The color gamut is one of the important parameters of a display device [1]. The wider the color gamut, the more color to represent a real object accurately. There are several color-gamut standards that have been proposed to evaluate color performance, such as the NTSC, sRGB, DCI-P3 and Rec.2020 standards [2, 3]. In recent years the wide color gamut has become more and more popular, because consumers demand vivid colors in displays. Therefore, improving the color gamuts of displays has become a hot research topic. In liquid-crystal displays (LCDs), the LCD panel does not emit light, but rather controls the transmittance of backlight; the white light emitted by the backlight source passes through the LCD panel, and a color filter is usually used to display three primary colors, from which the various colors can be obtained [4]. Therefore, the color gamut of the LCD is determined by the combination of the spectral characteristics of the backlight source and the spectral transmission factor for the color filters. Nowadays the phosphor-converted white-light-emitting diode (pc-WLED), which employs a blue LED to pump a yellow phosphor and generate white light, has replaced the cold-cathode fluorescence lamp (CCFL) as the major backlight technology. The pc-WLED has become the most prevalent backlight source for LCDs, because of its advantages of high efficiency, long lifetime, low cost, and technological maturity. However, its color gamut is limited to only 72% of NTSC (hereafter “72% NTSC”, etc.) in the CIE 1931 color space [5]. To enlarge the color gamut, the two-phosphor-converted white-light-emitting diode (2pc-WLED) and QD backlight have been developed. The 2pc-WLED employs a blue LED to pump red and green phosphors and generate white light, and its color gamut can reach 100% NTSC [6]. As a new backlight, QD has great advantages for a wide-color-gamut display. Cadmium-based QDs possess the features of narrow emission bandwidth and controllable emission peak, so the color gamut can reach 110% NTSC [7-9]. However, cadmium is a toxic heavy metal, and is strictly regulated. Cadmium-free QDs have the problems of low light-conversion efficiency and wide spectral distribution [10]. Perovskite QD has the advantages of wide color gamut (120% NTSC), easy processing, and low cost, and offers an important direction for the development of current and future QD backlight technology [11, 12]. However, the lead in perovskite QD technology is also a toxic heavy metal, and is also strictly regulated. In the end, a system with a good spectrum and without any heavy metals is needed, to achieve a wide color gamut.

In this paper we propose a bandpass filter that is used in the backlight unit to widen the color gamut of an LCD. A bandpass filter [13-18] efficiently transmits light in some wavelength ranges and reflects light for the remaining wavelengths. The effect of bandpass filters based on the (HL)²H structure, and of (HL)²H coated on a diffusion film, on the color gamuts of LCDs is investigated. Moreover, the color gamut can retain a high value when the incident angle of light is in the range of 0~30°.

Figure 1(a) shows the panel configuration with an edge-lit LED, and a bandpass filter inserted between the LCD and backlight module. Figure 1(b) shows a schematic diagram of the structure and transmission principle of the proposed bandpass filter, which consists of overlapping layers with low and high refractive indices. The practical structure here is a 5-layer film. Titanium dioxide (TiO₂) is selected as the high-refraction layer, because of its low optical loss and relatively high refractive index. Magnesium fluoride (MgF₂), as the low-refraction layer, is a low-refractive-index material with chemical stability and high hardness.

The transfer-matrix method [19, 20] is employed to analyze the optical properties of the bandpass filter. The characteristic matrix of the 5-layer film system can be expressed as:

where j is the number of layers, and η_j is expressed as:

in which η_j indicates the admittance of the exit medium, and n_j and θ_j are respectively the refractive index and incident angle for layer j. The equivalent phase of the j^th-layer film is:

Here λ is the wavelength and d_j is the thickness of the j^th-layer film.

The reflectivity and transmissivity of the 5-layer film can be expressed as:

where η₀ is the admittance of the incident medium.

According to optical thin-film interference theory, we know that the transmission band depends on the thickness of a multilayer film. Therefore, the thickness of each multilayer film is optimized to transmit only the red, green, and blue light, while reflecting the remaining light. A larger number of periodic layers can lead to a lower transmittance within the reflection band, but more layers will increase the manufacturing cost and complexity. Therefore, the minimum number of layers to achieve an acceptable transmittance is the aim of our optimization.

The transmittance spectrum of the bandpass filter based on the (HL)²H structure is shown in Fig. 2(a). Here H has a high refractive index n_H = 2.28, and its thickness d_H is 0.58 µm, while L has a low refractive index n_L = 1.38, and its thickness d_L is 0.1 µm. The normalized transmission intensity spectra of a pc-WLED with this bandpass filter are shown in Fig. 2(b). In addition, the normalized transmission intensity spectra of a blue LED with K₂SiF₆:Mn⁴⁺ (KSF-LED, a type of 2pc-WLED) and of a QD backlight with this bandpass filter are shown in Figs. 2(c) and 2(d) respectively. From Figs. 2(b)~2(d), the bandpass filter is seen to optimize the backlight spectra and improve the purities of the red, green, and blue colors. The color gamut of the LCDs is simulated using the TechWiz 1D software, and the color filter is that usually used in typical LCDs, with 72% NTSC for the LCD with pc-WLED backlight. From Figs. 2(e) and 2(f), we can see that the color gamuts of LCDs with pc-WLED, KSF-LED, and QD backlights can be improved from 72% to 95.3% NTSC, from 92% to 106.7% NTSC, and from 104.3% to 112.2% NTSC respectively. The detailed chromaticity coordinates for the displays without and with the bandpass filter are listed in Tables 1 and 2.

For any the multilayer film structure using interference effects, the angular dependence is a knotty issue. When the incident light is oblique, the transmittance spectrum of the bandpass filter will shift toward shorter wavelengths, as shown in Fig. 3(a). The reflection band shifts toward blue by about 2 nm when the angle of incidence increases from 0° to 10°; this is a very small value. The blue shift is more obvious with increasing incidence angle, exceeding 10 nm as the angle increases to 30°. Figure 3(b) shows the color gamut for different incident angles, without any change in the LCDs themselves. The color gamut of the LCD with the pc-WLED backlight only decreases by 2.9% (from 95.3% to 92.4% NTSC) as the incidence angle increases from 0° to 30°. For the KSF-LED backlight, the color gamut of the LCD slightly decreases, from 106.7% to 105.7% NTSC. For the QD backlight, the color gamut barely changes. The reason is that the peaks of the QD backlight can be kept within the transmitted-light ranges of the bandpass filter.

The multilayer film with (HL)²H structure must be coated on a substrate; the diffusion film in the backlight module can be used as that substrate. The refractive index n_S of the diffusion film is set at 1.5, and there is no interference effect in this diffusion film, because of its scattering effect. The transmittance spectrum of the band-pass filter based on the (HL)²H structure coated on the diffusion film (termed “(HL)²HD”) is shown in Fig. 4(a); the transmittance of the reflected light is a little larger than for the (HL)²H structure. As a result, the color gamuts of the LCDs with three different backlights can be improved from 72% to 92.6% NTSC, from 92% to 105.6% NTSC, and from 104.3% to 111.9% NTSC respectively. The detail chromaticity coordinates for the displays with the bandpass filter are listed in Table 3.

The bandpass filter based on the (HL)²HD structure has the same problem of angular dependence: As the incidence angle of light increases, the change in transmittance is similar to that for the (HL)²H structure, as shown in Fig. 5(a). Figure 5(b) shows the change in color gamut for different incidence angles and three different backlights. When the incidence angle increases from 0° to 30°, the color gamuts of LCDs with pc-WLED and KSF-LED backlights decrease from 92.6% to 90% NTSC and from 105.6% to 104.4% NTSC respectively. For the QD back-light, again, the color gamut hardly changes.

Figure 6(a) shows the variation of transmittance of the bandpass filter with different numbers of periodic layers within the whole structure. As the number of periodic layers increases, the transmittance within the reflection band gradually decreases, and the shape of the reflection band is improved, becoming close to rectangular. Figure 6(b) shows the color gamuts for different numbers of periodic layers. With increasing number of periodic layers, the color gamut of an LCDs can be improved. The color gamut of the LCD with pc-WLED backlight is saturated at 102% NTSC when the number of periodic layers is greater than 6. For the KSF-LED backlight, the color gamut is saturated at 107% NTSC when the number of periodic layers is larger than 3. For the QD backlight, the color gamut is saturated at 112% NTSC when the number of periodic layers is larger than 3. In each case, as the number of periodic layers increases further, the color gamut of the LCD practically does not change.

In summary, the optical properties of a bandpass filter are calculated by the transfer-matrix method. First we simulate the effect of (HL)²H and (HL)²HD structures on the color gamut of LCDs, and find that the bandpass filter based on the (HL)²H structure can enlarge the color gamut of LCDs with pc-WLED, KSF-LED, and QD backlights by 23.3%, 14.7%, and 7.9% respectively. When the incidence angle of light increases to 30°, the reduction of color gamut for the three different backlights is within 3%. For a bandpass filter based on the (HL)²HD structure, the color gamuts of LCDs with three backlights increase by 20.6%, 13.6%, and 7.6% respectively. The reduction of color gamut for the three different backlights is less than 3% for light incident at 30°. For projection display, a pc-WLED or 2pc-WLED is usually used to replace the RGB-laser light, due to the cost. A bandpass filter can be used to obtain a vivid image with a high color gamut, because the projection angle is limited to a 30° polar angle. The results show that the bandpass filter is an efficient potential approach to achieve a wide color gamut for an LCD. The deposition of the multilayer film can be realized via conventional electronbeam evaporation (CE) and plasma ion-assisted deposition (PIAD) on a glass substrate [21, 22]. However, it takes time to apply to large-area displays, because of the strict processing and high cost.