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This research uses a roll-to-roll based ultraviolet (UV) resin process to make sub-wavelength gratings for display applications. Based on the rigorous coupling wave analysis (RCWA), we analyze the relationship between the first order transmission/reflection efficiency and the pitch of the grating for various shapes as rays pass through the sub-wavelength gratings, patterned with a backlight. The objective is to turn the R/G/B (620 nm, 520nm, and 450nm) incident rays into uniformly and normally output white light with high illuminance from the surface of a light guide.
©2011 Optical Society of America
1. Introduction
The applications of sub-wavelength gratings in displays have been expanding in recent years. IBM first demonstrated a lithography molded sub-wavelength grating to separate colors [1] in which a 550 nm pitched sub-wavelength grating was combined with a cylindrical lens array to produce red-green-blue (RGB) colors for a color display. Philips then also used a similar structure and process for the same purpose [2]. To enhance efficiency, the pitch of the grating can be as low as 320 nm. In 2003, Samsung designed a series of sub-wavelength gratings for producing highly collimated white light to replace the diffuser and the prism sheet in a display [3]. Ye and Park proposed a similar approach to improve the light illuminance and uniformity by optimizing the grating depths. Their approach can control the scattering directions and eliminate the dark region or hot spots in the viewing direction [4,5]. However, the available fabrication area is generally smaller than 1 cm2 when the interferometry based gratings are made. In addition, the extremely low anti-abrasion ability of the grating applied in a backlight unit is another concern. In the other words, optical film with sub-wavelength patterns is not suitable to be placed on the top or bottom surface of a light guide.
The fabrication area can be increased by adopting the roll-to-roll process [6–9]. Therefore, in this study, we propose a light bar for backlight application, which is patterned with five different periodic gratings and can be fabricated by the roll-to-roll process. By mounted the grating on the side of a light guide, the abrasion issue can be improved. In addition, the light bar can shrink the coupling length between a point light source and a light guide, and avoid direct scratches that can easily happen to the surface of a regular display. Figure 1 illustrates the behavior after combining a light-emitting diode (LED) module light source with a light guide. Light propagating inside the light guide is restricted due to refraction to angles of ± 42° with respect the normal of the entrance facet of the guide (Fig. 1(a)). To shrink the coupling length by enlarging the light distribution, the facet is textured by notching or sand-blasting (Fig. 1(b)). In this design, the light incident on the light guide is from a light bar (LB) with an array of sub-wavelength gratings (SWG), allowing the design to employ an even shorter coupling distance (Fig. 1(c)), which can be applied to mobile phone displays. We analyze the optimum grating period and shape by investigating the relationship between the angular distributions of incident beams on the grating and the illumination characteristics of the LED. With low production costs and short coupling length, the design also has the potential to eliminate the brightness enhancement film (BEF) for a RGB LED or a cold cathode fluorescent lamp (CCFL) backlight module in the liquid crystal display (LCD) systems [10].
Fig. 1 Behavior of light rays at the junction between LED module and the light guide. (a) The entrance facet is flat. (b) The entrance facet is textured. (c) The light is from a light bar with an array of sub-wavelength gratings.
2. Design and simulation
The profile of SWG is mainly a blazed type, which is determined by the profile of diamond-tipped single-point cutting tools in the roll-to-roll process. To calculate its diffraction efficiency, the most commonly used method is the rigorous coupling wave analysis (RCWA) [11]. It is well suited in particular for binary gratings but can be used with continuous-profile gratings as well, assuming the profile is approximated with a large number of binary layers. The diffraction geometry for an ideal blazed grating is shown in Fig. 2 . One period of the grating is denoted as P and the maximum depth as H. The incident light of wavelength λ is coming from a material (zone I) with refractive index n I at an arbitrary angle of incidence θand is diffracted into a material (zone II) with refractive index n II.
The propagation of waves through the grating can be analyzed as the following. The tangential components (TE polarization) of the incident wave in zone I and II are given by
Ri and Ti are the normalized electric-field amplitude of the ith backward-diffracted and forward diffracted waves, respectively. The quantity kyi is determined from the Floquet condition and is
Here kI,xi and kII,xi are either positive real or negative imaginary. Solving the coupled wave equations for blazed gratings [12], the ith reflectance, Ri, and ith transmittance, Ti, may be calculated, and reflected and transmitted diffraction efficiencies at each diffraction order are calculated from the following equations, respectively.
Note that the sum of DEri and DEti keeps constant 100% always. The derivation for the other tangential components (TM polarization) of the incident wave is similar. Since the incident wave is from an un-polarized LED, the diffraction efficiency can be assumed to be the average of intensity of TE and TM modes.
If an SWG is considered for LB applications, its design must satisfy several conditions to function adequately. Usually the direction of light extraction from the LB through diffraction on the SWG is a function of the incident wavelength, incident angle, the refractive index of the material and the grating period, while the light extraction efficiency depends on the grating profile. The optical performance of grating is not only affected by the profile of the grating, but also the refractive index of the material used. It is found that it becomes difficult to maintain designed profile when the refractive index of UV resin is low because of the corresponding high fluidity. On the other hand, if a UV resin with higher refractive index is selected, the absorption rate is higher. Therefore, a UV resin with a refractive index 1.5 is used in our study. To achieve white balance, the grating period is designed to extract the incident beam on the grating vertically through the LB surface. As shown in Fig. 3 , the incident beams are composed of three representative wavelengths, 620nm (red color), 520nm (green color) and 450nm (blue color) in the current design. They mix with each other by using an array of five grating periods corresponding to five target wavelengths such as 620nm(R color), 570nm(R/G mixing color), 520nm(G color), 485nm(G/B mixing color) and 450nm(B color). To reduce direct reflection at the end of the LB and enhance the coupling efficiency, the LED is positioned on a slanted side facet.
Fig. 3 A light bar including an array of five gratings. The gratings on top of the LB separates incoming light into white, which is composed of different directions of red, green and blue colors.
2 0.1 Incident angle
Ideally, the LED produces a perfect Lambertian distribution of light, which means the radiant intensity I is directly proportional to the cosine of the angle θ between the viewer’s line of sight and the surface normal. This approximation is valid for most LEDs without an encapsulant. The radiant intensity can then be expressed as
where I0 is the radiant intensity on axis. Upon entering the LB from an LED, both reflection and refraction of the light occur due to the refractive index difference between the air and the LB material, polymethyl methacrylate (PMMA) (refractive index n ~1.5). The optical transmission coefficient is described by Fresnel’s equation under the assumption that the light from the LED is un-polarized.where Ts and Tp represent the transmission of s-polarized and p-polarized light, respectively. The indices of refraction of the media are labeled n1 for air and n2 for PMMA. θ1 and θ2 are the incident and refraction angles, respectively. The relative intensity distribution as a function of refracted angle is the multiplication of Eq. (7) and (8), as shown in Fig. 4 . The maximum of 96% occurs at normal incidence with a Fresnel reflection loss of 4%.Fig. 4 Calculated relative intensity distribution as a function of the refracted angle, which is determined by the radiant intensity of the LED and the transmission derived from Fresnel equations.
After entering the LB, the rays inside the substrate pass through the sub-wavelength gratings at angles restricted to the interval between 48° and 90∘with respect to the normal of the gratings. To create white balance, the overall out-coupling efficiency of the SWG is determined by two factors. One is the intensity distribution of the incident angles, which is described in Eqs. (7) and (8). The other is the characteristics of SWG for different wavelengths.
For simplicity, we limit our design to the cases where only the first order diffractions in the coupling are allowed. The merits were described in Roberto Caputo’s design [2]. This means that the SWG period will be in the range of λ/2 to λ for each wavelength of interest. In this article, the chosen period is from 350 nm to 500 nm. If the diffraction efficiency (DE) curve exhibits a smooth decreasing behavior with increasing angle for each wavelength, the SWG can compensate for the Lambertian distribution of the LED. Several numerical simulations were thus performed using G-solver based on RCWA [13,14]. Since the array of SWGs is fabricated by the single-point diamond turning based roll-to-roll process, the available shapes of SWG are limited. The process uses a monocrystal diamond cutting tool with a V-shape, nanometric edge sharpness to cut the Cu roller for making the master. Considering the process availability and stability, the adopted profile is an array of 90° vertex angle grooves. The behavior of the DE of the SWG for the first diffraction order (sum of −1R and −1T) was determined by varying the incident angle and the period over several wavelengths. The summarized results are reported in Fig. 5 , and show a smooth, decreasing behavior of the DE for all wavelengths of interest (450 nm < λ< 620 nm).
Fig. 5 Diffraction efficiency as a function of wavelength (horizontal axis) and incident angle (vertical axis) for different periods of the SWG with profile of 90° vertex angle grooves.
After investigating the characteristics of SWG for different wavelengths, the next step is to define the optimal incident angle. Roberto Caputo set the optimal incident angle θinc at 69∘because it corresponded to the central value of the cone of the incident angles (48 ∘< θinc <90∘) [2]. M.G. Lee and S.M. Lee considered θinc = 55∘without providing any reason [3]. The incident angle θinc we choose is the central angle, at which the incident beams are extracted by the five SWGs in a direction perpendicular to the LB with peak luminations for the beams of red, green, and blue wavelengths, respectively. Figure 6 shows the average DE, which is a linear-like function and can be calculated from the average of DE values shown in Fig. 5. θinc = 65∘is therefore obtained from the central value of the distribution of extracted intensity (Fig. 7 ), which is the multiplication of the incident beams’ intensity distribution and the corresponding average DE. Since the overall Lambertian distribution of the LED ranges in both the polar and azimuthal directions, θinc has to be modified to 66∘. In this design, to reduce direct reflection at the ends of the LB and enhancing coupling efficiency, the LED is positioned on a slanted side facet (slant angle θ = 11∘, as shown in Fig. 3), which means θinc = 60∘according to Snell’s law is adopted finally.
Fig. 6 Average diffraction efficiency as a function of incident angle for SWG periods ranging from 350 nm to 500 nm with profile of 90° vertex angle grooves.
Fig. 7 The distribution of extracted intensity, which is the multiplication of the incoming incident angle’s intensity distribution and the corresponding average DE.
2.2 SWG periods
The grating period is designed to vertically out-couple energy from the grating on the light bar. Periodic values are calculated for five representative wavelengths: 620nm, 570nm, 520nm, 485nm and 450nm. For a central incident angle of 60∘, these wavelength values, the conditions for obtaining the periods can be derived from the grating equation:
where θinc = 60° is the incident angle, θdif is the diffracted angle, n2 = 1.5 is the refraction index of incident medium PMMA, Λ is the SWG period, n1 = 1 is the refractive index of the diffracted medium air, and m is the diffraction order for the wavelength λ. For m = −1, the periods for wavelengths 620 nm, 570 nm, 520 nm, 485 nm and 450 nm are 477 nm, 439 nm, 400 nm, 373 nm and 346 nm, respectively.Besides the first transmission order (−1T), other orders 0R, −1R and −2R also exist. To avoid light loss, it is preferable to put a reflective layer underneath the light guide to recycle −1R, while the 0R and −2R orders can be reflected back inside the light bar by total internal reflection. The selection of profile was based on both the simulation result and the process-capability. Our simulation shows that a profile with a vertex angle between 80 and 90 degrees has a better optical performance. In the fabrication, a sharper angle is produced from a shaper tip of a diamond tool, which has a weaker abrasion resistance. Therefore, a higher vertex angle of 90 degrees is used in our study. Table 1 lists the DE for the five sub-wavelength gratings with the shape of the 90° vertex angle grooves under an incident angle θinc. Their extracted DE values ( = −1T + −1R) are almost the same.
Table 1. Calculated DE for Five Sub-wavelength Gratings with Shape of 90° Vertex Angle Grooves
3. Manufacturing
The large scale manufacturing of sub-wavelength gratings via a roll-based mastering method is based on the modification of single point diamond turning. The single point diamond tool possesses the characteristics of high hardness, high heat conduction rate, low friction coefficient and low heat expansion coefficient, so it can match the requirement of high accuracy and low surface roughness in optics. The drum roll lathe we use for fabricating the SWGs is shown in Fig. 8 , which is a piece of equipment recently developed by the Institute of Research and Technology of Taiwan (ITRI).
Fig. 8 Pictures of (a) the ITRI-made drum roll lathe and (b) the roller for imprinting the sub-wavelength gratings.
The diameter of the hard-copper roller was 200 mm. To make the master of the SWGs (with periods: 477nm, 439nm, 400nm, 373nm, and 346nm; zone size for each grating = 600 um; spacing between each grating:100 um, as shown in Fig. 9 .) with a width larger than 300 mm on the surface of the roller, the total cutting length was 35.9 km, which approached the lifetime of the diamond tool. It was beneficial to remove chips on the roller and reduce thermal effects to improve form accuracy and surface roughness.
Fig. 9 Zone width for each grating is 600 um; spacing between each grating is 100 um; the total width of 10 sets of gratings are about 350mm. The total cutting length is 35.9 km.
The optical requirement of SWGs in a display configuration is quite challenging, since the diffraction efficiency strongly depends on the value of the period and its profile. After the mechanically grooved structure was formed on an imprinting Cu roller using a diamond tool with the designed profile, the ultraviolet (UV) embossing equipment (Fig. 10(a) ) was applied: the UV resin was first dispensed on the PET film, imprinted by the roller, hardened by UV curing, and demolded from the roller to obtain the gratings on a 188μm thick PET film (T-A4300 by Toray Corp.). The schematic diagram of the process is as shown in Fig. 10(b).
Fig. 10 (a) The UV embossing equipment. (b) Schematic diagram showing the process: the UV resin was first dispensed on the PET film, imprinted by the roller, and cured with UV source.
In the UV curing step, the UV resin (LEN-B by Chishan Corp.) was hardened by absorbing the energy of UV light. Adequate exposure conditions were indispensable for the nano-structures on the PET film. Since the diffraction efficiency was highly dependent on the grating profile, the major challenge in the curing of the gratings was to achieve a high replication rate (>95%) and high demolding yield. After a series of tests (see Table 2 ), we found the forming feed-rate, 3~8 m/min, of feeding UV resin into the roller and UV intensity were the major factors controlling replication rate. A further test showed that an average feed-rate of 5 m/min and 100W of UV light were the optimal condition to improve the anti-sticking property in demolding.
Table 2. Curing Condition Between UV Power and Forming Feed Rate
4. Results and discussion
In Fig. 11 , scanning electron microscopy (SEM) images of the resulting geometry show that the fabrication periods matched the design values well with an error less than 3%. The vertex-angle of SWG D shown in Fig. 12 ranges from 80∘ to 90∘. For optical measurement, the SWGs-patterned film was then attached to a 5 mm -thick PMMA substrate with a bottom and side reflector, as shown in Fig. 13 .
Fig. 11 SEM images of the fabricated SWGs. The periods of SWG A, B, C, D, and E are 359 nm, 480nm, 456 nm, 410 nm and 382 nm, respectively.
To measure the performance of SWGs, a highly collimated white light source was setup, which consisted of three collimated beam expanders, one for each color, and two beam splitters (Fig. 14(a) ). The light source had peak values at 620 nm (R), 520 nm (G) and 450 nm (B). The SWG film was attached to a PMMA prism. The incident angle was set at 60∘. The color pattern of the LB with SWGs is shown in Fig. 14(b), which was captured by a CCD camera. Primary colors R, G and B occur in grating B (pitch = 480 nm), D (pitch = 410 nm) and A (pitch = 359 nm), which matched the performance of our design.
Fig. 14 (a) The measurement setup generates collimated white light to measure the performance of a LB with SWGs. (b) Photograph of color pattern of the LB with SWGs captured by a CCD camera.
To measure the performance of the SWG attached on a LB, another measurement setup was used. The incident light entered the LB directly from a LED (Fig. 15(a) ). Compared to the image obtained from a collimated beam illuminated on SWGs (Fig. 14(b)), the color distribution from each SWG shown in Fig. 15 (b) is not pure because of the wide angle distribution (48∘~90∘) of the incident beams. Figure 16 shows the color points in the chromaticity diagram (CIE) x-y plane, created by sampling the pattern shown in Fig. 15 (b). Points A, B, C, D and E of the red dashed polygon were measured at the viewing angle 0 ∘from the SWG A, SWG B, SWG C, SWG D and SWG E. D65 is within the red dashed polygon, which means the white balance can be obtained in the far field. The highest luminance (designed to be white light) measured from the viewing angle = 0° is shown in Fig. 17 . The LED’s color coordinates (points R, G and B) are also shown for reference. Points R, G and B of the black dashed triangle represent the gamut of colors of the LED. The use of a colored (RGB) LED allows us to investigate the characteristic of SWGs in more detail. Table 3 shows the pattern and the luminance values of the SWGs when only the red, only the green, or only the blue LEDs are used. For each color, the intensity in between the SWGs does not completely drop to zero. This is because the angular distribution of incident light for each SWG is not small, and can be as large as 42∘. For display backlights, the brightness uniformity is one of main concerns of customers and end users. Several approaches can be used. For example, a slant reflector could be attached at the end of light bar to recycle rays. By varying the grating depth and duty cycle along the light bar surface, the diffraction efficiency could also be controlled to perform a better uniformity [2]. A third possibility is that of varying the diffraction efficiency of the SWG by changing the profile of diamond-tipped single-point cutting tools in the roll-to-roll process.
Fig. 15 (a) LED attached on the side of LB to measure the performance of a LB with SWGs. (b) LED illuminated photograph of color pattern of the LB with SWGs captured by a CCD camera.
Fig. 16 Color points in CIE x-y space, created by sampling the pattern shown in Fig. 14 (b). Points A, B, C, D and E of the red dashed polygon correspond to the SWG A, SWG B, SWG C, SWG D and SWG E. The LED’s color coordinates (points R, G and B) are also shown for reference. Points R、G and B of the black dashed triangle represents the gamut of colors of the LED.
Fig. 17 Light propagating in the LB is extracted outwardly by a plurality of sub-wavelength grating. Highest luminance (designed to be white light) occurs at the viewing angle = 0°.
Table 3. Color Patterns and Luminance of Each Grating Area Illuminated by LED of (a) Red, (b) Green, and(c) Blue Light Source
From the cross sectional view of the SWG D shown in Fig. 12, the manufactured vertex-angle of SWG deviated from the design value of 90∘. The effect of this can be seen in Table 3. When illuminated by only the blue LED, the luminance values from SWG A are not much higher than from SWG D and E, which contradicts the design. This reveals some fabrication issues that the roll-to-roll process has to overcome before it is fully applied to fabricate SWGs in a production line. First, when cutting a grating with a period smaller than 3 micron according to our pre-tests, the cutting side of the tool is easily damaged, leading to rough SWG surfaces and asymmetric profiles. A typical example is shown in Fig. 18 . This means a more wearable cutting tool is required for future applications. As an example, a calculated efficiency variation for SWG D is shown in Table 4 . It shows that if the height drops from the design value of 202 nm to 151 nm or 101 nm because of the abrasion of the cutting tool, the designed efficiency will reduce by 20.16% and 50.24%, respectively. Second, the scale of depth and period of SWG is usually less than 500nm, meaning the temperature variation (< ± 0.1∘C) and equipment oscillation (< ± 0.1 period)) should be well controlled.
Fig. 18 In cutting, the cutting side of the tool is easily damaged, generating rough SWG surfaces and asymmetric profile.
Table 4. Calculated diffraction efficiencies of sub-wavelength gratings replicated from an imprinting Cu roller, cut using the wear of the diamond bite.
5. Conclusion
A SWG patterned LB was proposed to reduce the coupling length and improve the white color balance for display applications. To demonstrate this, an array of SWG composed of 90° vertex angle grooves with periods 477nm, 439nm, 400nm, 373nm and 346nm was manufactured to verify the corresponding color performance. The performance of the prototype matches the design well in both precision and profile. By carefully controlling the precision of the cutting routes and the parameters of UV power and forming feed-rate, roll-to-roll fabricated SWG film has the potential to be applied in other SWG patterned optical systems.
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