1. Introduction

For a long time, how to generate a uniform highly-collimated planar light source (HCPLS) or ultra-collimated planar light source (UCPLS) has been an attractive research topic. For coherent light, HCPLS can be used as a light source for metrology or diffractive components for display application [1–4]. As for incoherent light, HCPLS can be applied in the field related to illumination, projection, and display. Especially for display, the liquid crystal display (LCD) has dominated for all-size product as LCD industry rapid develops in this decade. Because LC itself cannot emit light, it needs an extra planar light source, a backlight generally. As energy-saving is paid more attention the HCPLS is further a solution to promote energy efficiency of the LCD. The HCPLS not only concentrates the emitting light toward the observer (i.e. normal direction) to avoid waste of energy, but also aids achieving some advanced functions such as polarized emitting-light, color separation, and local dimming to greatly raise energy efficiency [5–8]. Furthermore, the HCPLS can increase contrast of the LCD and benefit 3D application [9–11]. In addition to the above-mentioned merits for the traditional LCD, the HCPLS is also very useful to other new display technologies [12–14]. Therefore, the HCPLS has become a very important topic in the backlight research field. For backlight, designs of the HCPLS can be classified as two categories: a light guide plate (LGP) with collocating the optical film thereon, and a LGP alone. In general, the latter is more difficult to manufacture, but has much more collimated emitting light, even probably providing a UCPLS. Some typical designs of a LGP alone for HCPLS are described as follows. The first is to use a flexible mold to form the microstructures of the inverted cone array on the surface of a LGP, and the inverted cones can directly reflect the light propagating within the LGP into the normal direction by total internal reflection (TIR) [15]. The literature shows the range of angular distribution of the light emitted from the LGP is about 25 degrees in both horizontal and vertical direction. It should be noted that all the angular ranges in this paper mean full width at half maximum (FWHM), and the horizontal direction means the direction paralleling with the LED light bar (approximates as a linear light source); vertical direction means the direction orthogonal to the horizontal. The second is to form a LGP with the segmental prism-like microstructure that has two facets, one sinking in the LGP at an angle of 47 degrees with the horizontal, the other protruding from the LGP with an angle of 20 degrees with the horizontal. The angular distributions of the light emitted from the LGP in the vertical and horizontal are 23 and 38 degrees, respectively [16]. The third is to utilize grating on the LGP surface to diffract the light propagating within the LGP into the normal direction. Park et al. proposed the ‘grating-dot’ concept to modulate both angular and spatial distribution, and the angular distributions in the vertical and horizontal are 8 and 20 degrees, respectively when the LGP adopts single LED as light source [17]. A similar concept was also presented to imprint micro-dots made of UV glue on the LGP surface. Each of the micro-dots has grating of a different pitch, and all the micro-dots can provide uniform-color emitting light whose angular distribution is about 18 degrees [18]. The fourth is to pre-collimate the light emitted from a LED by an extra optical component before it enters a LGP and then further to make the light more collimated while it is emitted from the LGP by well-designed microstructures on the LGP or surface profile of the LGP [19–21]. The fifth is to utilize a stack of multiple layers of different refractive index to generate the highly-collimated emitting light whose vertical angular distribution is 10 degrees [22]. Despite its narrow angular distribution in the vertical, the horizontal angular distribution cannot be converged. As to the drawback, adding an extra optical film can narrow the horizontal angular distribution below 34 degrees [23].

According to the above-mentioned literature about LGP designs for the HCPLS, we can summarize as follows. First, the angular distribution ranges from 10 to 38 degrees. Second, most of the designs have complicated and sophisticated microstructures on the LGP such as sub-wavelength gratings or segmented prisms; some need different material to match refractive index; others need thicker or wider volume to accommodate the specific surface profile or an extra pre-collimation component. So, it is very difficult for them to be applied to a large-sized product. Therefore, we propose a novel design for a slim planar apparatus for the UCPLS in this paper, which can transfer the light from the discrete LED into uniform planar light source with ultra-collimated emitting light of 5 degrees (FWHM) below. Furthermore, this apparatus does not need a complicated process to form sophisticated microstructures on the LGP such that it is easy to be applied to large-sized product while keeping relative slim volume.

2. Design concept and principle model

In order to avoid the need for sophisticated microstructures formed on the LGP, we adopt the method similar to the above-mentioned fourth kind, firstly utilizing the compound parabolic concentrator (CPC) to pre-collimate the light emitted from a LED and then obtaining ultra collimated light emitted from the LGP by well-designed but relatively easily-manufactured microstructures on the LGP. The merit of our method is that the microstructures on the LGP can be simplified as the V-groove which can be processed by precise mechanical tooling. However, the drawback is that the CPC occupies extra space such that the apparatus becomes bulky. Therefore, we must mitigate this drawback as possible to keep the apparatus slim. How to mitigate this drawback will be detailed later.

The relationship between the angular range of the light entering the inlet of the CPC and that of the light emitted from the outlet of the CPC can be expressed as follows:

Equation (1) is applied to 2D cases, and Eq. (2) is for 3D cases, where A₁ and A₂ are the area of the inlet and outlet of the CPC; n₁ and n₂ are the refractive index of the material in which the CPC inlet and outlet are immersed respectively. From the equations, we know the collimation effect of the CPC depends on the ratio of its outlet area to inlet area; the higher the ratio is, the more collimated the emitting light is. However, for a higher ratio, dimensions of the CPC also become larger. Further, we also elongate a CPC but keep its ratio in order to improve both spatial and angular uniformity of the emitting light. They both need extra peripheral space, which make the apparatus bulky. Therefore, the slim planar apparatus proposed in this study adopts a two-layer folded frame; the upper and lower layers accommodate the LGP (called ‘upper LGP’ hereafter) and CPC, respectively. So, this frame provides sufficient space for the length and width of the CPC, but the space for thickness of the CPC is still limited. Consequently, thickness of the CPC is the bottleneck for the design. According to Eq. (1), we must maintain the higher ratio of outlet thickness of CPC to inlet thickness in order to let emitting light be more collimated in the vertical direction. With the limit on thickness of the slim apparatus, we can only reduce inlet thickness of the CPC. However, inlet thickness of the CPC also has a minimum limit because it must match the thickness of a LED that can provide enough luminous flux. In order to overcome this conflict, we proposed a new design ‘Distributed sub-layer feeding CPC (DSLF CPC)’ to resolve the problem. The design concept is to couple the light emitted from a LED of certain thickness dispersedly into the duplicate CPCs that parallel each other. We use a ‘feeder’ facing the emitting surface of the LED, which splits into several sub-layers to guide the emitting light to spread horizontally and then into each of the CPCs, as shown in Fig. 1. In the example of Fig. 1, the feeder splits into four sub-layers alternately spreading in the horizontal, and each sub-layer connects a CPC. Thus, the inlet thickness of the CPC can reduce into one fourth of the thickness of the LED, and the ratio of the outlet thickness to inlet thickness can increase up to four times at the same outlet thickness. Because we want the CPC to collimate the light both in the horizontal and vertical, the CPC is booleaned by two 2D CPCs, one for vertical collimation and the other for horizontal collimation. The cross-section of the resultant CPC is rectangular. In order to easily fix the CPC, the bottom and top surfaces of the CPC are designed to be planar and parabolic, respectively. Furthermore, we use the CPC made of PMMA to transfer light by TIR to avoid absorption loss.

 

Fig. 1 Illustration of the feeder used in DSLF CPC design: (a) perspective view; (b) front view (not drawn to scale).

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Next, we note that energy loss occurs during the process that the light emitted from LEDs horizontally spreads to be coupled into CPCs by the feeder. Generally, the light suffers less loss during the process when the light is more collimated in the horizontal. Therefore, we adopt the two-stage CPC design to address this issue. We use the first-stage CPC to preliminarily collimate the light emitted from the LED in the horizontal and then let the light enter the feeder, as shown in Fig. 2. Because the channel in the feeder has 45-degree corner facet for the purpose of keeping feeder volume compact, the entering light cannot propagate by TIR all the way in the feeder when it is not collimated enough. So, the corner facets should be coated with reflecting layer. Of course, it will suffer some energy loss due to absorption, but it is acceptable. The light from the LED is preliminarily collimated by the first-stage-CPC, then coupled into the second-stage CPC (i.e. DSLF CPC) by the feeder, and finally becomes highly collimated light through the second-stage CPC.

 

Fig. 2 Illustration of the component layout in the lower layer of the apparatus.

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Since the light exiting from the second-stage CPC is highly collimated, it is difficult to mix with the light of adjacent CPCs to integrate a uniform linear light source for the upper LGP sequent use. In order to overcome this issue, we set up a light-mixing plate behind the end of the second-stage CPC to improve horizontal spatial uniformity of light entering the upper LGP. The light-mixing plate is made of PMMA and has an array of lenticular micro-structures on its front end (as shown in the upper right inset of Fig. 2), which can horizontally spread the light emitted from the second-stage CPC to benefit light-mixing. The profile of the lenticular micro-structure affects diffusion and mix of the emitting light. For high-sag profile, effect of light-mixing is better, but collimation in the horizontal becomes worse; on the contrary, effect of light-mixing is poor. Therefore, how to make proper trade-off for the profile design is very important.

Next, we arrange a coupling prism to guide the light exiting from the light-mixing plate into the upper LGP. Such design can greatly reduce peripheral volume of the apparatus because the peripheral volume just needs to accommodate a coupling prism instead of a CPC. The coupling prism is an elongated pillar substantially with cross-section of an isosceles right triangle as shown in Fig. 3, which is made of PMMA. The light from the light-mixing plate enters the lower left facet of the coupling prism, then reflects on the two left slope facets, and finally exits from the upper left facet. If the light entering the coupling prism is sufficiently collimated in the vertical, the light can be almost fully coupled into the upper layer by TIR on the two right slope facets. On the contrary, some stray light will appear, and coupling efficiency decreases. In order to improve coupling efficiency, we cut the vertex corner of the coupling prism and coat reflective layer on the two right slope facets. Further, the coupling prism has a reflective protrusion on its center to keep the stray light of the lower layer from entering the upper layer.

 

Fig. 3 Cross-section of the coupling prism.

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Next, the light exiting from the light-mixing plate is guided into the upper LGP through the coupling prism. The object of the upper LGP is to transfer the linear light source from the coupling prism into a uniform and ultra-collimated planar light source (UCPLS) by its micro-structures with various distribution densities. Since the light entering the upper LGP is highly collimated, we just need to design the proper micro-structure such as V-groove, to deflect the light into the normal. In this study, the upper LGP has micro-structures of V-groove protruding from its bottom surface, and slope facet of the micro-structure has 43~44 degrees with the horizontal. If the light already uniformly distributes in the horizontal before entering the upper LGP, the V-groove micro-structure can elongate transversely (horizontally) across the entire upper LGP and thus variously distributes just along the longitudinal (vertical) direction; it is easier to fabricate such a mold by machining process. If the light distribution in the horizontal is not sufficiently uniform, we need the micro-structure of a segmented V-groove to modulate both horizontal and vertical distribution densities to obtain a uniform UCPLS. Such a mold with micro-structures of the segmented V-groove thereon cannot be fabricated by mechanical process, but needs photoresist process, which increases the cost. Further, slope of the V-groove micro-structure must be highly precise, but photoresist process cannot guarantee precision. In order to extract most of the light entering the upper LGP, we adopt a wedge upper LGP. Although energy utility is not much different between the flat and wedge LGP when the LGP has high ratio of its length to thickness, part of the such collimated light entering the flat upper LGP directly passes through the LGP without touching the V-groove micro-structure and cannot be extracted. The entire apparatus assembling the above-mentioned components is schematically illustrated in Fig. 4.

 

Fig. 4 Schematic illustration of the entire apparatus: (a) perspective view; (b) front view (not drawn to scale).

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3. Simulation results and discussion

According to the above-mentioned design concept, we want to design a slim and uniform UCPLS whose dimension has thickness of 2.2 mm and length of 280 mm in this paper. Because we can arrange the duplicate units in Fig. 2 side by side, this slim apparatus can extend in the horizontal without limit on width. If the apparatus collocates with a 16:9 LC panel, it can be a backlight for 23 inch LC panel. In the following simulation, we adopt the LED (NSSW206B, NICHIA Corp., Japan) as the initial light source. The dimension of the LED is 3.8 mmX0.6 mmX1 mm; emitting area is 2.8 mmX0.4 mm; angular light distribution approximates Lambertian; I_F is 20 mA; V_F is 3 V; luminous flux is 8 lumens. To save calculating time, we just simulate a stripe portion of the apparatus with a LED. We assume the left and right side walls of the stripe are ideal mirrors so the stripe portion is equivalent to the whole apparatus in the simulation. In order to ensure accuracy of the simulation results, we trace about twenty millions to fifty millions of rays for different simulation steps. Next, we implement simulation step by step and discuss the related results.

First, we implement simulation for the CPC, including two main parts: the first-stage CPC for preliminary collimation and the second-stage CPC for advanced collimation. Because coupling efficiency of the feeder only depends on light distribution in the horizontal, we just modulate dimensions of the first-stage CPC in width and length so three conditions are selected for analysis; the related parameters and simulation results are detailed in Table 1. It should be noted that the coupling efficiency in Table 1 is define as the ratio of luminous flux on the outlet of the feeder to that on emitting area of the LED. In Table 1, higher ratio of outlet width of the first-stage CPC to inlet width provides higher collimated emitting light and coupling efficiency. However, since the volume of the first-stage CPC and feeder also become larger as the ratio increases, the ratio must be limited. Therefore, we select 8.4 mm as outlet width of the first-stage CPC in the following simulation. According to Eq. (1), angular range of the light exiting from the first-stage CPC is about 20 degrees, which is consistent with the simulation result.

Table 1. Coupling efficiency for the various first-stage CPC designs.

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Next, the second-stage CPC is connected to the outlet of the feeder, which is used to further collimate the light both in the vertical and horizontal. Moreover, spatial distribution of light exiting the outlet of the second-stage CPC must be uniform so that the CPCs arranged side by side can provide a uniform linear light source for the upper LGP use. In this paper, width and thickness of the second-stage CPC at the inlet are 8.4 mm and 0.1 mm, respectively; width and thickness of the second-stage CPC at the outlet are 20 mm and 1 mm, respectively. Basically, at the constant ratio of the outlet area of the CPC to the inlet area, the longer CPC is more uniform for both angular and spatial distribution. We analyze some second-stage CPCs with different lengths; then the related parameters and simulation results are detailed in Table 2. It should be noted that one set of the second-stage CPC has four parallel sub-CPCs (referring to Fig. 2). Further, the definitions of the parameters in Table 2 are as follows: FWHM is angular distribution range of light exiting from the outlet of the second-stage CPC; uniformity is spatial distribution in the horizontal at the outlet; coupling efficiency is the ratio of luminous flux on the outlet of the second-stage CPC to that on emitting area of the LED. In Table 2, we can find length of the second-stage CPC has little impact on angular distribution range and coupling efficiency, but obvious impact on spatial uniformity. In general, the uniformity becomes better and reaches saturation as length of the CPC increases. Considering balance between CPC volume and uniformity, we select 150 mm as the length of the second-stage CPC in the following simulation.

Table 2. Simulation analysis for various length of second-stage CPC designs.

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Because the uniformity at the outlet of the second-stage CPC is still not good enough, we put a light-mixing plate with lenticular micro-structure array on its front end behind the outlet of the second-stage CPC to improve the uniformity of the light exiting from the second-stage CPC. Width and thickness of the light-mixing plate are 80 mm and 1 mm, respectively; the lenticular micro-structure has radius of 0.5 mm, height of 0.05 mm, and a pitch of 0.436 mm. We analyze the effects of the plate length on spatial distribution in the horizontal by implementing simulation for the light-mixing plates with lengths of 30 mm, 60 mm, and 90 mm. We first compare the horizontal spatial distribution at the outlet of the second-stage CPC with those at the outlet of the light-mixing plate, and the related results are plotted in Fig. 5(a). Figure 5(a) shows the spatial uniformity greatly improves if lenticular array is used. Moreover, the spatial uniformity becomes better as the plate length increases. Considering balance between spatial uniformity and plate volume, we select the 60-mm long light-mixing plate in the following simulation. Also, we investigate the effect of the 60 mm-long light-mixing plate on the angular distribution, and the related results are plotted in Fig. 5(b). In Fig. 5(b), we can find the lenticular array indeed broadens horizontal angular distribution while the vertical angular distribution still keeps the same, which benefits maintaining vertical collimation of the light emitted from the upper LGP. Although the horizontal collimation of the light emitted from the upper LGP suffers due to the lenticular array, we still need to pay for better uniformity.

 

Fig. 5 The effect of the light-mixing plate on light distribution: (a) horizontal spatial distribution; (b) angular distribution.

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Next, we adopt a coupling prism to guide the light exiting the light-mixing plate into the upper LGP in the upper layer of the apparatus. In our simulation model, the total thickness of the coupling prism is 2.2 mm; the thickness of its central protrusion is 0.2 mm; the width of the coupling prism is 80 mm. In order to enhance coupling efficiency, the two facets adjacent to the right angle are coated with reflectivity of 0.98. In simulation analysis, we find the coupling prism has very little impact on spatial and angular distribution of light except little part of the light is absorbed; the coupling efficiency of this component is about 0.93. Here, the upper LGP is a wedge LGP with taper angle of 0.12 degree, length of 280 mm, width of 80 mm, and thickness of the front end of 1 mm. Further, the upper LGP has V-groove micro-structures on its bottom surface to extract light out. The cross-section profile of the V-groove micro-structure is an isosceles angle with width of 25 um and vertex angle of 92 degrees. Also, we put a specular type of reflector with reflectivity of 0.98 (e.g. enhanced specular reflector, ESR, 3M Corp.) underneath the upper LGP. The simulation results of angular distributions and illuminance of the light resultant emitted from the upper LGP are shown in Figs. 6(a) and 6(b), respectively. In Fig. 6(a), we can find the resultant emitting light is ultra-collimated with average FWHM of 4.87 degrees in the vertical and substantially has the same trend in angular distribution from near to far region of the upper LGP. If we further optimize slope of the facet of the V-groove micro-structures regarding their respective positions, the resultant emitting light might be further collimated and have higher peak intensity. As for horizontal angular distribution of the resultant emitting light, it has FWHM of 24 degrees the same as Fig. 5(b) because the transverse-extension V-groove does not affect the horizontal angular distribution. In Fig. 6(b), we can find the illuminance varies within ± 9% longitudinally across the upper LGP. The result shows spatial uniformity of the resultant emitting light is 84% and acceptable. In addition, the average head-on luminance of the resultant emitting light is about 5600 nit.

 

Fig. 6 Energy distribution of the light emitted from the upper LGP: (a) angular distribution; (b) spatial distribution.

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Next, we analyze energy efficiency for each component of the apparatus. For non-image optics, energy efficiency is a very important factor. Especially for the era concerning energy-saving, the apparatus only with ultra-collimated emitting light is not enough, and it also must have higher energy efficiency. We list energy efficiency (simulation) of each component in Table 3. In Table 3, we can find energy loss mostly occurs in the first-stage CPC and feeder, about 20% loss, mainly due to absorption on the reflective layer. If the feeder has a smooth curved channel to guide light separately into the second-stage CPC, the feeder does not need reflective coating such that energy loss can greatly reduce [24]. However, such a design needs more space and is not as compact as the feeder proposed in this paper. The secondary energy loss occurs in the coupling prism, about 5% more, mainly due to absorption on the reflective layer. The third energy loss occurs in the 2nd-stage CPC, about 5% less, mainly due to Fresnel loss and bulk absorption of PMMA. The energy efficiency of the entire apparatus is about 69%; this value is not high but is acceptable, especially for such a UCPLS. If we can implement anti-reflective coating on some facets of the components or even glue some components together to reduce Fresnel loss, energy efficiency of the entire apparatus can further improve.

Table 3. Energy efficiency for the components of the apparatus.

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Finally, we discuss feasibility of this apparatus design. Indeed, the precise molds required for feeder are not easily fabricated. Especially for the feeder, tolerance of the mold must be tight; otherwise energy loss in the feeder will increase. The feeder might be divided into several sub-layers that can be inject-molded separately, and then the sub-layers are combined into a feeder. As for the CPC, the solid CPC has been used for solar collector or concentration, which can be fabricated by inject-molding. Although the CPC used in this apparatus is on the scale of millimeters, because the CPC used in the apparatus are surrounded by three paraboloidal surfaces and one planar surface, fabricating the mold for such a CPC is relative simple as compared with the mold for the freeform lens. Of course, if the mold is not precise or smooth enough, energy efficiency of the CPC will reduce. Although adopting the CPC increases cost and makes fabrication complex, the upper LGP can be fabricated more easily because the complicated micro-structures on the LGP are no longer required. As compared with the very complicated LGP proposed in the literature, our design is worth adopting, especially considering its outstanding performance and potential for large-sized application. By the way, we also need to arrange some pads in vacancy of the lower layer of the apparatus to support the reflector sheet and upper LGP; the pads are not shown in Fig. 4.

4. Conclusion

In this paper, we propose a novel slim apparatus that can transfer light emitted from discrete LEDs into a uniform planar light source with ultra-collimated emitting light. The apparatus has a two-layer folded frame and two-stage CPCs such that thickness of the entire apparatus can be minimized; especially the feeder in the two-stage CPC design can greatly reduce thickness of the CPC and make the light passing through the second-stage CPC become much more collimated. In addition, by side-by-side arrangement, a large-sized UCPLS can be obtained. We also introduce a “light-mixing plate” into the apparatus to integrate the light from horizontally separated CPCs into a linear light source with uniform spatial distribution in the horizontal for the upper LGP use. In our embodiment, the emitting area of the upper LGP is 280 mmX80 mm, and a LED with optical flux of 8 lumens is used as the light source. The performance according to the related simulation results shows as follows: angular FWHM of the resultant emitting light in the vertical and horizontal is 4.87 degrees and 24 degrees, respectively; spatial uniformity and total energy efficiency reach 84% and 69%, respectively; the average head-on luminance reaches up 5600 nit, yet this apparatus just consumes 60 mW. In addition, the results also demonstrate this design has potential to be applied to the product of 23 inches above while thickness of the entire apparatus is only 2.2 mm.