe rent refractive inde x to ma ke the inner light emerge with narrow vertica l angular distribution [3]. The fourth is to pre-collimate the light emitted fro m an LED by an ext ra optical co mponent before it enters an LGP and then to reflect the collimated light into the norma l d irection through microstructures on the LGP [4]. A mong those designs, using an e xtra pre-collimating co mponent is a simple r way but needs thicker or wider volu me to ac- commodate the component, which is adverse to a slim backlight. Thus, we proposed a UCPLS design, in which a slim LED coupler was used to pre-collimate the light e mitted fro m an LED and the overall thickness was 5 mm [5]. In this paper, we further analy ze the effects of para meters of the coupler on both spatial and angular d istrib u- tion of the output light to attain the optima l condition. 2. Principle The LED coupler used in the backlight must account for both light mixing and light-collimation. The coupler has a profile of the CPC to convert divergent light entering a small area (inlet) into collimated light emerging from a large area (outlet). The relationship between the angular distribution range (i.e., the “half-angle”) of the light entering the inlet and that of the outlet of CPC can be expressed as follows : 1 2 2 2 1 1 sin sin t n t n    (1) 2 11 2 22 2 1 )sin( )sin(   n n A A  (2) * Corresponding aut hor. Email: walt er.teng@ntnu.edu.tw Proceedings of Engineering and Technology Innovation , vol. 3, 2016, pp. 07 - 09 8 Copyright © TAETI Eq. (1) is applicable for the 2-D case, where t1 and t2 is the thickness of the inlet and outlet of the CPC, respectively; Eq. (2) is applicab le for the 3-D case, where A1 and A2 is the area of the inlet and outlet of the CPC, respectively; and n1 and n2 respectively represent the refractive inde x of the mediu m surrounding the inlet and outlet. The two equations indicate that the degree of collimation of the light e merging fro m the outlet depends on the ratio of the outlet area to the inlet area. As the ratio increases, both width and thickness of the CPC outlet become larger, thus adverse to backlight application. Moreover, output a uniform collimated light bea m is an- other focus if we intend to transversely connect mu ltip le of the CPCs side by side to form suffi- ciently wide and uniform co llimated light source for the LGP. For a CPC that can be accommodated in a slim backlight whose space is relatively wide but very thin, the horizontal angular distribution of the output light of the CPC would be re latively narrow, but the vertical angular distribution would be re latively wide. To solve this issue, an approach combining a CPC with V-groove mi- cro- structures was proposed. The coupler was designed as a thin and long CPC with a rectan- gular cross -section, and an array of V-groove microstructures longitudinally e xtended along the z-a xis was form on its bottom surface as shown in Fig. 1. The light propagating along the z-a xis within a thin but wide CPC e xhib its a narrow horizontal angular distribution (projected on the x-z plane) and a re latively wider vertica l angular distribution (projected on the y -z p lane). When a light beam with a narrow horizontal angle but comparatively wider vertical angle is incident to the slope facet of the V-groove mi- crostructures, it is reflected by total internal re - flection (TIR), and then continues propagating conversely with a narro w vertica l but co mpara- tively wider horizontal angle. Such a light beam with a wider horizontal angle is more likely to hit the curved surface on the left or right side of the CPC. Consequently, it is reflected by TIR, and then continues propagating with a narrower horizontal angle; in other words, the beam b e- comes more collimated. After many similar cy- cles, the original light propagating within the CPC converges both vertically and horizontally. In the process, the length of the CPC and the angle of the apex of the V-groove microstruc- tures have effects on both spatial and angular distributions of the output light. Fig. 1 CPC with V-groove microstructures 3. Results and Discussion In this study, we established an optical model whose related para meters are detailed as follows. A CPC was made of poly methyl methacrylate (PMMA), whose dimensions of its inlet and outlet were 3.6 1.2 (mm) and 13.82 2.4 (mm), respectively; its length was 50– 70 mm. A series of simu lations we re per- formed for different conditions such as: ape x angles of V-grooves and types of the profile of the CPC. Ape x angles included 90 o , 110 o , 130 o , and 150 o ; types of the profile had three: width and thickness simultaneously increasing (Case A); width increasing first and then thickness (Case B); thickness increasing first and then width (Case C). Table 1 Uniformity of illu minance vs. ape x angles Case A Case B Case C 0 o 0.80/0.87 0.88/0.90 0.83/0.85 90 o 0.69/0.76 0.79/0.90 0.69/0.85 110 o 0.92/0.94 0.97/0.98 0.95/0.95 130 o 0.84/0.99 0.98/0.99 0.80/0.97 150 o 0.89/0.98 0.98/0.99 0.78/0.93 Table 1 lists uniformity of illu minance in the three cases under the conditions of different apex angles. Uniformity is defined as the ratio of minimal illu minance to ma xima l. Angle of zero means the bottom of the CPC is bare flat; the uniformity data behind the slash are those of the CPC that is e xtended by an extra length of 20 mm with a constant cross -section. The results indicate that the apex angle of 90 o is adverse to uniformity for the three cases; apex angles of 110 o , 130 o , and 150 o imp rove uniformity for Case A and B; only the apex angle of 110 o im- proves uniformity for Case C. Case B performs the best uniformity; Case C performs the worst. However, a ll the uniformity is improved for the three cases when the CPC is extended. Proceedings of Engineering and Technology Innovation , vol. 3, 2016, pp. 07 - 09 9 Copyright © TAETI Angular distributions of output light of the CPC for Case A, B, and C are shown in Fig. 2. The left insets are those in the vertical direct ion; the right insets are those in the horizontal direc - tion. The effects of ape x angles of V-groove microstructures on angular distribution are demonstrated. The V-groove microstructure narrows the angular distribution in the vertical, and up to 47% at most as co mpared with the CPC without microstructures. However, it also slightly broadens the angular distribution in the horizontal. A mong the three cases, Case B has narrower and smooth vertical angular d istrib u- tion, but its horizontal angular distribution is wider. Considering uniformity of illu minance, Case B is an optimal solution. Fig. 2 Angular distributions of output light of the CPC: (a) Case A; (b) Case B; Case C 4. Conclusions In this paper, effects of V-groove mic ro- structures on both angular and illu minance dis- tributions have been demonstrated for the three types of CPCs. In the slim volu me , the vertica l angular distribution and illu minance uniformity of the output light is narrowed and improved, respectively. The CPC of the profile with width increasing first and then thickness is an optima l solution for a slim coupler p roviding a uniform collimated light source because of its smooth angular distribution and e xcellent illu minance uniformity. References [1] J. H. Lee , H. S. Lee, B. K. Lee , W. S. Choi, H. Y. Cho i, and J. B. Yoon, “Simp le liquid crystal display backlight unit co mprising only a single-sheet mic ropatterned polydi- methylsilo xane (PDM S) light-guide plate,” Opt. Lett., vol. 32, no. 18, pp. 2665-2667, 2007 [2] S. R. Park, O. J. Kwon, D. Shin, and S. H. 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