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The achromatic response and wide viewing angle for varying wavelength of incident light are of long waiting research to be utilized it for the display devices. Such response can be obtained by employing the retarder that exhibits negative birefringence and negative dispersion. In this paper, negative dispersion half-wave retarder and negative dispersion quarter-wave retarder have been demonstrated by optimizing the retardation and the angle between the extraordinary axes of polystyrene and poly-methylmethacrylate films. The optimum angles for half and quarter-wave retarders were found to be 40° and 70°, respectively for different retardation values of polystyrene and poly-methylmethacrylate films.
© 2015 Optical Society of America
1. Introduction
Generally, the phase retardation Г≡2πΔnd/λ of the natural birefringent materials decreases with longer λ, called as positive dispersion (PD) of birefringence. Here, Δn is defined as ne-no, where ne and no are the extraordinary and ordinary refractive index, respectively, and d is the thickness of the film. The PD medium also shows a decrease of Re(λ)≡Δnd with longer λ and this limits the bandwidth of the compensation film.
There have been many efforts to make a retarder with negative dispersion (ND) of birefringence whose birefringence or Re(λ) get increased with longer λ [1–4]. The ND retarder has a wider bandwidth than PD retarder, thus can be an achromatic retarder with constant phase retardation over the wide range of λ. The well-known method to obtain the ND retarder is stacking PD retarders with different dispersion property of Re(λ) [1–6]. Multi-layers of twist-oriented reactive mesogen have been also reported to show ND of birefringence [7,8]. Recently, single layer approaches using copolymers [9–11], biaxial reactive mesogens [12], and smectic liquid crystal-polymer composites have been developed [13–15].
Further, all previous ND retarders have been made of positive birefringence (PB) materials [16]. The PB medium means a substance showing ne>no, thus giving a positive sign of Δn. With this reason, the Rth value defined as [(nx + ny)/2-nz]d was always positive, where nx and ny are the in-plane refractive indices of the retarder and nz is the refractive index to the surface normal direction. To minimize the viewing angle dependence of the liquid crystal display (LCD) devices, the Rth value should be zero and this can be realized provided nz = (nxny)1/2 [16]. Since most of the liquid crystal displays (LCDs) use the liquid crystal (LC) with PB property, the Rth value of the LC layer is positive. Thus, to make the Rth of the LCD to be zero, the Rth value of the compensation film should negative. This can be satisfied by using a retarder which have negative birefringence (NB), ne<no. In spite of this, only limited numbers of research articles using only PB medium for ND retarder are reported in the literature [1–15].
In this paper, the fabrication of the ND retarder with a negative sign of Re(λ), i.e., the negative a-plate with ND property has been reported. In this study, we used negative birefringent materials namely polystyrene (PS) and polymethylmethacrylate (PMMA) films, which were stretched unidirectionally and investigated the dispersion property of the film stacked at various angle (φ) between the extraordinary axes of two films in order to find out optimum angle to get ND response in the retarder.
2. Experimental procedure
The molecular structure of commercially available PS and the PMMA molecules are shown in the Fig. 1 and they were used without any further chemical treatment. Both the PS and the PMMA molecules have side chains and were unidirectionally stretched at 120 °C. When the films are unidirectionally stretched, the pendants are aligned perpendicular to the stretched direction. Then, the in-plane refractive index to the stretched direction becomes ne and the out-of-plane refractive index normal to the ne direction becomes no. no of both films are larger than ne, i.e., both films have negative birefringence. The details about the mechanism of the generation of birefringence by stretching the PS and the PMMA film are also described in the literature [17]. The stretched ratio i.e. of ratio of the stretched film to the unstretched one of PS film was 2.0 and the final thickness was 45 μm. Whereas the stretched ratio of PMMA film was 2.5 and the final thickness was 35 μm. The Re (λ) values of the films were measured using a commercial retardation measurement instrument (Axo Scan-OPMF2, Axo Metrics) based on Muller matrix method. The Rth≡[(nx + ny)/2-nz]d and the NZ coefficient≡(nx-nz)/(nx-ny) were also measured by measuring Re(λ) value to the obliquely incident light. For the optical simulation, the commercial LCD simulation program Techwiz 2D (Sanayi System) was used.
3. Results and discussion
Figure 2 shows the Re(λ) values of the stretched PS and PMMA films. The Re(λ) data in Fig. 2 was measured when the slow axis of films was at 45° to the transmission axis of the linear polarizer. Re(550 nm) i.e. the value of Re at the wavelength of 550 nm of the PS and the PMMA films were −245.7 nm and −134.4 nm, respectively. The negative sign of Re is due to the negative Δn. The Δn of the PS and the PMMA films were −0.0055 and −0.0038, respectively. Both films showed the PD property, whose modulus or absolute value of Re(λ) decreases with longer λ. The difference Re(650 nm)-Re(450 nm) of the PS and the PMMA were 40 and 28 nm, respectively. Thus, the PS film showed relatively larger change of Re(λ) compared to the PMMA film.
Fig. 2 Re of the stretched PS and PMMA films vs λ. Both films have a negative birefringence and a positive dispersion property.
Figure 3(a) shows Re(λ) of the PS-PMMA films stacked at various φ, where φ is the angle set between the extraordinary axes of two films. The absolute value of Re(λ) decreased with longer λ in the wavelength range of visible light when φ was smaller than 30°, i.e., showed the PD property. At φ = 40°, the absolute value of Re(λ) increased monotonically with longer λ, thus showing the ND property. The ND of birefringence was shown until φ = 70°, but reconverted to PD when φ≥80°. Figure 3(b) shows Re(λ) of the PS-PMMA films normalized to Re(550 nm). It is clearly seen that Re(λ) shows ND of birefringence provided 40°≤φ≤70°. Particularly at φ = 40°, Re(550 nm) of the PS-PMMA film was −273 nm which is almost half of the wavelength of green light (λ = 550 nm). The relative ratio of Re(450 nm)/Re(550 nm) and Re(650 nm)/Re(550 nm) were 0.96 and 0.99, respectively and hence exhibits ND property. Thus, the PS-PMMA film stacked at φ = 40° can be used as a ND half-wave retarder for the green light of λ = 550 nm. The Rth and NZ coefficient of the PS-PMMA half-wave retarder film at 550 nm was −92 nm and 0.18. Thus, the film is optically negative a-plate with ND property.
Fig. 3 (a) Re of the PS and PMMA films assembled at various φ vs. λ. (b) Re(λ) normalized to Re(550 nm). Re(550 nm) of the PS film and the PMMA films were −245.7 nm and −134.4 nm, respectively.
We need to mention that the optimum assembly angle φ can be theoretically predicted using Jones matrix method [16]. The Jones matrix of the stacked film wherein the optic axis of the PMMA film is at φ from the optic axis of the PS film given by Eq. (1),
where, Г1 and Г2 are the phase retardation of the PS and the PMMA films, respectively. The left matrix in Eq. (1) is the multiplication result of the PMMA retarder and the coordinate rotation matrix. The details of the coordinate rotation are well described in the reference [16]. The Eq. (1) can be represented with a single retarder whose equivalent phase retardation and the optic axis orientation are given by Гe and φe.After matrix multiplications in Eq. (1) and equating the result to the corresponding matrix elements of Eq. (2), we obtain the following expressions for Гe.Thus, the optimum assembly angle φ for the half-wave retarder can be predicted by substituting Гe = π and the phase retardation value of the PS and the PMMA films, Г1 and Г2, respectively. The theoretically calculated φ value was 39.7° which well coincided with the experimentally found optimum value in Fig. 3. To have small wavelength dependence of Гe, dГe/dλ should be minimized. Given the Г1 and Г2 values, the assembly angle for the achromatic retarder was predicted by 40.5° similar to φ to obtain half-wave retardation [16].For getting ND quarter-wave retarder, the value of Re(550) must be equal to the one fourth of the wavelength of green light i.e. the value of Re(550) must be equal to ~138. However, we could not observed such values in Fig. 3(a) for ND case. In order to get the ND quarter-wave retarder, we modified the value of Re(λ) of the PS film by thermal annealing and accordingly optimize the value of φ to make a ND quarter-wave retarder for the green light. The thermal annealing the PS film was carried out at at 70 °C. The film shrinks at 70 °C and Re was reduced with time. After annealing for 25 min, the PS film with Re(550 nm) = −219.5 nm was obtained. We used the same PMMA film which was used for the half-wave retarder in Fig. 3. Figure 4(a) shows Re(λ) of the PS-PMMA films. In the visible wavelength range of light, Re(λ) showed PD of birefringence when 0°≤φ≤50°. ND of birefringence was shown when 60°≤φ≤70° and reconverted to PD when φ≥80°. Interestingly, at φ = 70°, Re(550 nm) of the PS-PMMA stacked film was −133.4 nm, which is nearly one fourth to the value of wavelength of green light and the relative ratio of Re(450 nm)/Re(550 nm) and Re(650 nm)/Re(550 nm) were 0.98 and 1.01, respectively. Hence, the PS-PMMA film stacked at φ = 70° can be used as a ND quarter-wave retarder for the green light, where Re(550 nm) of the individual PS and PMMA films were −219.5 and −134.4 nm, respectively. The theoretically calculated optimum assembly angle φ for a quarter wave retarder using Eqs. (1-3) with Гe = π/2 was 68.7° and also coincides with the experimentally found optimum value. In addition, the Rth and the NZ coefficient of the half-wave retarder film were −192 nm and −0.82, respectively. Thus, the PS-PMMA film assembled at φ = 60° is optically negative a-plate with ND property.
Fig. 4 (a) Re of the PS and PMMA films stacked at various φ vs. λ. (b) Re(λ) normalized to Re(550 nm). Re(550 nm) of the PS film and the PMMA films were −219.5 nm and −134.4 nm, respectively.
To investigate the performance of the ND-NB retarder, we used the PS-PMMA film as a λ/6 plate and simulated the viewing angle property. A pair of negative and positive λ/6 a-plate can compensate the decrossed polarization of the polarizers [16]. Figure 5 shows the transmittance (TR) of the IPS-LCD at dark state. We compared three cases; the LC layer without compensation film [Fig. 5(a)], the LC layer with PD -a and PD + a plates [Fig. 5(b)], and the LC layer with ND -a and PD + a plates [Fig. 5(c)]. The c-axis of the LC layer was parallel and perpendicular to the absorption axis of the polarizer and the analyzer, respectively. Re(550 nm) of the LC layer, -a plate, and + a plate were 275, −90, and + 90 nm, respectively. To make the ND λ/6 plate, we used the PS film with Re(550 nm) = 199 nm and the PMMA film with Re(550 nm) = 118 nm assembled at φ = 70°. We used Re(λ) of the PS-PMMA film as the ND -a plate. The dispersion of the ND λ/6 plate was Re(450 nm)/Re(550 nm) = 0.98 and Re(650 nm)/Re(550 nm) were 0.98 and 1.01, respectively, while those of the PD λ/6 plate was Re(450 nm)/Re(550 nm) = 1.03 and Re(650 nm)/Re(550 nm) were 0.97, respectively. The LCD without the pair of -a and + a plates showed a light leakage at oblique incident angle [Fig. 5(a)], while the LCDs with the compensation films showed better dark state [Figs. 5(b) and 5(c)]. The average TR of the samples in Figs. 5(a)-5(c) was 0.43, 0.08, and 0.05%, respectively. In particular, the LCD using the ND -a plate [Fig. 5(c)] showed better dark state at oblique angle compared to the one using the PD -a plate [Fig. 5(b)]. Thus, the better optical compensation effect of the ND-NB film was confirmed.
Fig. 5 Simulation results of the TR of IPS-LCD at dark state vs. viewing angle. (a) No compensation film, (b) PD -a and PD + a plates, and (c) ND -a plate and PD + a plates used.
We also estimated the performance of the PS-PMMA film as a quarter wave retarder of the antireflection (AR) film for the organic light emitting diode (OLED) displays [Fig. 6]. The AR film for the OLED displays is composed a linear polarizer and a quarter-wave retarder whose slow axis is at 45° to the absorption axis of the polarizer. Using the experimental Re(λ) data of the PS-PMMA quarter-wave retarder in Fig. 4, we simulated the reflectance from the panel. To compare the AR performance, we also simulated the reflection property of commercial quarter wave retarders such as S-film (Sumitomo), WR-M (Teijin) and Zeonor (Zeon). S-film is double-layered ND retarder wherein a half-wave and a quarter-wave retarders are stacked at 15° and 75°. Re(450 nm)/Re(550 nm) and Re(650 nm)/Re(550 nm) of the S-film are 0.92 and 1.05, respectively [16]. WR-M is a PD quarter-wave retarder whose Re(450 nm)/Re(550 nm) and Re(650 nm)/Re(550 nm) are 1.03 and 0.98, respectively. Zeonor is a flat-dispersion quarter-wave retarder whose Re(450 nm)/Re(550 nm) and Re(650 nm)/Re(550 nm) are 1.01 and 1.00, respectively. The external light was incident to the surface normal direction in the simulation. The AR film using WR-M and Zeonor showed rapid increase of reflectance approaching λ = 450 nm [Fig. 6]. In addition, the reflectance at 450 and 650 nm was not symmetric, which causes a blue shift of the reflected light. This asymmetry of the reflectance is due to the greater deviation of Г from π/2 at the short wavelength region compared to the long wavelength region. On the other hand, the S-film and the PS-PMMA film showed smaller total reflectance compared to the WR-M and Zeonor films. The reflectance of the PS-PMMA was slightly higher than the S-film due to the lower ND property, but always less than 3% through the visible light range. Moreover, the PS-PMMA film showed very symmetric reflectance at 450 and 650 nm regions, thus minimizing the color shift of the reflected light.
Fig. 6 Simulation results of the reflectance of the AR films using various quarter-wave retarders. The light was normally incident to the surface. For the PS-PMMA film, the PS film with Re(550) = −219.5 nm was stacked on the PMMA film with Re(550) = −134.4 nm at φ = 70° .
4. Conclusion
To summarize, we reported a ND retarder by stacking two NB films. We made both the ND half-wave and quarter-wave retarders by optimizing Re and φ of the PS and the PMMA films. The PS-PMMA ND film showed better performance in the LCD compensation film as well as in the AR film than the conventional PD retarders.
Acknowledgments
This research was supported by the Brain Korea 21 PLUS project and the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the ministry of Science, ICT & Future Planning (NRF-2013R1A1A1058681).
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