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JOURNAL OF DISPLAY TECHNOLOGY, VOL. 9, NO. 7, JULY 2013 561

Roll-to-Roll Process-Based Sub-Wavelength Gratingfor a Color-Separation Backlight

Chun-Wei Liu, Chi-Hung Lee, Chia-Jen Ting, Tsung-Hsin Lin, and Shih-Chieh Lin

AbstractFor this study, we designed a color-separation back-light to avoid the use of absorptive color filters in a conventionalbacklight. The module consists of sub-wavelength grating on alight-bar (SWG-LB) and a cylindrical lens array on a V-groovedlight guide to display R/B/G images more efficiently. We designedthe light bar to be a hexagon type in which partial total internalreflection (TIR) area is uniformly spaced between each SWG.The measurements showed that uniformity from the light barand NTSC are 92.8% and 99%, respectively. The optical compo-nents including the sub-wavelength grating and the cylindricallens array were mass produced, and the diamond turning wasproduced using a roll-to-roll process.

Index TermsColor-separation backlight, diamond turning,roll-to-roll process, sub-wavelength grating.

I. INTRODUCTION

C ONVENTIONAL liquid crystal displays (LCD) containabsorptive dye colorfilters to absorb certain wavelengthsof light and allow only a portion of the visible light in the elec-

tromagnetic spectrum to pass through.

Many attempts have been made to replace this type of low-

efficiency color filter. Lin et al. proposed a color separation

module consisting of a blazed grating and an aspheric-lenticular

lens array [1]. Chen et al. introduced a blazed grating embedded

into the LCD to separate the required left and right images from

a stereoscopic image without using a dye-based colorfilter [2].

Both designs require a high collimation backlight, which, how-

ever, is difficult to realize. Yamada et al. demonstrated diffrac-

tive grating with a pitch of 550 nm to separate colors combined

with a cylindrical lens array to generate primary colors [3]. Ca-

puto and Xu also used a holographic structure for the same pur-

pose but set the pitches of their interferometry-based gratings as

low as 320 nm and 400 nm to improve efficiency [4][6]. How-

ever, size feasibility was limited and the fabrication cost was

high.

This studyproposes an SWG system for color separation.The

system is divided into three modules: i) the SWG-LB module,ii) the light guide, and iii) the cylindrical lens array, as shown

Manuscript received June 27, 2012; accepted January 31, 2013. Date of pub-lication May 13, 2013; date of current version July 10, 2013.

C.-W. Liu and S.-C. Lin are with Power Mechanical Engineering, NationalTsing Hua University, Hsinchu, 30013, Taiwan (e-mail: [email protected]; [email protected]).

C.-H. Lee is with Electrical Engineering, Feng Chia University, Taichungcity, 40724 Taiwan (e-mail: [email protected]).

C.-J. Ting and T.-H. Lin are with Industrial Technology Research Institute,Mechanical and Systems Research Laboratories, Hsinchu, 31040, Taiwan(e-mail: [email protected]; [email protected]).

Color versions of one or more of the figures are available online at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JDT.2013.2249039

in Fig. 1. The first component, SWG-LB, is a light bar with

sub-wavelength grating. By using irregular patterns of the sub-

wavelength grating on top of the light bar, the SWG-LB can

separate a collimated light-emitting diode (LED) light source

[7] into primary colors at different angles.

These angularly separated colors then enter the light guide.

We attached a reflector at its V-grooved bottom to redirect

colors toward the cylindrical lens array. After passing through

the cylindrical lens array, the angular rays were mapped into

their corresponding sub-pixel positions in the LCD, showing

color images. The design procedures of the light guide and the

cylindrical lens array are similar to that in [8]. In this paper, wefocus on the design of the SWG-LB module.

II. DESIGN AND SIMULATION

A. Incident Angle

The following design criteria was used to couple the sub-

wavelength grating structure on the light bar: The direction of

light extraction from SWG-LB should be a function of the in-

cident wavelength, incident angle, the refractive index of the

material, and the grating period, whereas the light extraction

efficiency should be related to the grating profile. To generate

uniform and well-separated red, green, and blue lights simulta-

neously, a hexagon-type light bar with a wedge angle of was

proposed. As shown in Fig. 2, the LED rays entered the light

bar from both sides of the wedge and formed parallelogram-like

rays. The wedge angle is determined by the refractive index of

the light bar material:

(1)

For (PMMA-made light bar), the wedge angle is

54 and the corresponding incident angle to the grating on the

light bar is 63 .

The grating period was designed to vertically out-couple the

green rays ( nm) from the light bar. The central inci-

dent angle is known, and the grating period is derived from the

grating equation:

(2)

where is the incident angle, is the diffracted angle,

is the refraction index of the incident medium PMMA, is the

refractive index of air, and is the diffraction order. Through

this grating, the first-order diffraction angles for the red light

( nm) and blue light ( nm) are 15 and

10 , respectively.

1551-319X/$31.00 2013 IEEE


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562 JOURNAL OF DISPLAY TECHNOLOGY, VOL. 9, NO. 7, JULY 2013

Fig. 1. Schematic configuration of the system.

Fig. 2. Parallelogram-like rays formed by the LED rays entered from both sideof the wedge.

Fig. 3. Diffraction efficiency as a function of wavelength and incident angle( nm).

B. Primary Design

The grating and arrangement of the grating on the light

bar are two major factors influencing extraction uniformity.

To optimize the grating design, a series of simulations were

conducted first. The simulations were conducted using acommercial software, G-Solver, which was developed using

the rigorous coupling wave analysis (RCWA). The rigorous

coupling wave analysis is well suited, in particular, for planar

gratings bounded by two different refractive indexes [9].

Fig. 3 shows the diffraction geometry for an ideal blazed

grating. The period of the grating is denoted as and the max-

imum depth of the grating is denoted as . The incident light

with a wavelength of is coming from a material with refrac-

tive index (region I) at an incident angle and is diffracted

into a material with refractive index (region II).

The tangential components (TE polarization) of the incident

light wave in regions I and II are

(3)

(4)

where and are the normalized electric-field amplitude of

the th backward-diffracted and forward diffracted waves, re-

spectively. The quantity is derived from the Floquet condi-

tion and it is

(5)

(6)

Fig. 4. Diffraction efficiency as a function of wavelength and incident angle( nm).

Here and are either positive real or negative imagi-

nary. and can be calculated by solving the coupled wave

equations for blazed gratings. The diffraction efficiency is de-

fined as diffracted power of a particular order divided by the

input, and reflected and transmitted diffraction efficiencies at

each diffraction order are calculated from the following equa-

tions, respectively:

(7)

(8)

Note that the sum of DEri and DEti is always 100%. The other

tangential components (TM polarization) of the incident wave

is similar to the above expression since the light source is from

an un-polarized LED, the diffraction efficiency is assumed to be

the average of intensity of TE and TM modes [10].

We conducted a series of simulations to design a grating pro-

file and found that when the grating pro

file was triangular withan apex angle of 90 , the diffraction efficiency of the first trans-

parent diffraction order ( ) for wavelengths ranged between

470 and 630 nm, and the incident angles varied from 43 to 90

when the grating profile was triangular with an apex angle of

90 (as shown in Fig. 4). However, the grating profile is limited

by the process used in this study.

The grating arrangement on the light bar was optimized by

combining the SWG areas with flat areas, which were designed

to balance the overall intensity. The diffraction efficiency de-

rived using G-Solver was also used as inputs to the Advanced

Systems Analysis Program (ASAP) [11]. We conducted a series

of simulations using the ASAP to determine the proper ratio be-

tween the SWG areas and flat areas, to obtain a uniform light

extraction from the light bar. According to our simulation, as


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LIU et al.: R2R PROCESS-BASED SUB-WAVELENGTH GRATING FOR A COLOR-SEPARATION BACKLIGHT 563

Fig. 5. (a) Simulation of thecylindrical lens array.(b) Full pixel R/B/G pattern.

Fig. 6. (a) Roller and the single-point diamond-cutting tool for imprinting thesub-wavelength gratings. (b) Schematic diagram showing the roll-to-roll UVembossing process.

the average ratio of the SWG area to the flat area approached ap-

proximately 2:1, the extraction uniformity reached 90% for all

three primary colors. In the light guide, the depth and period of

V-grooves at the bottom were designed to provide uniform light

distribution [8]. The period of the cylindrical lens was 600 m,

which is equal to the full width of three sub-pixels. The radius of

curvature for the cylindrical lens (made of ultraviolet-exposedresin with a refractive index of approximately 1.5) was 608 m.

Fig. 5 shows the simulated result of the R/B/G periodical line

pattern.

III. MANUFACTURING AND EXPERIMENT RESULTS

We used single-point diamond turning to produce a me-

chanically grooved sub-wavelength structure formed on an

imprinting hard-copper roller [Fig. 6(a)]. The UV resin was

then placed on a 188 m PET film, imprinted by the roll, hard-

ened by UV curing, and demolded from the roller, as shown

in Fig. 6(b). The overall feasible area was 70 mm 10 m. Theperiod measured using scanning electron microscopy (SEM)

was within 384 5 nm of the sub-wavelength area and the flat

area, as shown in Fig. 7. We also used a roll-to-roll process to

fabricate the cylindrical lens array, of which the curvature of

the radius of each lens was 608 3 m.

For an 8-in. backlight, we designed the length, width, and

height dimensions to be 70 mm, 10 mm, and 10 mm, respec-

tively. The assembled SWB-LB is shown in Fig. 8(a). The actual

grating period was relatively close to the designed values, with

a difference of less than 3%. We used red (633 nm), green (532

nm), and blue (465 nm) laser diodes to test the SWB-LB sub-

system and measured diffraction angles of 19 , 4.5 , and 7 ,

respectively. These values matched the diffraction angles de-

rived from (2). Fig. 8(b) shows the illumination pictures pro-

Fig. 7. SEM imagesof thefabricatedsub-wavelengthgrating andthe boundarybetween the SWG area and the flat area.

Fig. 8. (a) Light bar illuminated by the R(633n m)/G(532 nm)/B(465 nm) laserbeam expanders. (b) Light bar with sub-wavelength grating prototype. (c) Nor-malized intensity generated by the prototype.

Fig. 9. Prototype backlight illuminated by the SWG-LB.

duced by red, green, and blue laser diodes. The uniformities of

normalized intensities are all above 88%, as shown in Fig. 8(c).

To measure the performance of SWG-LB, a highly collimated

white light source was setup, which consisted of three colli-

mated beam expanders, one for each color, and two beam split-

ters (Fig. 9). The light source was focused by a lens with an EFL

of 25.4 mm first. Another lens with an EFL of 100 mm was then

used to expand the focused light into parallel rays. The light

source had peak values at 630 nm (R), 520 nm (G) and 465 nm

(B). These colors were then mixed and transmitted to the same


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