Antireflective circular polarizers in OLED display

The image quality of OLED display can suffer from the reflection of ambient light from the bottom metal electrodes of the display. In this example, we demonstrate how to use a circular polarizer to suppress the reflection and visualize its effect in a realistic environment by applying the physics-based Lumerical Sub-Wavelength model (LSWM) to a mock-up mobile phone.

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Overview

Understand the simulation workflow and key results

The bottom metal electrode of OLED display can be used to enhance the light extraction efficiency of the device. However, it also has the detrimental effect of increasing the reflection of the ambient light, resulting in a reduced contrast ratio when the display is used outdoors. In this example, we demonstrate the use of circular polarizer for minimizing the reflection of light with certain linear polarization [1]. The configuration and working principle of the circular polarizer is illustrated below:

For simplicity, the multi-layer OLED structure is represented by a metallic reflector. The light incident on the linear polarizer become 30 ^o linearly-polarized after it propagates through the half-wave plate and then is circular-polarized after passing quarter-wave plate. The reflected light would finally become orthogonally-polarized with respect to the polarization of the linear polarizer, hence blocked out by it.

The reflected light can be decomposed into two parts as is shown in the illustration above. R1 represents the reflection at the air/polarizer interface and R2 is associated with the circular polarizer. In this example, we will be focusing on how we can minimize the R2. For minimization of R1, please refer to the "Taking the model further" section.

For decomposing R1 and R2, one approach is to add an artificial layer with refractive index 1.5 as the illustration below.

The refractive index 1.5 is chosen to be close to the refractive index of the linear polarizer so that the overall reflection of the circular polarizer is almost the same with or without the artificial layer. We will then convert the reflectance from STACK solver (brown arrow) to R2 (blue arrow) by script commands. Details could be found in "Taking the model further" section.

The polarizer and wave plates are made of anisotropic materials, meaning their refractive indices can be different in different directions. Their rotations of the polarization/slow axis are fully considered in the Ansys STACK solver by rotating the corresponding permittivity tensors.

The workflow includes the following steps:

Step 1 Initial test

The main purpose of this step is to ensure the simulation is set up correctly and to validate the anti-reflection behavior of the circular polarizer at normal incidence.

Step 2 Sweep angles

In this step, the reflection properties of the circular polarizer is characterized by sweeping the incident angles (theta and phi). This metric can be useful when further assessing the behavior of a display in terms of viewing angles in ray optics tools such as Ansys SPEOS.

Step 3 Lumerical STACK for layers without metallic mirror

In SPEOS simulation, a display light source is placed between the metallic mirror and the antireflection films. Therefore, Lumerical STACK is rerun to exclude the metal layer. The result would then be packaged via Lumerical subwavelength model, which is later imported into SPEOS in step 4.

Step 4 SPEOS simulation

Multiple light sources are included in SPEOS simulation so that the antireflection performance as well as the light emission behavior are evaluated together. The layer configuration in SPEOS simulation is illustrated in the following figure:

The antireflection film is attached on the top of the glass and a mirror is set to the bottom of the glass. Also, the display source is placed between the metallic mirror and the antireflection films.

Run and results

Instructions for running the model and discussion of key results

Step 1  Initial test

The thicknesses of the wave plates were chosen for a minimal reflection at the target wavelength of 0.55 um, which is confirmed in the above plot. The small ripples in the reflection spectrum can be attributed to the Fabry-Perot resonance by the multlayer films.

Step 2  Sweep angles

We could find that the higher reflection for larger incident angle theta, which implies the antireflection breaks down at large incident angles. User may find there are some negative reflection. This is due to the interpolation from (theta, phi) system to (u1, u2) system since we plot polar image in (u1, u2) system. This could be further improved by increasing the number of interpolation points or setting negative points to be zero directly.

Next, referring to paper [1], we study two different anisotropic films:

Nz is one of the key parameters of an anisotropic materials film, which is defined as (nx-nz)/(nx-ny). From the figure above, we could find Nz=0.5 could achieve a better antireflection performance for all incident angles, which agrees with paper [1].

Step 3 Lumerical STACK for layers without metallic mirror

The antireflection film in this step excluded the metal layer. The Lumerical script would first sweep over different incident angles and then export a json file via Lumerical-subwavelength model (LSWM). Several settings in Lumerical & SPEOS are made to ensure a correct mapping from Lumerical json file to SPEOS. Detail explanations could be found in “Lumerical json file and SPEOS configuration” session of ”important model settings”.

Step 4 SPEOS simulation

The antirecflection performance could be examined through SPEOS results below. The display attached with antireflection film did reduce reflection from ambient light.

By switching “Display layer” in the spectral map result window, we could only consider the display source. Then, it is straightforward to evaluate how the antireflection film reduced light intensity of the display source.

Important model settings

Description of important objects and settings used in this model

Permittivity rotation

The STACK solver always assumes the plane of incidence to be the xz plane (phi=0). To obtain the response of the anisotropic layers to an incident light with a certain polar angle (phi), we need to rotate the optic axis (equivalently, the permittivity tensor) of the corresponding materials by -phi.

Reflection correction

We utilize an artificial layer to decompose R1 and R2 in this example. However, it is needed to convert the result of STACK solver to R2.

From the figure above, we utilized stackrt command to obtain R _pol . T _ag stands for the transmission of the air-glass interface. (ag: from air to glass, ga: glass to air) R2 is then obtained using R2=T _ag *R _pol *T _ga .

Lumerical json file and SPEOS configuration

In SPEOS, the normal direction of a surface is always pointing out from the non-air material to air ("lower" to "upper"), which could be illustrated in the following figure:

For example, considering light coming from “upper” to “lower” material in SPEOS, the software reads json file data with “upper” suffix.

Consequently, we need to ensure that SPEOS and LSWM json file share the same lower and upper material definition. The below figure illustrates two possible configurations in LSWM json file. In the left one ,we flipped the lower and upper material so that the LSWM configuration is consistent with SPEOS. In contrast, the unflipped one (right side) shows an incorrect result.

In SPEOS, user could identify the normal direction of a surface by "measure".

Updating the model

Instructions for updating the model based on your device parameters

Customized materials

The refractive indices in this example are non-dispersive. To update the model with dispersive materials, please refer to this page . Note that the material database allows only a diagonalized permittivity. To obtain a broadband response, the permittivity rotation should be applied to the diagonal permittivity matrix for each frequency.

Taking the model further

Information and tips for users that want to further customize the model

Antireflection coating for minimizing reflection at air-polarizer interface

In this example, we ignore the reflectance R1 at the air-1.5 interface. A multilayer reflection coating could be further attached on the top of the polarizer to reduce the interface reflection [2].

Simulation considering microstructures and antireflection films

This example demonstrates a simulation for antireflection films only. However, in practical applications, antireflection films are attached on the top of display micro-pixels. Apparently, micro-pixels would diffract ambient light sources. Applying several assumptions, it is possible to simulate those components separately. While STACK solver is applied for antireflection films, RCWA is used for light diffraction simulation and FDTD captures light emission behavior. These component could then be imported to SPEOS, fulfilling a holistic system simulation [3].

Additional Resources

Additional documentation, examples and training material

Related Publications

1. Bong Choon Kim, Young Jin Lim, Je Hoon Song, Jun Hee Lee, Kwang-Un Jeong, Joong Hee Lee, Gi-Dong Lee, and Seung Hee Lee, "Wideband antireflective circular polarizer exhibiting a perfect dark state in organic light-emitting-diode display," Opt. Express 22, A1725-A1730 (2014)
2. Qi Hong, Thomas X. Wu, Ruibo Lu, and Shin-Tson Wu, "Wide-view circular polarizer consisting of a linear polarizer and two biaxial films," Opt. Express 13, 10777-10783 (2005)
3. Chih-Hao Chen, Xing Tong, James Pond, Fatema Chowdhury, "Integration of wave optics and ray optics simulations for advanced display design," Proc. SPIE 12664, Optical Modeling and Performance Predictions XIII, 1266402 (2023)

Appendix

Coherence break

STACK solver captures multi-reflection between interfaces of each layer. For stack layer with large thickness, this results in an oscillating angular response. However, in practice, tiny roughness on top of glasses or polarizers breaks the interference condition such that the angular distribution is smooth and less oscillating.
There are several ways to reduce the oscillation behavior. One idea is to apply smooth algorithms as a post processing. In contrast, we demonstrate another approach in the script file, which could be illustrated in the following figure:

An artificial layer is inserted between two materials. Then, we split the stack layers into two segments. The reflectance of STACK2 is dropped as such eliminating multi-reflection between n2 & n3. The overall transmission is then the product of transmission of two segments, which is T1*T2.
The refractive index on the artificial layer “nn” is chosen to be close to n2 & n3 so that extra reflectance/transmittance changes is minimized. The following figures shows the original oscillating distribution and result of this coherence break approach.