In this article, a tunable grating made with anisotropic liquid crystal (LC) material is characterized with the RCWA solver. The thickness of the cell and the orientation of the LC molecule are tuned to reach 100% efficiency in the first orders of diffraction at certain wavelengths, and eliminate therefore the 0 th order.
In this workflow, we use Ansys Lumerical to construct the grating model and simulate its response with the RCWA solver. The grating is formed with liquid crystal molecules having their long axis oriented in the XY plane, providing in-plane anisotropy. A periodic spatial variation on the LC orientation is induced to design the grating. The diffraction characteristics are then exported into the Lumerical Sub-Wavelength Model (LSWM) JSON format for modelling this grating in a system-level simulation in Zemax.
[[NOTE:]] The RCWA support of in-plane anisotropy requires Ansys Lumerical version 2024R1.3 or higher.
Overview
Understand the simulation workflow and key results
The diffraction grating consists of a single layer of liquid crystal (5CB). The grating structure is obtained by inducing a periodic spatial variation on the orientation of the long axis of the LC molecules within the XY plane. By designing the grating properly with a cycloid diffraction pattern, it is possible to eliminate the 0 th order and to distribute the light entirely to the 1st orders
This article is divided in 3 main steps as follows:
Step 1: Design a grating with a cycloidal director pattern
In this section, we show how to use Ansys Lumerical to setup a LC cell where the orientation of the long axis is varying spatially.
Step 2: RCWA simulation with in-plane anisotropy
The efficiency in the different orders is computed with the RCWA solver. The thickness is tuned to obtain the elimination of the 0 th order at the desired wavelength.
Step 3: Export grating characteristics toward Zemax
The results of the RCWA simulation can be saved in .json format and imported directly into Zemax so that the grating can be included in a ray-tracing system.
Run and Results
Instructions for running the model and discussion of key results
Step 1: Design a grating with a cycloidal director pattern
- Open the file [[lc_grating_RCWA.fsp]]
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Right click on the model in the object tree and examine the Setup
- In the variable tabs, the main parameters for the systems are defined. It includes the wavelength range of the simulation, the thickness and the material of the LC cell, and the period of the grating.
- In the Script tab, examine how the different parameters are used to construct the setup. In particular, the LC rotation attribute is defined with a spatial variation where the vector defining the direction of the LC long axis is set as a function of the spatial dimension X.
During the fabrication process of a LC cell, the default orientation of the molecules is defined by a photo-alignment layer. In the simulation setup, the spatial variation is set according to a cycloidal pattern so that the angle between the long axis of the LC molecules and the x-axis is as follows:
$$\theta (x) = \cos(\frac{\pi x}{\Lambda})$$
Where \(\Lambda\) is the period of the grating. For more information on how to define the spatial variation with an attribute, see LC Rotation - Simulation object , or Matrix Transformation - Simulation object for a more general tool.
The LC pattern can be visualized directly in the viewport, where one period of the cycloidal pattern is shown (not on scale). The overall system is illustrated below:
Step 2: RCWA simulation with in-plane anisotropy
- Run the script [[lc_grating_RCWA_script.lsf]]
The RCWA is set to run over a spectral range of 0.37µm to 0.9µm, at normal incidence. The script runs the solver and extracts the diffraction efficiency in the first orders (DE 1st order = DE +1 + DE -1 ) for two different thicknesses (3µm and 5µm).
The results highlight the fact that at certain wavelengths (e.g. 0.44µm) 100% of the energy is sent to the first orders.
Step 3: Export grating characteristics toward Zemax
- Select the RCWA solver. In the result tab right click on ‘grating_characterization’ and 'Export to JSON'
- Open ‘lc_grating_RCWA_ray_tracing.zprj’ with Zemax
- Trace rays for different wavelengths, 498nm and 600nm, and for different polarization of the source (linear and circular) and observe the impact on the Transmission properties of the grating.
The .json file is applied to define the diffraction characteristics of the ‘Diffraction Grating’ object. The source sends light at normal incidence on the grating and two detectors capture respectively the reflection and transmission signals.
By modifying the wavelength of the system, we can verify that the transmission behavior computed with Lumerical is well transcribed to the optical system. At some wavelengths, the 0th order is completely eliminated (e.g. @600nm) while for other spectral components (e.g. @498nm) there is no energy diffracted away from the 0 th order.
By using linear polarization, the grating distributes the light equally between the +1 and -1 order. By setting the polarization to be circular (Jx=Jy=1, and either X-Phase or Y-phase set to 90), all the energy is directed to a single order (+1 or -1 for either left of right circular polarization).
Important model settings
Description of important objects and settings used in this model
- The RCWA solver only supports in-plane anisotropy. The characterization of a LC cell like this one can be done only as long as the rotation remains within the XY plane.
- To be imported in Zemax, the .json file should be placed in the folder ZemaxDLLDiffractive
Updating the Model with Your Parameters
Instructions for updating the model based on your device parameters
- The simulation was performed with the material 5CB-Li, that is commonly used for nematic liquid crystal. The desired material can easily be selected in the model properties
- The results are shown for two different thicknesses of the LC cell. Similarly, the period may be adjusted to control the angle of diffraction.
Taking the Model Further
There are some considerations that are not covered in this demonstration but users could pay more attention when they try to follow this process for their systems.
- In this demonstration, the simulations are performed in two different conditions to highlight the diffraction properties of such structures. An optimization run or a simple sweep can be performed to automatically find the optimal thickness of the cell required for the desired wavelength.
Additional Resources
Additional documentation, examples and training material
Related Publications
- Katarzyna A. Rutkowska and Anna Kozanecka-Szmigiel "Design of Tunable Holographic Liquid Crystalline Diffraction Gratings", Sensors 2020, 20(23), 6789 https://doi.org/10.3390/s20236789