† Corresponding author. E-mail:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11304074, 61475042, and 11274088), the Natural Science Foundation of Hebei Province, China (Grant Nos. A2015202320 and GCC2014048), and the Key Subject Construction Project of Hebei Province University, China.
The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display. Compared with the matrix optic methods and the refractive method, the finite-difference time-domain method, which is used to directly solve Maxwell’s equations, can consider the lateral variation of the refractive index and obtain an accurate convergence effect. The simulation results show that e-rays and o-rays bend in different directions when the in-plane switching blue phase liquid crystal display is driven by the operating voltage. The finite-difference time-domain method should be used when the distribution of the liquid crystal in the liquid crystal display has a large lateral change.
In recent years, blue phase liquid crystal displays[1–3] (BPLCD) have become increasingly attractive because of their features, such as: no need for a surface alignment layer, submillisecond response time, and isotropic dark state for wide viewing angle. The optical simulation of a liquid crystal display (LCD) is usually based on matrix-type solvers. The earliest solver is the simple Jones 2 × 2 method,[4] this method is only used to calculate the optical properties of normal incident light. The Berreman 4 × 4 method was proposed to simulate the optical properties of oblique incident light, and it is still a priceless tool to predict the optical properties of liquid crystals.[5] The extended Jones 2 × 2 method was also proposed to simulate the oblique incident through sampling the Berreman method.[6] In these matrix-type methods, the dielectric tensor of the liquid crystal is assumed to change only along the normal direction of the liquid crystal layer. The liquid crystal layer is first divided into many layers, and then each layer is assumed to be represented by a uniform dielectric tensor. These methods are only used for simple liquid crystal displays (LCDs) without non-uniform distribution of liquid crystal in the horizontal direction. The LCD modes that are used in a large screen LCDs are multi-domain vertical alignment (MVA) and in-plane-switching (IPS). The optical profiles simulated by the extended Jones or Berreman method match to the experimental results, even if the distribution of the liquid crystal is complex in the horizontal direction, but it cannot simulate complex optical phenomenon, such as the convergence effect.[7] In a BPLCD, in-plane electrodes are usually needed to obtain the birefringence in the horizontal direction. The distribution of the refractive index is complex,[8] which needs an accurate method to simulate the optical characteristics. The finite-difference time-domain (FDTD) method directly solves Maxwell’s equations and the effect of both the transverse field and the longitudinal field could be taken into account.[9] Therefore, this method can be used to calculate the complex optical profile of the multi-dimensional inhomogeneity of a liquid crystal system. The simulation results compared with those of the matrix-type methods and experiments demonstrate that the FDTD method can give more accurate results.[10–17]
In BPLCD, the BPLC turns into anisotropic from isotropic when an electric field
In our simulation, the IPS electrodes’ width and gap are set as 5 μm, the wavelength of light is λ = 633 nm, the grid of the simulation space is called a Yee cell,[9] and the Yee cell is set as Δx = Δy =Δz = 20 nm, which is approximately equal to λ/30. The time step is Δt = 3.81 × 10−17 s. The saturated induced birefringence and the saturation electric field of BPLC are Δns = 0.09 and Es = 2.2 V/μm, respectively, the average refractive index is 1.615, and the dielectric constants of the liquid crystal are ɛ// = 112 and ɛ⊥ = 18. The simulation space is chosen as 20 μm × 0.1 μm × 7.5 μm, corresponding to the thicknesses of the x, y, and z directions of the liquid crystal layer. This means that the thickness of the LC layer is 7.5 μm and the period of the electrodes is 20 μm. The computational space is terminated along the z direction by imposing a perfectly matched layer (PML).[19] In x and y directions, the periodic boundary conditions (PBC) are set to simplify the computational process. Two polarizers’ transmissive axial directions are oriented at ±45° with respect to the IPS electrode, respectively. A schematic of the structure of the liquid crystal layer is shown in Fig.
To calculate the optical characterization of IPS- PLCD, the flowchart in Fig.
![](cpb_25_9_094221/cpb161072ieqn3.gif)
![](cpb_25_9_094221/cpb161072ieqn4.gif)
Voltage dependent transmittance curves of IPS-BPLCD simulated by different methods are shown in Fig.
![]() | Fig. 3. Voltage dependent transmittance curves of IPS-BPLCD obtained by different simulation methods. The result of refractive method and experimental results are from Ref. [18]. |
![]() | Fig. 4. Transmittance for the cell driven by the operating voltage using (a) Jones method, (b) FDTD method, and (c) refractive method.[18] |
After light penetrates through the LC cell, the convergence effect can be seen. Set the PML at four positions z = 0 μm, z = 1 μm, z = 2 μm, and z = 3.2 μm, where z is distance from the top surface of the cell, and the thickness of the glass and polarizer is ignored. The transmittance versus x-position for the operating voltage is shown in Fig.
The angle between the polarizer and the x axis is 45°. Therefore, the polarization light could be considered as two same strength linear polarized lights when the light passes through BPLC layer because the electric field changes in the xoz plane. The two linear polarization light’s directions are along x and y axes, corresponding to the e-ray and o-ray. For the o-ray, the refractive index of the BPLC layer is no, which is the ordinary refractive index of BPLC, it is noteworthy that no is not a constant because it relates to the electric field strength. For the e-ray, the effective refractive index of the BPLC layer is
![](cpb_25_9_094221/cpb161072ieqn5.gif)
Considering the electrode structure and the Kerr effect of BPLC, we find that the variation of the refractive index occurs in the xoz plane. As shown in Fig.
As shown in Fig.
![]() | Fig. 7. Wave surface and strength of short pulse (a) e-rays and (b) o-rays penetrating through IPS-BPLCD and driven by the operating voltage. |
A short pulse light is used to simulate the transmittance when it is propagating in IPS-BPLCD driven by the operating voltage. The results at different times are shown in Fig.
The FDTD method has been used to simulate the optical characteristics of IPS-BPLCD. Compared with the Jones matrix method and the refractive method, the FDTD method has the most rigorous theory. When light passes through the IPS-BPLC cell, a convergence effect can be calculated. The simulation result indicates that the convergence zones are reversed for o-rays and e-rays, but the convergence effect of the o-rays is infinitesimally small and can be ignored. The convergence effect is mainly seen for e-rays in IPS-BPLCD, which leads a part of the light to bend to the electrode gaps from the edges of the electrodes and improves the transmittance of IPS-LCD.