This study proposes a slim planar apparatus for converting nonpolarized light from a light-emitting diode (LED) into an ultra-collimated linearly polarized beam uniformly emitted from its top surface. The apparatus was designed based on a folded-bilayer configuration comprising a light-mixing collimation element, polarization conversion element, and polarization-preserving light guide plate (PPLGP) with an overall thickness of 5 mm. Moreover, the apparatus can be extended transversally by connecting multiple light-mixing collimation elements and polarization conversion elements in a side-by-side configuration to share a considerably wider PPLGP, so the apparatus can have theoretically unlimited width. The simulation results indicate that the proposed apparatus is feasible for the maximal backlight modules in 39-inch liquid crystal panels. In the case of an apparatus with a 480 × 80 mm emission area and two 8-lumen LED light sources, the average head-on polarized luminance and spatial uniformity over the emission area was 5000 nit and 83%, respectively; the vertical and transverse angular distributions of the emitting light were only 5° and 10°, respectively. Moreover, the average degree of polarization and energy efficiency of the apparatus were 82% and 72%, respectively. As compared with the high-performance ultra-collimated nonpolarized backlight module proposed in our prior work, not only did the apparatus exhibit outstanding optical performance, but also the highly polarized light emissions actually increased the energy efficiency by 100%.
© 2014 Optical Society of America
The rapid development of liquid crystal (LC) panel technology has caused liquid crystal display (LCD) technologies to become widely used in various devices, ranging from large products, such as televisions, computer monitors, and notebooks, to small products, such as mobile phones and various consumer electronics. In addition to providing optimal display quality and greater functionality, the energy-conservation properties of the aforementioned devices have been widely researched . Although technological advancements have improved the energy efficiency of LCD technologies, the overall optical efficiency remains relatively low. In general, approximately 6% of the light emitted from an LCD backlight module is transmitted through the LC panel, primarily because of the polarizer and color filter in the LC panel. Specifically, the polarizer absorbs at least 50% of the incident light, and it transmits linearly polarized light. Therefore, the optical efficiency can be doubled if the light emitted from the backlight is linearly polarized in advance. Thus, developing a polarized backlight (i.e., a backlight that emits linearly polarized light) is a crucial research topic.
Polarized backlight design concepts can be broadly divided into five categories. The first concept, which is the most frequently used design, involves using a dual brightness enhancement film (DBEF) (proposed by 3M Ltd. Corp.), which is a multilayer stack of thin film composed of birefringence materials that linearly polarize the light emitted from the backlight [2–5]. The DBEF transmits the light linearly polarizing in one direction but reflects the light linearly polarizing in the orthogonal direction. The similar concept is also proposed by Nitto Chemical Ltd. Corp , which involves using cholesteric liquid crystal polarizer to transmit the light circularly polarizing in one direction (e.g. left-hand circular polarization light) but reflects the light circularly polarizing in another direction (e.g. right-hand circular polarization light); subsequently another 1/4-lambda plate converts the transmissive circularly polarized light into linearly polarized light. The second concept involves forming a subwavelength grating by using double-layer materials on the surface of a light guide plate (LGP) that emits linearly polarized light [7–9]. The third concept involves forming subwavelength gratings on a film substrate to transmit the light linearly polarizing in one direction but reflects the light linearly polarizing in the orthogonal direction [10–12]. The fourth concept involves stacking a layer composed of birefringent material on microstructures of the LGP surface (called ‘birefringent LGP’). The microstructures selectively reflect the light linearly polarizing in one direction out of the LGP, p-wave or s-wave only, to achieve the linearly polarized emitting light [13–16]. Finally, the fifth concept involves using a specific type of LGP that preserves the polarization of the polarized light source (polarized LED or LD) to provide the linearly polarized emitting light [17,18]. Among the aforementioned concepts, DBEF is the most successful and widely used design because it has little dependency on both the wavelength and angle of incident light. However, because the size of DBEF increases in conjunction with the size of the LCD, the cost of DBEF increases considerably for the large-sized LCD. Regarding the second and third concepts, accurately fabricating subwavelength grating on a large area of a substrate or LGP surface is extremely difficult. Moreover, because diffraction efficiency is critically dependent on both wavelength and angle of incident light, the impracticality of these concepts is further compounded . In addition, how to eliminate the large absorption loss in the metal film on the grating is an extra challenge. In fact, the experimental results in the literatures indicated that the grating method has absorption loss of 10% and lower gain value than DBEF by 12%~25% . Regarding the fourth design concept, although it has little dependence on wavelength, acquiring appropriate birefringent material is difficult because the birefringence of the material must be obvious and also low-cost. Moreover, the angular distribution of the light entering the LGP must be narrowed in advance for better efficiency. Regarding the fifth concept, preserving the polarization of light emitted from the polarized light source is a challenge. Specifically, because obtaining uniform planar light requires the light propagating in the LGP to be adequately mixed, the degree of polarization is inevitably reduced during the mixing process. Furthermore, except for the fifth concept, all the designs proposed in the literatures need to repeat the cycle that depolarize the reflected polarized light and reflect it back to the reflective polarizer again until the reflected polarized light is completely converted into the light linearly polarizing in the orthogonal direction to propagate through the polarizer. However, repeating such cycles cause the reflected polarized light to be inevitably partially absorbed by the other components in the backlight, and thereby the absorption increases with the number of the components. For DBEF, the practical gain value is about 1.2~1.77, below the theoretical value 2 [19,20]. For the birefringent LGP, the practical gain value is about 1.4~1.65 .
Based on the advantages and disadvantages of the aforementioned concepts, this paper proposes an all-new design for an apparatus uniformly emitting a highly polarized light from its top surface. The proposed apparatus features a polarization conversion element that adopts a DBEF-like structure and complete polarization conversion just in one cycle, thereby minimizing the related absorption. Therefore, it can efficiently convert the nonpolarized light emitted from an LED into the highly linear polarized light for applications requiring large uniform planar light emissions such as backlights. Moreover, this design is relatively simple, slim, low-cost, and feasible as compared with those proposed in the literatures. The design will be detailed in the next section.
2. Design concept and model principles
Based on the aforementioned relevant studies, the narrower angular range of incidence of the emitted light benefits the efficiency of polarization [4,12,14]. Regarding DBEF-like reflective polarizer, wider angular range of incidence means requiring more layers stacked together, thereby increasing cost. However, the light-mixing processes involved in producing a uniform planar light emission will conflict with the collimation of the incident light. In addition, if the light is mixed after the light is polarized, the degree of polarization is reduced because of the light-mixing process. Therefore, the ideal design concept should be based on the following process: 1) adequately mix the nonpolarized light emitted from an LED; 2) collimate the mixed light; 3) polarize the collimated light; and 4) convert the polarized light into uniform planar light emission with polarization preserved. Accordingly, the proposed apparatus was designed based on the following three sequential components: 1) a light-mixing and collimation (LMC) element for the light source; 2) a polarization conversion (PC) element; and 3) a polarization-preserving light guide plate (PPLGP). First, the LMC element adequately mixes and collimates the non-polarized light emitted from the LED. Next, the PC element—which should be simple, reliable, and efficient—transforms the nonpolarized collimated light into highly linear polarized light. Finally, the PPLGP converts the linearly polarized light into uniform planar light emission while maintaining the polarization of the emitted light at the highest level possible. Moreover, because the apparatus must have additional space to accommodate the LMC element and keep the margin of the border minimum, we adopted a folded-bilayer structure design; specifically, the lower layer of the backlight module housed the LED, LMC, and PC elements, whereas the upper layer housed the PPLGP. Furthermore, the thickness of the entire apparatus must be reduced to attain a slim LCD backlight. Next, the design concepts and the related theoretical models of the elements are detailed as follows.
2.1 Polarization converting element
Because a PC element is the core element determining the feature function of the proposed apparatus, both the concept and principles of the PC element are first detailed. The PC element with the following two functions was designed in this study: 1) convert the nonpolarized incident light into linearly polarized light; and 2) guide the light exiting a LMC element (on the lower floor of the apparatus) into the PPLGP (on the upper floor). The PC element was composed of multiple PC units (PCUs). The PCU is essentially a trapezoidal prism combined with a “spiral” coupler comprising three-jointed right-angle prisms in Fig. 1(a).The trapezoidal prism includes Slope Facets 1 and 5; the spiral coupler includes Slope Facets 2, 3, and 4. The working principle of the PCU is detailed as follows (refer to illustration of Fig. 1). Nonpolarized collimated-light exits the LMC element and propagates along the negative y-axis incident to Slope Facet 1 in the PCU. Facet 1 is coated with a reflective polarizing film to reflect the s-wave and transmit the p-wave. Thus, the nonpolarized incident light is divided into two beams at Facet 1 (i.e., p-wave and s-wave). The path of the s-wave follows a relatively simple direction: the s-wave propagates along the z-axis and into the upper floor after being reflected by Facet 1; subsequently, the incident s-wave is reflected by Facet 5 and propagates along the y-axis and enters the PPLGP on the upper floor of the apparatus; the direction of its polarization remains unchanged as it is guided by the PCU from the lower LMC into the upper PPLGP. However, the p-wave is relatively more complex. When the p-wave passes through Facet 1, it enters the spiral coupler and is reflected by Facet 2. Consequently, its directions of both propagation and polarization are changed to the z- and y-axes, respectively. Sequentially, the p-wave is reflected by Facet 3, and its direction of propagation changes to the x-axis, although its polarization direction remains unchanged (y-axis). Next, the p-wave is reflected by Facet 4, and its directions of both propagation and polarization are changed to the y- and x-axes, respectively. Thus, all of the light exiting the PCU has identical polarization direction, the x-axis direction (i.e., s-wave), and successfully guided into the PPLGP on the upper floor from the LMC element on the lower floor. Special note is that the polarization-reflective coating can be achieved by multilayer coating, or even glued a strip of DBEF on the slope facet. In general, if the incident half-angle is limited to a narrow range, fewer layers of reflective coating are required, thereby improving the polarization-separation effect. Therefore, a LMC element providing the PC element a highly collimated light beam to facilitate the polarization-separation effect is necessary.
Because the PPLGP need a sufficiently wide polarized light beam emitted from the PC element, multiple PCUs must be transversely linked in an adequate manner to form the PC element and avoid interference between the PCUs. Figure 2 shows a pair of connected PCUs. Figure 2(a) shows the 3-D exploded view of the PCUs; the colored rectangular is aligned with the dashed rectangular frame of the same color in the x-z plane. Figures 2(b) and 2(c) show the top assembling view and ray path diagram, respectively. In Fig. 2(c), the colored ray passes through the dashed rectangular frame of the same color. Figure 2(b) indicates the trapezoidal prisms of two connected PCUs extending along the x-axis, but the spiral Coupler 1 of PCU1 and spiral Coupler 2 of PCU2 are shifted separately each other along the y-axis between. This arrangement was designed to prevent the both spiral couplers of PCU1 and PCU2 from interfering with each other. Moreover, the converted s-wave exiting the spiral Coupler 2 of PCU2 partially enters the middle right-angle prism of the spiral Coupler 1 of PCU1. However, because the facets of the middle prism are either perpendicular or parallel to the y-axis, the directions of both the propagation and polarization of the converted s-wave is very little affected by PCU1 if the converted s-wave exiting the spiral Coupler 2 of PCU2 is sufficiently collimated. Thus, the efficiency of the PCU depends considerably on the collimation of light exiting the LMC element. Therefore, we put an additional right-angle filling prism between the Coupler 1 and Coupler 2 as shown in Fig. 2(a), to keep the light exiting from Coupler 2 collimated. Furthermore, when the light is adequately collimated, the slope facets in the spiral coupler reflect the incident light through TIR alone (i.e., no reflective coating is required), which can reduce fabrication costs and enhance the energy-efficiency of the apparatus. By linking the multiple pairs of PCUs and extending them along the x-axis to form a PC element in Fig. 2(d) exhibits a thin but wide area for emitting linearly polarized collimated beam, which is the optimal linear light source for the PPLGP. Such design concept ensures that of the PC element will produce highly polarized light in a simple and reliable manner, while considerably reducing the area requiring polarization-reflective coating, thereby both enhancing the practical value of the proposed apparatus and effectively reducing the overall fabrication costs.
2.2 Light-mixing and collimation element
The LMC element must account for light mixing and light-collimation. Light collimation typically involve using compound parabolic concentrators (CPCs) to convert divergent light entering a small area into collimated light emitted from a large area. The relationship between the angular distribution range (i.e., the “half-angle”) of the light emitted from the inlet and that of the outlet of CPC can be expressed as follows:Equation (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 applicable 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 index of the medium surrounding the inlet and outlet. For these two equations, the degree of collimation of the light emitted from the outlet depends on the ratio of the outlet area (or dimensions) to the inlet area (or dimensions), and higher ratios indicate that the outlet emits more collimated light. However, as the ratio increases, both width and thickness of the CPC outlet become larger; the CPC must be also longer. In addition to collimation of light, how to uniformly emit collimated light beam from the outlet of the CPC is another focus, especially when we intend to transversely connect multiple of the CPCs in a side-by-side configuration to emit sufficiently wide and uniform collimated light beam. The CPC can be lengthened to improve the uniformity of both the spatial and angular distribution of the light emitted from the outlet. Alternatively, a CPC-like design can be employed to obtain the same function by replacing the parabolic-curved surface with a Bezier-curved surface . Because of the slim and planar dimensions of the proposed apparatus, the length and width of the space attainable is more than the thickness that must be minimized. For a CPC that can be accommodated in such a space, the horizontal angular distribution of the light emitted from the CPC outlet (i.e., the angular distribution projected on a plane parallel to the top surface of the apparatus) would be relatively narrow, although the vertical angular distribution of the light (i.e., the angular distribution projected on a longitudinal plane perpendicular to the top surface of the apparatus) would be much relatively wide. To solve this problem, we previously conducted a study to narrow the vertical angular distribution of the light emitted from the CPC outlet while keeping the CPC thickness minimum . However, because the aforementioned method would cause the uneven transverse distribution of the emitted light, an additional light-mixing component was required to improve the uniformity of the light distribution. However, the light-mixing component would reduce the collimation of the light, thereby reducing the conversion efficiency of the subsequent PC element; thus, this method is unsuitable under these conditions here. Accordingly, a new approach must be proposed.
This study proposes a well-design LMC element that involves combining a CPC with V-groove microstructures to mix the light adequately during the collimation process to achieve uniformly collimated light emitted from the LMC element. The LMC element was designed as a thin and long CPC with a rectangular cross-section featuring an array of V-groove microstructures longitudinally extended along the z-axis on its bottom surface. The working principle of the LMC element is detailed as follows. In Fig. 3, the light propagating along the z-axis within a thin but wide CPC exhibits a narrow horizontal angular distribution (i.e., projected on the x-z plane) and relatively much wider vertical angular distribution (i.e., projected on the y-z plane). When a light beam with a narrow horizontal angle but comparatively wider vertical angle is incident to the slope facet of the V-groove microstructures, it is reflected by the total internal reflection (TIR), and then continues propagating conversely with a narrow vertical but comparatively 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 the TIR, and then continues propagating with a narrower horizontal angle; in other words, the beam becomes more collimated. After many similar cycles, the original divergent light propagating within the CPC converges both vertically and horizontally. The cross-sectional apex of the V-groove microstructures determines the final angular distribution of the light emitted from the CPC outlet. The CPC combined with an array of longitudinally extended V-groove microstructures is called a “V-cut CPC”.
2.3 Polarization-preserving LGP
The linearly polarized collimated light exiting the PCUs enters the PPLGP. The only task of the PPLGP is to emit uniform beams of collimated light proximal to the normal direction of its top surface while maintaining the direction of polarization of the incident light; accordingly, the light had better be extracted only through TIR on the facets of microstructures on the bottom surface of the PPLGP, and the direction of the light propagating within the PPLGP must be kept from diverging transversely as possible. Moreover, the microstructure must be reliable and simple for fabrication. Therefore, we adopted a V-groove microstructure. The V-groove microstructure protrudes from the bottom of the PPLGP and extends laterally across the PPLGP; in addition, its cross-sectional profile is a triangle with base angles of approximately 43° to 45°. The required mold for such V-groove microstructures can be fabricated using traditional machining processes. However, the V-groove microstructures must be longitudinally distributed using various densities to modulate the spatial luminance of the PPLGP along the longitudinal direction; consequently, the spatial luminance along the transverse direction depends considerably on the uniformity of the light exiting the outlet of the V-cut CPC. Therefore, whether the light is adequately mixed in the V-cut CPC plays a key role in the performance of the proposed apparatus. Furthermore, to enhance the efficiency of light usage, the PPLGP was designed as a wedge plate that had thicker front end and thinner back end, to prevent the collimated light from passing through the PPLGP directly to the back end without contacting the microstructure.
3. Simulation results and discussion
In this paper, we will demonstrate a slim apparatus of the proposed folded-bilayer structure can be indeed used as a large polarized backlight for the LC panel. Moreover, the apparatus can be extended transversally by connecting multiple V-cut CPCs in a side-by-side configuration to share a considerably wider PPLGP. Provided that the apparatus is seamless (i.e., no partition lines are perceived), a device of unlimited width is theoretically possible. If the apparatus was used as the backlight of a 16:9 LC panel, its whole thickness and length would respectively be 5 mm and 480 mm for a 23-inch (LEDs arranged on the shorter edge) or 39-inch panel (LEDs arranged on the longer edge). To verify whether the proposed design could function as anticipated, we established an optical model and performed a series of the related simulations. The related parameters in the model are detailed as follows. Two pieces of 8-lumen 3.8 × 0.6 × 1.0 mm LEDs (NSSW206B, Nichia Corp, Japan) were used as the original light source, which exhibited an approximately Lambertian luminous intensity distribution with a light-emission area of 2.8 × 0.4 mm, (IF = 20 mA, VF = 3 V). To reduce the simulation time, the optical model comprised only two LEDs, two V-cut CPCs, a PPLGP with an area of 480 × 80 mm, and a PC element composed of multiple PCUs; both side boundaries of the module were assumed to exhibit completely specular reflective properties, as shown in Fig. 4.Therefore, the simulation results of the model are fully equivalent to the model containing more pieces of LEDs and V-cut CPCs. In addition, we verified whether any partition lines were perceived on the PPLGP. The following paragraph details the simulations and presents a discussion of the results.
3.1 Simulation for the polarization conversion element
We simulated a 5 × 80 mm PC element that was designed to convert the nonpolarized collimated light (received from the V-cut CPC) into highly linear polarized light, and then guide it into the PPLGP. To ensure that the slope facets reflected the incident light through TIR alone (thereby reducing the energy loss caused by reflection), all of the slope facet surfaces were uncoated, except for the facet with reflective polarizing film (i.e., Facet 1, refer to Fig. 1). Here we assumed the absorption of the reflective polarizing film is 3% the same as DBEF . However, to fully exploit the TIR, the incident light must be maximally collimated. Also, the higher refractive index of the PCU facilitates utility of the TIR. Therefore, we investigated the effect of both the refractive index and half-angle of the incident light on the coupling efficiency of the element. The simulation results in Fig. 5 show that the coupling efficiency decreased as the half-angle (measured in ambient air) increased, particularly at relatively low refractive index values. Moreover, the coupling efficiency that just accounts for the polarized light exiting the PC element further decreased as the half-angle increased. If the half-angle of the light exiting the V-cut CPC exceeds 10°, the optimal PC element should be composed of material with a minimal refractive index of 1.6 to attain a coupling efficiency of up to 90%. However, the material of higher refractive index will increase the cost. Therefore, the half-angle of the light emitted from the outlet of the V-cut CPC had better less than 10°.
3.2 Simulation for the V-cut CPC
We simulated the V-cut CPC and investigated the influence of the apex angle of the V-groove microstructure of the V-cut CPC on both the spatial and angular distributions of light exiting the outlet of the V-cut CPC. Because the PC element requires the incident collimated light beam with half-angle less than 10°, the ratio of the width of the V-cut CPC outlet (width = 40 mm, and 1.6 mm) to that of the V-cut CPC inlet (width = 2.8 mm, thickness = 0.4 mm) was designed to be considerably higher than the ratio of the thickness. Generally, longer V-cut CPCs exhibit more uniform spatial and angular distributions. In this simulation, the length of the V-cut CPC was set at 450 mm, and the width of the V-groove was set at 50 μm. We performed the simulations by using various apex angles for the V-groove. Table 1 shows the relevant parameters and simulation results. The data in the table show that the apex angle exerted a considerable impact on both the spatial and angular distributions. In the absence of the V-groove microstructure (i.e., an apex angle of 180°), the horizontal angular distribution was considerably narrower than the vertical angular distribution. When the V-groove microstructure was positioned at the bottom of the CPC, the horizontal angular distribution increased, but the vertical angular distribution decreased significantly; both became nearly equal. In addition, when the apex angle was increased, the angular distribution gradually exhibited an axially symmetrical distribution, and the spatial distribution also became more uniform. However, the intensity peak of the V-groove microstructure was slightly reduced. Based on the performance of both the uniformity and angular distributions, we selected an apex angle of 150° for the V-cut CPC in the subsequent optical model.
3.3 Simulation for the polarization-preserving LGP
We simulated the linearly polarized light (from the PC element) entering the PPLGP. In this simulation, the PPLGP was a wedge plate with a taper, length, width, and front-end thickness of 0.12°, 480, 80, and 3.2 mm, respectively. The PPLGP featured laterally extended V-groove microstructures on its bottom surface. The cross-section of the V-groove microstructure was substantially an isosceles triangle with a width of 25 um and an apex of approximately 92°, which was fine-tuned based on its position on the PPLGP. A typical white reflective sheet with a reflectivity of approximately 0.98 was placed below the PPLGP to diffuse the reflected light, which is generally disadvantageous for the PPLGP to emit polarized collimated light. However, here, most of the light propagating in the PPLGP was reflected by the V-groove microstructures, and only a negligible amount passed through the V-groove microstructures and reached the white reflector; moreover, this non-reflected light was diffused, thereby preventing partition lines from being generated. In addition, the white reflector material is relatively inexpensive. Figures 6(a) and 6(b) show the simulation results of the spatial and angular distributions of the s-wave emitted from the top surface, respectively. Figure 6 shows that the emitted light is ultra-collimated and exhibits an acceptable overall uniformity of 83%. Although an 80-mm-wide PPLGP received light from two 40-mm-wide V-cut CPCs, no partition lines were visible because the light was adequately mixed in the V-cut CPCs. In addition, the spatial average illumination and luminance were 310 lux and 5000 nit, respectively, with horizontal and vertical angular distributions of only 9° and 5°, respectively. Of course, such extreme collimated light beam would be diffused by a diffuse film adhering to the panel screen for widening angle of view in the practical use of the backlight . Once the collimated light is appropriately diffused, the luminance would drop and be approximately proportional to the illumination. Therefore, we modulated a uniform distribution of illumination instead of luminance. Furthermore, as the luminance drops, a higher power LED might be necessary.
Because the proposed apparatus outputs polarized light beams, the degree of polarization (DOP) of the emitted light, which is a crucial performance index, was evaluated using the following equation:Fig. 7 and angular distributions plotted in Fig. 8.Figures 7(a) and 7(b) show the spatial DOP values over the entire emitting surface and along the longitudinal central line of the emitting surface, respectively. The figures show that the DOP values gradually increased from 73% near the front end (at the position of y = −240 mm) up to 90% near the back end (at the position of y = 240 mm) because of the higher amount of p-waves emitted in the region near the front end. Most of the s-waves that were inadequately collimated were easily extracted from the PPLGP in the region near the front end; moreover, part of them became p-waves. Figure 8(a) shows the overall angular DOP values over the entire emitting surface, and Fig. 8(b) shows those along the longitudinal and transverse central lines across the intensity peak. Figure 8 shows that the light emitted in the normal direction within ± 5° exhibited minimal angular DOP values of 90%; furthermore, if the transversal range is extended by ± 10°, the angular DOP values remain higher than 80%. Therefore, the overall performance of polarizing the emitted light was relatively favorable.
3.4 Efficiency analysis of the apparatus
We analyzed the energy efficiency of the three main components of the apparatus. Energy efficiency is a crucial factor for assessing the performance of nonimaging optical devices. Because of recent concerns regarding energy conservation, devices must exhibit favorable performance and energy efficiency. The energy efficiency results for each component listed in Table 2 were separately based on the following two different conditions: 1) calculate the energy efficiency (regardless of the polarization state); and 2) calculate the energy efficiency of the s-wave. Under Condition 1, the least energy-efficient component was the PC element (approximately 10% loss), followed by the V-cut CPC (approximately 6% loss), and the PPLGP (4% loss). The energy loss in the PC element was primarily caused by inadequately collimated light for TIR to occur on the slope facets in the PCUs, whereas the energy loss in the V-cut CPC and PPLGP was mainly caused by absorption by the bulk material. For Condition 2, the energy loss of the PC element and PPLGP were approximately 14% and 10%, respectively. The energy loss increased primarily because part of the light entering the two components was inadequately collimated. Regarding the PC element, the inadequately collimated p-wave could not be completely converted into an s-wave. Moreover, the polarization direction of the inadequately collimated s-waves entering the PPLGP could not be fully preserved during the light-extraction process. The simulation results indicate that the energy efficiency of the overall system is approximately 72%, which is comparable to that of the ultra-collimated nonpolarized backlight module proposed in our prior work (69%) . However, because this calculation considers only the s-waves, the proposed design is actually twice as efficient as the prior work.
Finally, we discuss how accurate the above simulation results are. Although our new work did not implement experiments, we attained the convincing values of the key parameters such as absorption of grating, DBEF, and other components comprising the backlight for our simulation. The accurate key parameters can make our simulation results more convincing. Our new model includes three main parts: polarization conversion element, light-mixing and collimation element, and polarization-preserving LGP. Except for the polarization conversion element, the optical behavior of the light propagating in the other two parts can be accurately predicted just by ray-tracing software. The polarization conversion element has two functions: polarization splitting and rotating the polarizing direction of the transmitted polarized light into the orthogonal direction. The optical behavior involving rotation of the polarizing direction can be accurately predicted just by ray-tracing software, but polarization splitting cannot be directly predicted because the absorption, reflection and transmission of the reflective polarizing film must be attained in advance. For DBEF used as a polarization splitter, the literature demonstrated the absorption of DBEF was less than 3%; reflection and transmission were 97% above . Those values were adopted in our simulation to ensure the accuracy of the simulation results.
3.5 Feasibility of manufacture
Although the proposed apparatus demonstrated excellent performance, the feasibility of manufacture might become a concerned issue. For easy manufacture and assembling, we can divide the polarization conversion element into three parts as shown in Fig. 9; each part can be transversely extending based on requirement and manufactured by injection-molding. The left part (first part) contains the trapezoidal prism and a portion of Coupler 1 (refer to Fig. 2); the middle part (second part) contains a portion of Coupler 1 and Coupler 2; the right part (third part) contains the right-angle filling prism and a portion of Coupler 2. The colored rectangle and the dashed rectangular frame in the same color must be aligned with each other in the x-z plane; similarly, the colored triangle and the dashed triangular frame in the same color must also be aligned with each other in the x-z plane, which helps the reader figure out how to assemble the polarization conversion element. Because Facet 1 (refer to Fig. 1) is a transversely extending strip on the first part, affixing or coating a reflective polarizing film to Facet 1 is feasible. Then, the three parts can be glued together to complete the polarization conversion element. We implemented simulation for the polarization conversion element assembled in this way, and the results were the same as the assembling way in Fig. 2. Therefore, such manufacture method is feasible in principle.
This study proposes a slim planar apparatus for converting nonpolarized LED light into an ultra-collimated linearly polarized light beam that is uniformly emitted from its top surface. The proposed apparatus was designed based on a folded-bilayer configuration comprising LMC and PC elements, as well as a PPLGP. Because the well-designed LMC element (V-cut CPC) can be used for simultaneously adequately mixing and collimating the light to emit a spatial-uniform collimated beam with an axial-symmetric angular distribution, multiple V-cut CPCs can be transversely connected in a side-by-side configuration to emit a uniform collimated light beam with a sufficient width for use by the subsequent PC element and PPLGP; thereby the planar apparatus has a theoretically unlimited width. Moreover, the V-cut CPC can greatly reduce the thickness of the required space as compared with the general CPC, which facilitates a slim planar apparatus. Then, the well-designed PC element following the V-cut CPCs can efficiently convert the nonpolarized collimated light beam from the V-cut CPCs into a polarized collimated light beam in a thin space for use by the subsequent PPLGP. Finally, the PPLGP receives the polarized collimated light beam and emits uniform beams of collimated light proximal to the normal direction of its top surface while maintaining the direction of polarization of the incident light. Based on our simulation results, no partition lines were observed on the emitting surface of the apparatus, and the proposed apparatus is feasible for the maximal backlight modules of 39 inches with a thickness of only 5 mm. In the case of an apparatus with a 480 × 80 mm emission area with two 8-lumen LEDs as the light source, the average head-on polarized luminance, spatial uniformity, and average degree of polarization over the emission area are 5000 nit, 83%, and 82%, respectively. Moreover, the vertical and transverse angular distributions of the emitted light are only 5° and 10°, respectively, and the energy efficiency of the entire apparatus is approximately 72%, which is 100% more efficient than the ultra-collimated nonpolarized backlight module proposed in our prior work because of its polarized emitted light. Thus, the energy-efficiency of the proposed apparatus can contribute to the development of environmentally friendly products.
This study was sponsored by Ministry of Science and technology of Taiwan under Grant No. NSC 102-2221-E-008-028 and MOST 103-2221-E-003 −006 -MY2.
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