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A novel polarized light-guide plate (LGP) for the illumination of liquid crystal display is proposed in this paper. For the substrate of the LGP, stress-induced birefringence is introduced to achieve the polarization state conversion. An aluminum sub-wavelength grating (SWG) is designed on the top surface as a polarizing beam-splitter (PBS). The structure of the novel LGP is optimized for three wavelengths of LEDs: 625nm, 533nm and 452nm, and high efficiencies of polarization conversion are obtained. The backlight system with the designed LGP does not require prism sheets and quarter wavelength plate. The backlight with the novel LGP achieved large gain in energy efficiency, and the peak luminous intensity is about 2 times higher than that of a conventional backlight.
©2005 Optical Society of America
1. Introduction
Liquid crystal displays (LCDs) are widely used in a range of electronic productions. The LCD panel has no function of emitting light spontaneously. And there are three LCD panel illumination technologies: transmissive LCD, transflective LCD and reflective LCD. The transmissive LCD panel for portable multimedia devices always needs edge-lit backlight system (BLS) for illumination. The conventional BLS always consists of a light source, a LGP and some optical sheets, such as a reflection sheet, a diffusion sheet and two crossed prism sheets. In order to make the backlight thinner and lighter, Käläntär et al.[1] have proposed a BLS, in which only one prism sheet is used instead of one diffusion sheet and two crossed prism sheets. Based on highly scattering optical transmission, Okumura et al. [2] have reported a highly-efficient BLS without any optical sheet. In these un-polarized BLSs, the optical efficiency is low due to the lack of polarization conversion. In the generation of polarized light, over 50% of the energy is absorbed by the rear polarizer of the LCD panel. For high efficiency, in recent years, lots of researches focus on the polarized BLS which recycles the undesired polarized light and emits linearly polarized light directly. Z. Pang and L. Li have proposed a high-efficiency polarized BLS based on the thin film PBS on the bottom surface of the LGP [3]. However, because there are no patterns on the bottom surface of the LGP, the backlight uniformity is difficult to control. For the blue light, the extinction ratio is only 20. Henri J.B. Jagt, Hugo J. Cornelissen et al. have reported a polarized BLS, in which the s-polarized light is extracted owing to the selective total internal reflection at microgrooves in the anisotropic layer [4]. However, the smoothness requirements of microgroove surfaces are stringent for reducing scattered light. Ko-Wei Chien et al. have reported an integrated polarized LGP and a 1.7 gain factor of polarization efficiency is achieved [5]. But the slot structures on the bottom surface of the LGP can not control the illumination angle easily. Moreover, all these polarized BLSs require achromatic quarter wavelength plates to achieve the polarization state conversion.
In the polarized BLS, the two essential issues are the reflecting PBS and the polarized light conversion. The reflecting PBS separates polarized light, such as transmitting the p-polarized light and reflecting the s-polarized light. Then, the reflected s light is turned into p light by the polarization conversion device, and then emitted by the PBS. Finally both p and s light are utilized.
In this paper, a novel LGP is developed for three wavelengths of 625nm, 533nm and 452nm which emitted by red, green and blue (RGB) LEDs. The LGP substrate with the stress-induced birefringence realizes the conversion of polarized light and this is described in detail in Section 2. In Section 3, an aluminum SWG is designed on the top surface as a PBS to extract linearly polarized light. Compared with the conventional BLS, the polarized BLS with the novel LGP is simulated in Section 4.
2. Polarized light conversion
In the published polarized BLSs, quarter wavelength plates are used to realize p-s polarized light conversion [3, 5]. In this Section, the stress-induced birefringence is introduced instead of the quarter wavelength plate, and the stress is optimized. The stress-optical law of the plane photoelasticity can be expressed as
The amount of produced birefringence ( ∆n ) is proportional to the stress difference ( ∆σ = σy - σx ) provided the stress is not too large. C indicates the stress-optical coefficient.
As shown in Fig. 1, σx axis is perpendicular to σy axis and the angle between σx axis and x axis is denoted as β. The stress is applied along σx axis and σy axis directions respectively. The thickness of the LGP substrate denotes as a . The phase retardation value δ of passing through the substrate twice can be written as
where λ denotes the wavelength of the incident light, and L = 2a.
In x-y coordinates, the Jones matrix T of the substrate can be expressed as
The incident y-directional polarized light can be written as , here A denotes the light wave amplitude. The light passed the substrate twice can be written as
The intensity of the x-directional polarized light transmitted from the PBS is
Under the conditions of
the intensity achieves the maximum value A 2 , and the efficiency of polarization conversion is 100% . Eq. (6) means that the LGP with applied stress is similar to the quarter wavelength retardation plate. As the achromatic BLS, the phase retardation value should be close to 2kπ + π for the multiple wavelengths of λR(625nm) , λG(533nm) and λB(452nm) . Hence, the stress difference ∆σ should be optimized. The optimization problem can be expressed as
where mod denotes modulus after division, abs returns absolute value, and δR , δG and δB denote the phase retardation values for wavelengths of λR , λG and λB respectively. wR, wG and wB denote weight factors of the light of red, green and blue respectively. In our design, all the weight factors are set to 1.0.
The LGP substrate of 0.8mm thickness is made of Bisphenol-A Polycarbonate (BAPC), which is a traditional plastic material and widely used in BLSs. The value of the BAPC’s stress-optical coefficient C is 8.9×10-12 Pa -1 [6]. The objective function values with respect to the stress difference ∆σ are plotted in Fig. 2.
When ∆σ = 10.31×107 Pa, the local minimum value of Eq. (7) is obtained. The phase retardations of the red, green and blue light are:
Compared with the ideal achromatic wave plate, the maximum error is only 7%. As β = π/4, Eq. (5) indicates that the polarization conversion efficiency of this substrate is more than 99%. The 7% error of phase retardation only leads to a 1% decrease in conversion efficiency. The LGP substrate with applied stress can realize the polarization conversion, and the quarter wavelength plate can be left out. The stress-induced birefringence can remain in LGP by using the stress-freezing techniques [7]. Be similar, the strain-induced birefringence can be applied to achieve the polarization conversion too.
3. Polarizing beam splitter
Fig. 3. the coordinate system and the structure of the SWG on the top surface of the LGP. Here, θ denotes the incident angle, φ denotes the azimuthal angle, and f denotes the grating duty cycle.
The PBS is the other key issue in the polarized BLS. As a PBS, the wire-grid SWG is studied for visible light in both classical and conical mounting by M. Xu et al [8]. Based on the rigorous coupled-wave theory [9], we design a SWG on the top surface of the LGP as shown in Fig. 3. The SWG as a reflecting PBS transmits p-polarized light and reflects s-polarized light. Aluminum is chosen as the material of the grating, and the material of the substrate is BAPC as mentioned in Section 1. The period of the SWG d is chosen as 0.14μ m. In order to achieve achromatism, the SWG should have the same performance for the red, green, and blue light. The desired goals are gain the maximum transmission for the p light, the minimum transmission for the s light, the maximum extinction ratio and the achromatism.
As shown in Fig. 4, the transmission of the p- and s-polarized light depends on the duty cycle f of the grating. Figure 4 shows that the duty cycle of 0.5 is appropriate.
Fig. 4. the calculated dependences of the transmission on the duty cycle for (a) p-polarized light and (b) s-polarized light of red, green and blue. Here, incident angle θ = 0.
As shown in Fig. 5, the transmission of the red, green and blue light depends on the depth of the aluminum h respectively too.
Fig. 5. the calculated dependences of the transmission on the grating depth for (a) p-polarized light and (b) s-polarized light of the red, green and blue light. Here, incident angle θ = 0.
Based on the desired requirements, the depth of the grating h is optimized as 0.16μ m. At this depth, the p-polarized transmission ratios of the red, green and blue light are all equal to 0.91 as shown in Fig. 5(a). The calculated results of the designed SWG are shown in Fig. 6.
Fig. 6. Calculated results of the designed SWG with different wavelengths; (a) transmission of the p-polarized light, (b) transmission of s-polarized light and (c) extinction ratio as a function of the incident angle.
When θ < 40°, the transmission of the p-polarized light is high. The s light transmission is low, and the minimum extinction ratio is as high as 11000. Because of the high extinction ratio of the SWG, the rear absorbing polarizer of the liquid crystal display panel is not required anymore.
4. Polarized light-guide plate
Fig. 7. Ray tracing in the proposed LGP. The s light is converted into the p light by the stress-induced birefringence of the LGP substrate.
The substrate of the LGP acts as an achromatic quarter wavelength plate, and the SWG on the top surface acts as a reflecting PBS. The patterns on the bottom surface of the LGP are v-type grooves as shown in Fig. 7, the base angle and the apex angle are optimized as 53 and 74 degrees respectively. They are used to change the incident angle (to θ < 40°) and control the backlight illumination angle instead of the prism sheets. There is a reflection sheet under the LGP, and the source is the LED array. The 2-inch polarized BLS with the novel LGP is simulated by the Monte Carlo non-sequential ray tracing program. An absorb polarizer is used in the conventional BLS to obtain the polarized light. The luminous intensity at the center of the top light-emitting surface of the polarized BLS and that of the conventional BLS are compared in Fig. 8.
Fig. 8. Polar luminous intensity plots of polarized light emitting form (a) the proposed BLS and (b) the conventional BLS. Here, φ denotes the azimuthal angle, and θ denotes inclination angle.
For the polarized BLS, the peak luminous intensity is about 28, and that of the conventional BLS is about 14. The gain factor is 2, and the optical efficiency is substantially improved. By optimizing the prism distribution and the prism size on the bottom surface of the LGP, the polarized BLS achieved an illumination uniformity of 78%.
5. Conclusion
In this paper, the stress-induced birefringence is introduced to the substrate of the LGP. The SWG is designed on the top surface of the LGP to emit linearly polarized light. Both the stress and the structure of the SWG are optimized for the red, green and blue light to realize achromatism. The polarization conversion and separation are realized in one LGP. For the BLS with this LGP, the prism sheets, the diffusion sheet and the quarter wavelength plate are not needed anymore. The simulation results show that the luminous intensity greatly increased. We believe it will make the LCD thinner, lighter and brighter.
In our design, the material of the LGP substrate is polycarbonate, however, other polymers, such as polystyrene (PS) and polymethylmethacrylate(PMMA), can be selected too.
Acknowledgments
The authors thank Lifeng Li for providing KAPPA, a computer program for calculation of periodic diffraction gratings.
References and links
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