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Abstract
Broadband reflective polarizers for liquid crystal displays (LCDs) are designed. The working principle is based on giant form birefringence generated by engineering the materials of the subwavelength gratings. The optical performances of the proposed polarizers are investigated by the finite difference time domain (FDTD) method. The proposed polarizers show an ultra-thin profile, high transmission, large extinction ratio and wide acceptable angle, all of which are highly desirable for high-efficiency ultra-thin LCDs. Finally, the fabrication tolerance of the proposed structure is discussed in detail.
© 2017 Optical Society of America
1. Introduction
Polarizers are essential optical elements in liquid crystal displays (LCDs), and are influential on the optical efficiency and contrast ratio of the systems [1]. Polarizers act as filters of the polarizations of the propagating light, and they are generally divided into two categories: absorptive type and reflective type. Absorptive polarizers are widely used in conventional LCDs because of their low cost and high performance [2]. However, more than 50% of the backlight is absorbed by the polarizers, which is a significant waste of energy. To improve the light efficiency of the displays, reflective polarizers are the favorable choice. By recycling the reflected polarization with a quarter wave plate and a mirror, the optical efficiency of the display systems can be increased by 60% [3,4]. Reflective polarizers are also preferred in high intensity beam systems, such as projectors, because they can avoid heat dissipation problems.
Conventional reflective polarizers in LCDs are the 3M dual brightness enhancement films (DBEFs) based on multi-layer constructive and destructive interference [5,6]. Hundreds of pairs of polyethylene naphthalate (PEN) and a copolymer co-PEN are stacked and uniaxially stretched to generate a refractive index difference along one in-plane direction and match the refractive index along the orthogonal in-plane direction. The birefringence of the stretched PEN with a drawing ratio of 5 is just 0.24. Therefore the bandwidth of the reflection is around 50 nm and hundreds of layers are required to achieve a reflectivity of 0.99. To work as a broadband polarizer for LCDs, several sets of the multi-layer films with gradually changed central wavelengths are laminated together, which further increases the film thickness and fabrication cost. For the development of ultra-thin LCDs, polarizers with a thin profile are eagerly anticipated [7,8]. The wire-grid polarizer (WGP) consists of fine grid of parallel metal wires shows large extinction ratio with a thin thickness of hundreds of nanometers [9–11]. However, the light efficiency of the WGP is not sufficiently high, and the transmission is around 0.85, whose loss is due to the absorption of the metal wires. Besides, the absorption will result in the increase of the material’s temperature and thermal damage problems, and makes it not suitable for high power applications [12].
In this paper, we propose to generate giant form birefringence by subwavelength grating and present the design of a simple structure to realize ultra-thin high-performance broadband reflective polarizers. Section 2 will demonstrate its configuration and operating principle. Optical characteristics are investigated by the finite difference time domain (FDTD) method in Section 3. Fabrication tolerance is discussed in detail in Section 4. Finally, a conclusion is given in Section 5.
2. Structure and operation principle
Multi-layer thin film reflective polarizers consist of N pairs of an isotropic layer and anisotropic layer, and the schematic diagram is illustrated in Fig. 1. The thicknesses of the isotropic and anisotropic layers are hI and hA respectively. The refractive indices of the isotropic layer and the substrate are nL and nS, while those of the anisotropic layer along the x and y axes are demonstrated as nH and nL respectively. Its birefringence (∆n) is the difference between nH and nL (∆n = nH–nL). The refractive indices of layers along one polarization (transverse magnetic (TM) wave) are matched, and the refractive indices along the orthogonal polarization (transverse electric (TE) wave) are deviated between the isotropic and anisotropic layers. Therefore, most of light of the TM polarization is transmitted, while the light of the TE polarization is mainly reflected. For every layer, quarter wave conditions (nHhA = λ0/4, nLhI = λ0/4) are satisfied to construct destructive interference along the TE polarization at the central wavelength λ0. The reflectivity of the TE wave at λ0 of the N pairs of alternate layers is calculated by the transfer matrix method and given by [13–15]
The reflection spectrum (TE polarization) of a multi-layer polarizer is calculated by transfer matrix method [14] and the result of five pairs of alternating isotropic and anisotropic layers is calculated and shown in Fig. 2(a). The refractive indices of the substrate and isotropic layer are set as 1.5, and the central wavelength of the reflection band is around 525 nm. When the birefringence of the anisotropic layer is small, like 0.2, the reflectivity is less than 50%, meaning that more than 50% of the TE light is leaked in the transmissive direction. But when the birefringence is large enough, like 1.5, the reflectivity of the TE light is close to 100%. Therefore the extinction ratio of the polarizer, which is defined as the ratio of the transmission of the TM wave over the TE wave (ER = TTM/TTE), is high. If we increase the number of layers of the multi-layer polarizer to 25 multi-layer pairs, it reflectivity is demonstrated in Fig. 2(b). The reflectivity becomes close to 1, even though the birefringence is just 0.2, but the bandwidth of the reflection is quite narrow, at around 50 nm. To cover the entire visible region, the birefringence of the anisotropic layer should be at least 1.5. Therefore, it is shown that the value of the birefringence is significant to achieve a broadband polarizer with a small number of layers.
Fig. 2 The calculated reflection spectra (TE polarization) of a multi-layer polarizer of N pairs of alternate isotropic and anisotropic layers. nL and nS are both 1.5. (a) 5 pairs. (b) 25 pairs.
Natural birefringence results from anisotropic materials, like calcite, liquid crystals and stretched plastic films, and the maximum value is around 0.3, which is not sufficient for broadband polarizers. Form birefringence is one way to generate the difference in the refractive indices by orderly arranging isotropic materials in dimensions scaled to wavelength [16]. The structure of a subwavelength grating is demonstrated in Fig. 3. The refractive indices of the two isotropic materials are n1 and n2 respectively. The period of the grating is Λ, which should be much smaller than the working wavelength, and it is set as 100 nm here. The linewidths of the two materials are w1 and w2 respectively. The duty ratio of material 1 is the fraction of the material in a period and is defined as f = w1/Ʌ. According to effective medium theory, the equivalent refractive indices of polarizations parallel and perpendicular to the lines are approximately given by the following expression [17–19]:
where and are the refractive indices for the TE and TM waves respectively. If we assume material 1 is the air (n1 = 1) and the duty ratio of material 1 is 0.5 (f = 0.5), which is always the case, we can calculate and as exhibited in Fig. 4 when the refractive index of material 2 is modified. The birefringence (∆n = nTE–nTM) increases as the refractive index of material 2 increases, and a birefringence of more than 1.5 can be realized when materials of a large refractive index, such as silicon, are employed.Fig. 3 The schematic diagram of a subwavelength grating. The refractive indices of the two isotropic materials are n1 and n2 respectively. The period of the grating is Λ, and is set as 100 nm.
Fig. 4 Calculated refractive indices of a subwavelength grating by zero order EMT. The grating period is 100 nm and aperture ratio is 0.5. (a) Equivalent refractive indices of the TE and TM waves. (b) Birefringence.
3. Optical characteristics of the proposed polarizer
The cross-section view of the proposed broadband polarizer is illustrated in Fig. 5, showing N pairs of alternating form birefringent layers and isotropic layers with an additional form birefringent layer, and its total number of layers is 2N + 1. The insertion of the additional form birefringent layer between the isotropic layer and the incident medium is to increase the reflection of the TE wave. The birefringent layer is a subwavelength grating with a period of 100 nm. The material of the grating is chosen as silicon because of its large refractive index and mature manufacturing process at subwavelength scale. The refractive index of the isotropic layer should be close to the refractive index of the grating along the TM polarization, and there are many choices of materials, such as silicon dioxide, Poly(methyl methacrylate) (PMMA), and so on.
Fig. 5 Cross-section view of the multi-layer polarizer of N pairs of anisotropic and isotropic layers. The thicknesses of the two alternate layers are hA and hI respectively. The period of the subwavelength grating is Λ, and the refractive indices of the materials are n2, and n1 is 1(air). The width of the grating grid is w2. The light is incident with an angle θ.
The optical characteristics of the proposed polarizers are analyzed by the FDTD method and simulated by the commercial software FDTD Solutions (Ver. 8.6.3, Lumerical Solutions, Inc.), which is a widely used numerical analysis technique to solve Maxwell equations in the time domain [20–22]. The refractive index of the silicon is 4.08 at 550 nm [23]. The refractive index of the isotropic layer (PMMA) is set at 1.49 and is frequency independent. The substrate is glass, with an index of 1.46. The thickness of the grating and isotropic layers are set as 43 nm and 92 nm respectively to satisfy the quarter wave condition around 550 nm along the TE polarization (nTEhA = λ0/4, n0hI = λ0/4). One period of the proposed configuration is simulated and the boundary conditions of the x and y axes are set as periodic to simplify the computation. A perfect match layer boundary condition along the z axis is assumed. The incident plane wave is a broadband Gaussian-modulated pulsed light, and it can be expressed as
where toff is the offset time, tωis the half width of the pulse, and ω is the central frequency of the incident light. Here toff = 7.5 × 10−15 s, tω = 2.4 × 10−15 s, and ω = 5.9 × 1014 Hz. The time step and minimum mesh step are set to be 3.9 × 10−18 s and 0.25 nm respectively to ensure the stability and accuracy of the calculation. By using this broadband excitation source, the transmission and reflection in the whole visible spectrum can be obtained in a single calculation [24].Firstly, we estimate the number of layers needed for the proposed polarizer to obtain a high extinction ratio. The optical performance of the proposed polarizer with different numbers of pairs under the normal incident conditions is demonstrated in Fig. 6. The transmission of the TM wave (TTM) from 400 nm to 450 nm dramatically decreases because of the absorption of silicon in the short wavelength region. The small variation in the long wavelength results from imperfect index matching of the TM wave between adjacent layers. Even more important, the extinction ratio at the central wavelength (550 nm) exponentially increases when more pairs are added. Considering the transmission of the TM wave and the manufacturing complexity and cost, the polarizer with four pairs is chosen as the optimal structure, with a high extinction ratio of more than 103 under normal incidence, which is sufficient for high-quality displays. The number of layers is nine, and the total thickness of the proposed polarizer is less than 1 μm, which is much thinner than the conventional reflective polarizer 3M DBEF, whose thickness is usually more than 25 μm. The transmission of the TM wave is larger than 0.9 from 485 nm to 700 nm, and the average value in the whole visible region is 0.87, which is quite high. The average reflectivity of the proposed polarizer is 0.73, and around 50%-60% of the TE wave is converted to TM wave after recycling [25]. Therefore, the overall efficiency improvement of the proposed polarizer is around 50% compared with conventional absorptive iodine polarizers, whose transmission is also around 0.87 [8].
Fig. 6 Optical performance of the proposed polarizer with different numbers of pairs under the normal incident conditions. (a) Transmission of the TM wave. (b) Extinction ratio at 550 nm.
The backlight of LCDs is not collimated; therefore the acceptable angle of the polarizer should be taken in consideration [26]. The optical characteristics of the proposed polarizer under oblique incidence are demonstrated in Fig. 7. Compared with normal incidence, the TTM shows a small change, even when the light is incident with an angle of 45 degrees. The cutoff wavelength of RTE in the short wavelength region is blue shifted when the oblique angle increases, due to the effective optical path decreasing under oblique incidence [25], and the central wavelength of the reflection band is expressed as
where n and h are the refractive index and thickness of the layer, θis the incident angle, and λ0 is the central wavelength of the reflection band. The extinction ratio is enhanced under an oblique angle, so the proposed polarizer can also be applied as a polarizing beam splitter in projection systems, which usually work under 45-degree oblique incidence [27].Fig. 7 Angular performance of the proposed polarizer: (a) Transmission of the TM wave. (b) Reflectivity of the TE mode. (c) Extinction ratio.
4. Fabrication tolerance
In real manufacturing, the fabrication of such fine structure is challenging. Electron beam lithography, which shows high resolution of sub-10 nm, is a sophisticated way to make the subwavelength grating [28]. Nanoimprint technique is a promising candidate to duplicate the fine grids in a high-throughput and low-cost way [10,29]. Moreover, in nanometer scale, the geometric parameters of the proposed polarizer may have small deviation; therefore the fabrication tolerance should be taken into account. The most important parameter of the polarizer is the period of the silicon grating, because the grating can no longer be regarded as an equivalent form birefringence layer if the period of the grating is not much smaller than the working wavelength. The transmission of the TM wave and extinction ratio of the proposed polarizer with modified periods is exhibited in Fig. 8. When the width of the silicon grid gets closer to the working wavelength, blue light of the TM polarization is also reflected and results in a big drop in the transmission. If the period of the grating increases further, most of the TM wave will be reflected and the polarizations cannot be split. The reflectivity of TE wave slightly increases and the extinction ratio is improved when the period of the grating increases.
Fig. 8 Fabrication tolerance of the period of the silicon grating: (a) Transmission of the TM wave. (b) Reflectivity of the TE mode. (c) Extinction ratio.
The aperture ratio of the grating is defined as 1-w2/Λ, where w2 is the width of the silicon grid. As the aperture ratio increases, the width of the silicon grid decreases, and the silicon’s absorption at short wavelength range is reduced. Therefore the transmission of TM increases when the aperture ratio increases, and the results are shown in Fig. 9. However, the leakage of the TE wave along the transmission direction also increases and results in the slight decrease of the extinction ratio. Therefore, the proposed polarizer with an aperture ratio ranging from 0.5 to 0.6 is quite satisfactory for high transmission applications, whose average transmission from 400 nm to 700 nm is more than 0.85. Although the transmission of the polarizer with an aperture ratio ranging from 0.4 to 0.5 is less, the extinction ratio is larger than 1500, which is favorable for high extinction ratio cases.
Fig. 9 Fabrication tolerance of the aperture ratio of the silicon grating: (a) Transmission of the TM wave. (b) Extinction ratio.
As regards the deposition of the isotropic layer, there are plenty of materials having the refractive index around 1.49 including PMMA [23], so oblique evaporation technique could also be considered besides the diverse coating methods [30]. The sinking effect of the PMMA layer to the air gap should be taken into consideration, which is shown in Fig. 10. The effective refractive indices of TM and TE waves are modified because of the intrusion of the isotropic material, so the refractive indices of TM waves are not matched between the grating layer and isotropic layer, which increases the reflection of the TM wave. As the aggravation of the sinking effect, the transmission of the TM wave is reduced sharply, and the average transmission from 400 nm to 700 nm decreases to 0.63 when the entire air gap is occupied by the PMMA. The relative variation of the refractive index of TE wave of the grating layer is much smaller, so the reflectivity of TE wave is less affected. Moreover, a fractional drop of the extinction ratio to 1200 can only be observed when the air gap is fully filled by the PMMA, which shows great feasibility of the fabrication of the proposed structure.
Fig. 10 Fabrication tolerance of the sinking effect of the isotropic layer: (a) Diagram of the sinking effect. D is the sinking depth. (b) Transmission of the TM wave. (c) Reflectivity of the TE wave. (d) Extinction ratio.
The influence of the layer thickness of the silicon grating and PMMA are mainly embodied in the shifting of the reflection band of the TE wave. The wavelength of the reflected TE light can be roughly estimated by the following equation [31]:
where and are the thickness of the silicon grating and PMMA layer respectively. The optical performances of the proposed polarizer when the thicknesses of the two layers are varied are demonstrated in Fig. 11 and Fig. 12. The thickness of silicon grating layer is fixed at 43 nm when the thickness of PMMA layer is varied. The thickness of PMMA layer is fixed at 92 nm when the thickness of silicon grating layer is modified. The transmission of the TM wave from 400 nm to 450 nm is reduced with an increasing thickness of the silicon grating due to its absorption. The reflection band of the TE wave is red shifted when the thicknesses of the silicon grating and PMMA layer increase, and this results in the same movement of the extinction ratio spectra. Besides this, the highest extinction ratio achieved at a shorter wavelength is slightly larger than that achieved at a longer wavelength because of the higher birefringence at the shorter wavelength. Moreover, this shows a convenient way to modify the working band of the proposed polarizers, because the central wavelengths of the backlight light emitting diodes may be different.Fig. 11 Fabrication tolerance of the thickness of the silicon grating layer: (a) Transmission of the TM wave. (b) Reflectivity of the TE wave. (c) Extinction ratio. The thickness of the PMMA layer is fixed at 92 nm.
Fig. 12 Fabrication tolerance of the thickness of the PMMA layer: (a) Transmission of the TM wave. (b) Reflectivity of the TE wave. (c) Extinction ratio. The thickness of the silicon grating layer is fixed at 43 nm.
5. Conclusion
We have proposed an approach to generate giant form birefringence based on a subwavelength silicon grating, and designed a broadband reflective polarizer in the visible region. The total number of layers of the proposed polarizer is just nine, and its total thickness is less than one micrometer, which is much thinner than the conventional DBEFs and is highly desirable for ultra-thin LCDs. The optical characteristics of the proposed polarizer are investigated by the FDTD method, and show high transmission, large extinction ratio and wide acceptable angle. The fabrication tolerance of the proposed structure is discussed in detail, including the grating’s period and aperture ratio, and thickness of the grating and PMMA layers. The proposed polarizer cannot only reduce the thickness of LCDs but also improves the efficiency by 50% via combining the backlight recycling technique.
Funding
The Hong Kong Government Innovation and Technology Fund and the State Key Laboratory on Advanced Displays and Optoelectronics Technologies ITC-PSKL12EG02.
Acknowledgments
This work was mainly supported by the State Key Laboratory on Advanced Displays and Optoelectronics Technologies of the Hong Kong University of Science and Technology, and was partially supported by Hong Kong Applied Science and Technology Research Institute.
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